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ScienceWeek
SCIENCEWEEK
ScienceWeek
April 4, 2003
Vol. 7 Number 14
An Online Digest of Research in the Sciences
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What is the path? There is no path.
-- Niels Bohr (1885-1962)
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Section 1
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Symposium: Physics: Bose-Einstein Condensation
1. Introduction
2. Atom Condensation
3. Molecule Condensation
4. Atom-Molecule Coherence
5. Condensates and Matter Waves
6. Exciton Condensates
7. Ultracold States
Notices and Subscription Information
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Section 2
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1. INTRODUCTION
ON BOSE-EINSTEIN CONDENSATES
Because the particles of systems whose behavior can be described
only by the rules of quantum mechanics occupy a discontinuous
spectrum of energy states, only special (i.e., non-Boltzmann)
statistics can be applied to energy distributions in such
systems. From the standpoint of the mathematics of statistical
physics, the essential general constraint of quantum statistics
is that in partition functions of quantum systems it is sums over
energy levels that must be used rather than integrals over phase
space.
In general, quantum statistics is concerned with the equilibrium
distribution of elementary particles of a particular type among
the various possible quantized energy states, with an assumption
that these particles are indistinguishable. Quantum statistics,
in turn, takes one of two forms, depending on distribution
constraints: Fermi-Dirac statistics or Bose-Einstein statistics.
In "Fermi-Dirac statistics", the Pauli exclusion principle is
obeyed, so that no identical particles (called "fermions" if they
obey this condition) can be in the same quantum state (as
specified by the set of quantum numbers that define such a
state). In a Fermi-Dirac system, the exchange of two identical
fermions (e.g., two electrons) does not affect the probability of
distribution, but it does involve a change in the sign of the
wave function (the exchange is "antisymmetric").
In Bose-Einstein statistics, the Pauli exclusion principle is not
obeyed, so that any number of identical particles (called
"bosons" if they obey this condition) can be in the same quantum
state. In a Bose-Einstein system, the exchange of two bosons of
the same type affects neither the probability of distribution nor
the sign of the wave function (the exchange is "symmetric").
At high temperatures and low concentrations, both forms of
quantum statistics reduce to classical Boltzmann statistics.
In quantum mechanics, electrons, protons, and neutrons have an
intrinsic angular momentum known as "spin", and a magnetic moment
parallel or antiparallel to that angular momentum. When electrons
are combined together to form an atom or ion, there is a
resultant angular momentum which is a combination of the
intrinsic spin of the electrons and the angular momentum due to
their motion about the nucleus, and this is the "spin" of the
atom or ion. Atoms or ions with non-zero spin are magnetic atoms
or ions. The idea of electron spin was first proposed by Goudsmit
and Uhlenbeck in 1925 to explain the splitting of atomic
spectroscopic emission lines in the presence of a magnetic field.
Elementary particle spin involves a virtual rotation about the
axis of the particle, which means only two spin states are
possible, one clockwise and one counterclockwise.
All particles in nature are either fermions or bosons, with
fermions (always elementary particles) having half-integer spin
(spin-states characterized by half-integer multiples of Planck's
constant divided by 2 pi), and bosons (all other particles)
having integer spin (spin-states characterized by integer
multiples of Planck's constant divided by 2 pi).
What is important in this context is that particular real systems
can be manipulated in the laboratory into a condition in which
quantum behavior becomes both apparent and controlling. An
example is the Bose-Einstein condensate, a system long ago
predicted but first experimentally realized in 1995, a system in
which a gas of atoms at extremely low temperature becomes a gas
of bosons obeying Bose-Einstein statistics.
In general, "Bose-Einstein condensation" is a phenomenon
occurring in a macroscopic system consisting of a relatively
large number of bosons at a sufficiently low temperature
(microkelvins down to nanokelvins) in which a significant
fraction of the particles occupy a single quantum state of lowest
energy (the ground state). In an atomic Bose-Einstein condensate,
several thousand atoms essentially become a single atom, a
"superatom", and this effect has been observed experimentally
with atoms of rubidium and lithium, the atoms trapped and cooled
by special methods. The excitement in contemporary physics
concerning Bose-Einstein condensates derives from the expectation
that these manipulable real systems can illuminate the
fundamentals of quantum mechanics, superfluidity,
superconductivity, the properties and interactions of atoms,
laser physics, and nonlinear optics, i.e., some of the most
important research areas in modern physics.
ON S.N. BOSE
"Satyendra Nath Bose (1894-1974) was an Indian physicist who made
one outstanding contribution to quantum theory, the development
of what became known as Bose-Einstein statistics. Born in
Calcutta on 1 January 1894, Bose studied at Presidency College
there, and became a lecturer in physics at the University of
Calcutta, before moving to take up a lectureship at the
University of Dacca when it was founded in 1921. In 1924 he
found a way to derive Planck's equation for black body radiation
using a statistical approach based entirely on the idea that
light is made up of tiny particles (photons). This echoed the
statistical mechanics approach of Ludwig Boltzmann to the
behavior of gases, but using a different statistical rule; it
derives the black body relation entirely in quantum terms,
without using the idea of electromagnetic radiation at all. Bose
wrote a paper about his discovery and sent it to Albert Einstein,
who immediately saw its significance, translated it into German
and arranged for its publication in the prestigious Zeitschrift
fur Physik. Einstein developed the idea to apply to other kinds
of particle, not just to a 'gas' of photons, which is why this
approach is usually referred to as 'Bose-Einstein statistics'.
Paul Dirac coined the name 'bosons' for particles which obey
Bose-Einstein statistics. It is no coincidence that the name
'photon' was coined for the particle of light only in 1926, after
Bose had put the quantum theory of light on a secure mathematical
footing.
"Although Bose obtained leave to spend two years in Europe, where
he visited Einstein and many of the other pioneers of quantum
mechanics, he made no other major contribution to science. As he
commented late in life, 'I was like a comet, a comet which came
once and never returned again.' But the light shed by that comet
changed the way physicists thought in the mid-1920s, at a crucial
time in the development of quantum theory, and has affected the
way they have thought ever since. Bose had a distinguished career
in education, inspiring generations of young Indian scientists by
his example and through his skill as a teacher. He died in
Calcutta, on 4 February 1974."
John Gribbin: Q is for Quantum: An Encyclopedia of Particle
Physics. Simon & Schuster 2000, p.57.
ON THE PHYSICS OF LOW TEMPERATURES
"The lure of lower temperatures has attracted physicists for the
past century, and with each advance towards absolute zero, new
and rich physics has emerged. Lay people may wonder why "freezing
cold" is not cold enough. But imagine how many aspects of nature
we would miss if we lived on the surface of the sun. Without
inventing refrigerators, we would only know gaseous matter and
never observe liquids or solids, and miss the beauty of
snowflakes. Cooling to normal earthly temperatures reveals these
dramatically different states of matter, but this is only the
beginning: many more states appear with further cooling. The
approach into the kelvin range was rewarded with the discovery of
superconductivity in 1911 and of superfluidity in helium-4 in
1938. Cooling into the millikelvin regime revealed the
superfluidity of helium-3 in 1972. The advent of laser cooling in
the 1980s opened up a new approach to ultralow-temperature
physics. Microkelvin samples of dilute atom clouds were generated
and used for precision measurements and studies of ultracold
collisions. Nanokelvin temperatures were necessary to explore
quantum-degenerate gases, such as Bose-Einstein condensates first
realized in 1995. Each of these achievements in cooling has been
a major advance, and recognized with a Nobel prize."
Wolfgang Ketterle: Revs. Mod. Phys. 2002 74:1131
ON BOSE-EINSTEIN CONDENSATES
"The notion of Bose statistics dates back to a 1924 paper in
which Satyendranath Bose used a statistical argument to derive
the black-body photon spectrum (Bose, 1924). Unable to publish
his work, he sent it to Albert Einstein, who translated it into
German and got it published. Einstein then extended the idea of
Bose's counting statistics to the case of noninteracting atoms
(Einstein, 1924, 1925). The result was Bose-Einstein statistics.
Einstein immediately noticed a peculiar feature of the
distribution of the atoms over the quantized energy levels
predicted by these statistics. At very low but finite temperature
a large fraction of the atoms would go into the lowest energy
quantum state. In his words, 'A separation is effected; one part
condenses, the rest remains a saturated ideal gas' (Einstein,
1925). This phenomenon we now know as Bose-Einstein condensation.
The condition for this to happen is that the phase-space density
must be greater than approximately unity, in natural units.
Another way to express this is that the de Broglie wavelength, L
of each atom must be large enough to overlap with its neighbor...
This prediction was not taken terribly seriously, even by
Einstein himself, until Fritz London (1938) and Laszio Tisza
(1938) resurrected the idea in the mid 1930s as a possible
mechanism underlying superfluidity in liquid helium 4. Their work
was the first to bring out the idea of Bose-Einstein condensates
(BEC) displaying quantum behavior on a macroscopic size scale,
the primary reason for much of its current attraction. Although
it was a source of debate for decades, it is now recognized that
the remarkable properties of superconductivity and superfluidity
in both helium 3 and helium 4 are related to BEC, even though
these systems are very different from the ideal gas considered by
Einstein."
E.A. Cornell and C.E. Weiman: Revs. Mod. Phys. 2002 74:875
ON HELIUM SUPERFLUIDITY AND BOSE-EINSTEIN CONDENSATION
"If we put a large number of helium atoms, of isotopic mass 4, in
a box, then at temperatures above about 4 K they will form a gas.
As we cool below this temperature they form a liquid (with, of
course, a few atoms left as a gas above the liquid), but this
liquid does not have any particularly spectacular properties; in
this phase it is called helium-I (He-1). However, if we cool it
further, below a specific temperature close to 2 K,
conventionally called T-lambda (because the graph of specific
heat near there, when plotted against temperature, has a shape
resembling the Greek letter lambda), the liquid suddenly starts
to display quite abnormal and spectacular properties: it flows
through tiny capillaries without apparent friction, climbs, in
the form of a film, over the edge of vessels containing it ('film
creep'), spouts in a spectacular way when heated under certain
conditions ('fountain effect') and displays a host of other
abnormal properties... This complex of effects is generally
lumped together under the name of superfluidity, and the liquid
in its superfluid phase is known as helium-II (He-11). The
transition between the two phases is called the lambda-
transition... It is generally believed that the phenomenon of
superfluidity is directly connected with the fact that the atoms
of helium-4 obey Bose statistics, and that the lambda-transition
is due to the onset of the peculiar phenomenon called Bose
condensation...
"The phenomenon of Bose condensation, and the closely related
phenomena which occur in some Fermi systems, are absolutely
crucial to our modern understanding of the anomalous phenomena
which occur in superfluids and superconductors, and particularly
of the way in which they display the effects of quantum mechanics
on a macroscopic scale... Imagine that you are on a mountain-top
looking down at a distant city square on market day. The crowd is
milling around at random, and each individual is doing something
different; from that distance it is very difficult to make out
precisely what. Now suppose, however, that it is not market day
but the day of a military parade, and the crowd is replaced by a
battalion of well drilled soldiers. Now every soldier is doing
the same thing at the same time, and it is very much easier to
see (or hear) from a distance what that is. The physics analogy
is that a normal system is like the market day crowd -- every
atom is doing something different -- whereas in a Bose condensed
system the atoms (or, more accurately, the fraction of them
which is condensed at the temperature in question) are all forced
to be in the same quantum state, and therefore resemble the well
drilled soldiers: every atom must do exactly the same thing at
the same time! ... This means, among other things, that effects
which are far too small to be detectable at the level of single
atoms may be quite easily observable in a Bose condensed (or
similar) system; this is one feature which makes such systems so
unique and exciting."
Anthony Leggett: in P. Davies (ed.): The New Physics. Cambridge
University Press 1989, p.275.
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2. ATOM CONDENSATION
BOSE EINSTEIN CONDENSATION OF ATOMIC GASES
J.R. Anglin and W. Ketterle (Massachusetts Institute of
Technology, US) discuss Bose-Einstein condensation, the authors
making the following points:
1) The early experiments on Bose Einstein condensation in dilute
atomic gases accomplished three long-standing goals. First,
cooling of neutral atoms into their motional ground state, thus
subjecting them to ultimate control, limited only by Heisenberg's
uncertainty relation. Second, creation of a coherent sample of
atoms, in which all occupy the same quantum state, and the
realization of atom lasers -- devices that output coherent matter
waves. And third, creation of a gaseous quantum fluid, with
properties that are different from the quantum liquids helium-3
and helium-4. The field of Bose Einstein condensation of atomic
gases has continued to progress rapidly, driven by the
combination of new experimental techniques and theoretical
advances. The family of quantum-degenerate gases has grown, and
now includes metastable and fermionic atoms. Condensates have
become an ultralow-temperature laboratory for atom optics,
collisional physics and many-body physics, encompassing phonons,
superfluidity, quantized vortices, Josephson junctions and
quantum phase transitions.
2) The essential techniques for making quantum-degenerate gases
are cooling techniques, because at high temperatures a dilute gas
of atoms behaves classically. As long as the atoms' de Broglie
wavelength is small compared to the spacing between atoms, one
can describe their motion with classical trajectories. (The de
Broglie wavelength [dB] is essentially the position uncertainty
associated with the thermal momentum distribution, and increases
with decreasing temperature T and atomic mass M.) Quantum
degeneracy begins when dB and the interatomic distance become
comparable. The atomic wave packets overlap, and the gas starts
to become a "quantum soup" of indistinguishable particles. If the
atoms are bosons, a condensate -- a cloud of atoms all occupying
the same quantum state -- appears at a precise temperature. If
the atoms are fermions, cooling gradually brings the gas closer
to being a "Fermi sea" in which exactly one atom occupies each
low-energy state.
3) Creating a BEC or a Fermi sea is thus simple in principle --
make a gas extremely cold. In most cases, however, quantum
degeneracy would simply be pre-empted by the more familiar
transitions to a liquid or solid. This more conventional
condensation can be avoided only at extremely low densities,
about one-hundred-thousandth the density of normal air, so that
the formation time of molecules or clusters by three-body
collisions (which is proportional to the square of the inverse
density) is stretched to seconds or minutes. Because the rate of
binary elastic collisions drops only proportionally to the
density, these collisions are much more frequent and let the gas
equilibrate within about 10 ms, so that degeneracy can be
achieved in an effectively metastable gas phase. However, such
ultralow density lowers the temperature requirement for quantum
degeneracy into the nanokelvin range.
4) Sub-microkelvin temperatures are reached by combining two
procedures. Laser cooling precools the gas so that it can be
confined in a magnetic trap(1). In the second stage -- forced
evaporative cooling(2) -- the trap depth is reduced, allowing the
most energetic atoms to escape while the remaining atoms
rethermalize at steadily lower temperatures(3). Most experiments
with BECs reach quantum degeneracy between 500 nanoK and 2
microK, at densities between 10^(14) and 10^(15) cm^(-3). The
largest condensates are of 30 million atoms in Na, and a billion
in H; the smallest are just a few hundred atoms. Depending on the
magnetic trap, the shape of the condensate is either
approximately round, with a diameter of 10 50 microns, or cigar-
shaped with a diameter about 15 microns and length 300 microns.
The full cooling cycle that produces a condensate may take from a
few seconds to as long as several minutes (4,5).
References (abridged):
1. Arimondo, E., Phillips, W. D. & Strumia, F. Laser Manipulation
of Atoms and Ions (North-Holland, Amsterdam, 1992)
2. Masuhara, N. et al. Evaporative cooling of spin-polarized
atomic hydrogen. Phys. Rev. Lett. 61, 935-938 (1988)
3. Ketterle, W., Durfee, D. S. & Stamper-Kurn, D. M. in Bose-
Einstein Condensation in Atomic Gases (eds Inguscio, M.,
Stringari, S. & Wieman, C. E.) 67-176 (IOS Press, Amsterdam,
1999)
4. Gu‚ry-Odelin, D., S”ding, J., Desbiolles, P. & Dalibard, J. Is
Bose-Einstein condensation of atomic cesium possible? Europhys.
Lett. 44, 25-30 (1998)
5. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E.
& Cornell, E. A. Observation of Bose-Einstein condensation in a
dilute atomic vapor. Science 269, 198-201 (1995)
Nature 2002 416:211
Related Background:
BOSE-EINSTEIN CONDENSATION OF CESIUM
T. Weber et al (University of Innsbruck, AT) discuss Bose-
Einstein condensation, the authors making the following points:
1) Cesium (Cs) is an atom of particular interest in physics. It
serves as our primary frequency standard (1) and has various
important applications in fundamental metrology, such as
measurements of the fine-structure constant (2), the electric
dipole moment of the electron (3), parity violation (4), and the
Earth's gravitational field (5). Cs, a heavy alkali atom with
small photon recoil, is well suited for laser cooling and
trapping methods. However, because of quantum-mechanical
scattering resonances, collisions between Cs atoms at ultra-low
energy exhibit unusual properties with drastic consequences, such
as large frequency shifts in atomic clocks (1). A further
consequence of this resonant scattering is the fact that Cs has
so far resisted all attempts to produce Bose-Einstein
condensation (BEC). In contrast, all other stable alkali species
-- 87Rb, 23Na, 7Li, 85Rb, and 41K -- have been condensed, along
with hydrogen and metastable 4He.
2) In summary: The authors report the achievement of Bose-
Einstein condensation of cesium atoms by evaporative cooling
using optical trapping techniques. The ability to tune the
interactions between the ultracold atoms by an external magnetic
field is crucial to obtain the condensate and offers intriguing
features for potential applications. The authors explore various
regimes of condensate self-interaction (attractive, repulsive,
and null interaction strength) and demonstrate properties of
imploding, exploding, and non-interacting quantum matter.
References (abridged):
1. C. Salomon et al., Proceedings of the 17th International
Conference on Atomic Physics (ICAP 2000), E. Arimondo, P. D.
Natale, M. Inguscio, Eds. (American Institute of Physics,
Melville, NY, 2001), pp. 23-40
2. J. M. Hensley, A. Wicht, B. C. Young, S. Chu, Proceedings of
the 17th International Conference on Atomic Physics (ICAP 2000),
E. Arimondo, P. D. Natale, M. Inguscio, Eds. (American Institute
of Physics, Melville, NY, 2001), pp. 43-57
3. C. Chin, V. Leiber, V. Vuletic, A. J. Kerman, S. Chu, Phys.
Rev. A 63, 033401 (2001)
4. C. E. Wieman, Proceedings of the 16th International Conference
on Atomic Physics (ICAP 1998), W. E. Baylis, G. W. Drake, Eds.
(American Institute of Physics, Woodbury, NY, 1999), pp. 1-13
5. M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, M. A.
Kasevich, Phys. Rev. Lett. 81, 971
Science 2002 299:232
A CONTINUOUS SOURCE OF BOSE-EINSTEIN CONDENSED ATOMS
A. P. Chikkatur et al (Massachusetts Institute of Technology, US)
discuss Bose-Einstein condensed atoms, the authors making the
following points:
1) The gaseous Bose-Einstein condensate (BEC) is a macroscopic
quantum system with analogies to superconductors, superfluids,
and optical lasers (1,2). However, unlike these other systems,
BECs have so far been only produced in pulsed mode. As with
optical lasers, pulsed operation has less stringent technical
requirements. In the optical domain, the leap from a pulsed ruby
laser (3) to a more complex continuous wave (CW) helium-neon
laser (4) took only about 6 months, whereas for atomic
condensates, it has taken considerably longer to produce a
continuous source of coherent atoms. Such a source is the most
crucial prerequisite for realizing continuous atom lasers.
2) The challenge in realizing a continuous BEC source originates
in the extreme parameter space covered during a typical cooling
cycle required for BEC production, which consists of laser
cooling followed by evaporative cooling. During optical cooling,
atoms scatter around 10^(7) photons/s, whereas during evaporative
cooling any photon scattering would cause heating and trap loss
and, therefore, has to be less than 10^(-1) photons/s. During
evaporative cooling, atoms are cooled by a factor of a thousand
from about 100 microkelvins to sub-microkelvin temperatures. This
requires a near-perfect isolation of the hot atoms from the cold,
because a single laser-cooled atom has enough energy to knock
thousands of atoms out of the condensate.
3) Until now, little progress has been made toward continuous
Bose-Einstein condensation. Early theoretical work considered the
realization of a continuous-atom laser using optical pumping of
incoming atoms into the laser mode (5). More recently,
evaporative cooling of a slow atomic beam from the typical phase-
space density of laser cooling (106) into quantum degeneracy has
been suggested. Experimental work has so far only addressed the
production and guiding of a beam of laser-cooled atoms.
4) In summary: The authors report that a continuous source of
Bose-Einstein condensed sodium atoms was created by periodically
replenishing a condensate held in an optical dipole trap with new
condensates delivered using optical tweezers. The source
contained more than 10^(6) atoms at all times, raising the
possibility of realizing a continuous atom laser.
References (abridged):
1. W. Ketterle, D. Durfee, D. Stamper-Kurn, Proceedings of the
International School of Physics-Enrico Fermi, M. Inguscio, S.
Stringari, C. Wieman, Eds. (IOS Press, Amsterdam, 1999), pp. 67-
176
2. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, S. Stringari, Rev.
Mod. Phys. 71, 463 (1999)
3. T. H. Maiman, Nature 187, 493 (1960)
4. A. Javan, W. R. Bennett, D. Herriott, Phys. Rev. Lett. 6, 106
(1961)
5. R. J. C. Spreeuw, T. Pfau, U. Janicke, M. Wilkens, Europhys.
Lett. 32, 469 (1995)
Science 2002 296:2193
Related Background:
BOSE-EINSTEIN CONDENSATE IN A SURFACE MICROTRAP
According to current physics, all particles in nature are either
fermions or bosons, with fermions (always elementary particles)
having half-integer spin (spin-states characterized by half-
integer multiples of Planck's constant divided by 2Ć), and bosons
(all other particles) having integer spin (spin-states
characterized by integer multiples of Planck's constant divided
by 2Ć). In general, bosons are particles that obey Bose-Einstein
statistics, and they include photons, pi mesons, all nuclei
having an even number of particles, and all particles with
integer or zero spin. Pi mesons (pions) are subatomic particles
with masses approximately 270 times the mass of the electron.
Bose-Einstein statistics is the statistical mechanics of a system
of indistinguishable particles for which there is no restriction
on the number of particles that may simultaneously exist in the
same quantum energy state. Particles that obey Bose-Einstein
statistics are called "bosons".
In general, "Bose-Einstein condensation" is a phenomenon
occurring in a macroscopic system consisting of a relatively
large number of bosons at a sufficiently low temperature
(microkelvins down to nanokelvins) in which a significant
fraction of the particles occupy a single quantum state of lowest
energy (the ground state). In an atomic Bose-Einstein
condensate, several thousand atoms essentially become a single
atom, a "superatom", and this effect has been observed
experimentally with atoms of rubidium and lithium, the atoms
trapped and cooled by special methods.
H. Ott et al (University of Tuebingen, DE) discuss Bose-Einstein
condensates, the authors making the following points:
1) Trapped ultracold atoms are fascinating model systems for
studying quantum statistical many-particle phenomena. Confined in
optical or magnetic trapping potentials, the atomic gas reaches
quantum degeneracy at ultra-low temperatures (typically less than
1 microkelvin) and very small densities (approximately 10^(14)
atoms per cubic centimeter). In this regime, the interaction
between the atoms is still weak and the system is accessible to
precise theoretical description.
2) One of the most intriguing properties of such ultracold atomic
ensembles is the formation of macroscopic matter waves with
extraordinarily large coherence lengths. For single thermal
atoms, the coherence length is determined by the thermal de
Broglie wavelength and is thus limited to the micron range, even
for temperatures as small as 1 microkelvin. In contrast, a Bose-
Einstein condensate may show coherence effects over a much larger
distance. It is therefore of interest to combine degenerate
quantum gases with magnetic micropotentials, which may allow for
coherent atomic optics on the surface of a microstructured "atom
chip". But from an experimental standpoint, it is unclear how a
degenerate Bose gas behaves in a waveguide structure, where it
acquires a quasi-one-dimensional character.
3) The authors report they have experimentally generated a Bose-
Einstein condensate in a microstructured magnetic surface trap,
the setup allowing for investigation of coherence phenomena of
degenerate quantum gases in extremely anisotropic magnetic
waveguides.
Phys. Rev. Lett. 2001 87:230401
Related Background:
TRANSPORT OF BOSE-EINSTEIN CONDENSATES WITH OPTICAL TWEEZERS
T.L. Gustavson et al (Massachusetts Institute of Technology, US)
discuss transport of Bose-Einstein condensates, the authors
making the following points:
1) Since the achievement of Bose-Einstein condensation in dilute
gases of alkali atoms in 1995, intensive experimental and
theoretical efforts have yielded a great deal of progress in
understanding many aspects of Bose-Einstein condensation [1,2].
Bose-Einstein condensates are well-controlled ensembles of atom
useful for studying novel aspects of quantum optics, many-body
physics, and superfluidity. Condensates are now used in
scientific studies of increasing complexity requiring multiple
optical and magnetic fields as well as proximity to surfaces.
2) Conventional condensate production techniques severely limit
optical and mechanical access to experiments due to the many
laser beams and magnetic coils needed to create the condensates.
This conflict between cooling infrastructure and accessibility to
manipulate and study condensates has been a major restriction to
previous experiments. So far, most experiments are carried out
within a few millimeters of where the condensate was created.
What is highly desirable is a condensate "beam line" that
delivers condensates to a variety of experimental platforms.
Transport of charged particles and energetic neutral particles
between vacuum chambers is standard, whereas it is a challenge to
avoid excessive heating for ultracold atoms. Thus far, transport
of large clouds of atoms has only been accomplished with laser-
cooled atoms at microkelvin temperatures [3,4]. Condensates are
typically a few orders of magnitude colder and hence much more
sensitive to heating during the transfer.
3) The authors report a demonstration of an application of
optical tweezers that can transfer Bose condensates over
distances of at least 44 centimeters (limited by the vacuum
chamber) with a precision of a few micrometers. This separates
the region of condensate production from that used for scientific
studies. The "science chamber" has excellent optical and
mechanical access, and the vacuum requirements in this region may
well be less stringent than those necessary for production of
condensates. The authors suggest this technique is ideally suited
to deliver condensates close to surfaces, e.g., to microscopic
waveguides and into electromagnetic cavities. The authors report
they have used this technique to transfer condensates into a
macroscopic wiretrap located 36 centimeters away from the point
where the condensates were produced.
References (abridged):
1. W. Ketterle, D. Durfee, and D. Stamper-Kum, in Proceedings of
the International School of Physics Enrico Fermi, edited by M.
Inguscio, S. Stringari, and C. Wieman (IOS Press, Tokyo, 1999),
p. 67.
2. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari,
Rev. Mod. Phys. 71, 463 (1999).
3. M. Greiner, I. Bloch, T. W. Hansch, and T. Esslinger, Phys.
Rev. A 63, 031401 (2001).
4. T. Kishimoto, P. Schwindt, Y.-J. Wang, W. Jhe, D. Anderson,
and E. Comell, DAMOP/DAMP Poster (London, Ontario, Canada, 2001).
Phys. Rev. Lett. 2002 88:020401
Related Background:
FESHBACH RESONANCES IN A BOSE-EINSTEIN CONDENSATE
The term "Feshbach resonance" refers to a transient "sticking" of
two colliding atoms, the sticking involving a resonance coupling
that occurs when the molecular state has nearly zero energy. The
term "optical trapping" refers to the confinement of entities in
a restricted geometry by the controlled action of light. In this
report, the term "inelastic" refers to a collision process in
which the total kinetic energy of the colliding particles is not
the same after the collision as before it, and the term "coherent
beams of atoms" refers to beams composed of atoms moving in
unison.
Inouye et al (6 authors at Massachusetts Institute of Technology,
US) report new observations in a Bose-Einstein condensate. It has
long been predicted that the scattering of ultra-cold atoms can
be altered significantly through a so-called "Feshbach
resonance". Two such resonances have now been observed in
optically trapped Bose-Einstein condensates of sodium atoms by
varying an external magnetic field. The resonances gave rise to
enhanced inelastic processes and a dispersion variation of the
scattering length by a factor of over two. The authors suggest
these results open new possibilities for the study and
manipulation of Bose-Einstein condensates, may also be important
in atom optics, for modifying the atomic interactions in an atom
laser, or more generally, for controlling nonlinear coefficients
in atom optics with coherent beams of atoms.
Nature 1998 392:151
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3. MOLECULE CONDENSATION
FIRST MOLECULES IN A BOSE-EINSTEIN CONDENSATE
In 1997, Steven Chu, Claude Cohen-Tannoudji, and William D.
Philips shared the Nobel Prize in Physics for their work in the
1980s involving laser-cooled atoms, work that ultimately led to
the cooling of atoms to extremes close to absolute zero degrees
kelvin, and finally to the creation by Anderson et al (Science
269:198 1995) of a Bose-Einstein condensation in a dilute gas of
rubidium atoms. The essential idea behind these techniques
involves a reduction in the momentum of an atom when it absorbs a
photon. Bose-Einstein statistics is the statistical mechanics of
a system of indistinguishable particles for which there is no
restriction on the number of particles that may simultaneously
exist in the same quantum energy state. Bosons are particles that
obey Bose-Einstein statistics, and they include photons, pi
mesons, all nuclei having an even number of particles, and all
particles with integer spin. In low temperature physics, the
Bose-Einstein condensation is a phenomenon that occurs in the
study of systems of bosons: below a critical temperature, the
quantum ground state becomes highly populated, individual wave
equations merging into a single wave equation, the particles
indistinguishable, and the condensate of particles behaving as a
singe entity.
R. Wynar et al (5 authors at University of Texas Austin, US) now
report the production of rubidium-87 dimers that are essentially
at rest by assembling them from ultracold rubidium atoms in an
atomic Bose-Einstein condensate. In a commentary in the same
journal, C.J. Williams and P.S. Julienne (National Institute of
Standards and Technology, US) point out that this work is the
first observation of molecule formation in a Bose-Einstein
condensate, that a method for the ultraprecise measurement of
molecular binding energies has now been introduced, and that the
work is the first measurement of the interaction energy between a
condensate and a molecule.
Science 2000 287:986,1016
Releated Background:
FIRST ELECTROSTATIC TRAPPING OF AMMONIA MOLECULES
The ability to cool and slow atoms with light for subsequent
trapping allows investigations of the properties and interactions
of the trapped atoms in unprecedented detail. Although in general
the complex structure of molecules prohibits this type of
manipulation, magnetic trapping of calcium hydride molecules
*thermalized in ultra-cold buffer gas, and optical trapping of
cesium dimers generated from ultra-cold cesium atoms have been
reported. These methods, however, depend on the target molecules
being paramagnetic (e.g., calcium hydride) or able to form
through the association of atoms amenable to laser cooling (e.g.,
cesium dimers), thus restricting the range of molecular species
that can be studied.
H.L. Bethlem et al (6 authors at 2 installations, NL) now report
the slowing of an *adiabatically cooled beam of deuterated
ammonia molecules by time-varying inhomogeneous electric fields,
and subsequent loading into an electrostatic trap. The authors
report they are able to trap ammonia molecules with a density of
10^(6) per cubic centimeter in a volume of 0.25 cubic centimeters
at temperatures below 0.35 degrees kelvin. The authors report
they observe pronounced density oscillations caused by the rapid
switching of the electric fields during loading of the trap. The
authors suggest their results illustrate that polar molecules can
be efficiently cooled and trapped, thus providing an opportunity
to study collisions and collective quantum effects in a wide
range of ultra-cold molecular systems.
Nature 2000 406:491
Notes:
*thermalized: In general, to bring entities into thermal
equilibrium with their surroundings.
*adiabatically cooled: In general, an adiabatic process is any
thermodynamic process, reversible or irreversible, that takes
place in a system without exchange of heat with the surroundings
of the system. All real processes are nonadiabatic in the sense
that some heat exchange always occurs. But close approximation to
an adiabatic ideal can be realized in practice.
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4. ATOM-MOLECULE COHERENCE
ATOM MOLECULE COHERENCE IN A BOSE EINSTEIN CONDENSATE
E.A. Donley et al (University of Colorado, US) discuss atom-
molecule coherence, the authors making the following points:
1) Recent advances in the precise control of ultracold atomic
systems have led to the realization of Bose Einstein condensates
(BECs) and degenerate Fermi gases. An important challenge is to
extend this level of control to more complicated molecular
systems. One route for producing ultracold molecules is to form
them from the atoms in a BEC. For example, a two-photon
stimulated Raman transition in a 87Rb BEC has been used to
produce 87Rb2 molecules in a single rotational-vibrational
state(1), and ultracold molecules have also been formed(2)
through photoassociation of a sodium BEC. Although the coherence
properties of such systems have not hitherto been probed, the
prospect of creating a superposition of atomic and molecular
condensates has initiated much theoretical work(3).
2) A Feshbach resonance is a scattering resonance for which the
total energy of two colliding atoms is equal to the energy of a
bound molecular state, and atom molecule transitions can occur
during a collision.
3) The authors report the use of a time-varying magnetic field
near a Feshbach resonance to produce coherent coupling between
atoms and molecules in a 85Rb BEC. A mixture of atomic and
molecular states is created and probed by sudden changes in the
magnetic field, which lead to oscillations in the number of atoms
that remain in the condensate. The oscillation frequency,
measured over a large range of magnetic fields, is in excellent
agreement with the theoretical molecular binding energy,
indicating that the authors have created a quantum superposition
of atoms and diatomic molecules -- two chemically different
species.
References (abridged):
1. Wynar, R. H., Freeland, R. S., Han, D. J., Ryu, C. & Heinzen,
D. J. Molecules in a Bose-Einstein condensate. Science 287, 1016-
1019 (2000)
2. McKenzie, C. et al. Photoassociation of sodium in a Bose-
Einstein condensate. Phys. Rev. Lett. 88, 120403-1-120403-4
(2001)
3. Anglin, J. R. & Vardi, A. Dynamics of a two-mode Bose-Einstein
condensate beyond mean-field theory. Phys. Rev. A 64, 013605-1-
013605-9 (2001)
4. Cusack, B. J., Alexander, T. J., Ostrovskaya, E. A. & Kivshar,
Y. S. Existence and stability of coupled atomic-molecular Bose-
Einstein condensates. Phys. Rev. A 65, 013609-1-013609-4 (2001)
5. Calsamiglia, J., Mackie, M. & Suominen, K. Superposition of
macroscopic numbers of atoms and molecules. Phys. Rev. Lett. 87,
160403-1-160403-4 (2001)
Nature 2002 417:529
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5. BOSE-EINSTEIN CONDENSATES AND MATTER WAVES
So-called "matter waves" are de Broglie waves, a set of waves
that represent the behavior, under appropriate conditions, of a
particle (for example, the diffraction of the particle by a
crystal lattice). The wavelength is the de Broglie wavelength and
is given by the de Broglie equation L = h/mv, where (L) is the
wavelength, (h) is Planck's constant, (m) is the mass and (v) the
velocity of the particle.
NONLINEAR AND QUANTUM ATOM OPTICS
S.L. Rolston and W.D. Phillips (National Institute of Standards
and Technology, US) discuss coherent matter waves, the authors
making the following points:
1) Coherent matter waves in the form of Bose Einstein condensates
have led to the development of nonlinear and quantum atom optics
-- the de Broglie wave analogues of nonlinear and quantum optics
with light. In nonlinear atom optics, four-wave mixing of matter
waves and mixing of combinations of light and matter waves have
been observed; such progress culminated in the demonstration of
phase-coherent matter-wave amplification. Solitons represent
another active area in nonlinear atom optics: these non-
dispersing propagating modes of the equation that governs Bose
Einstein condensates have been created experimentally, and
observed subsequently to break up into vortices. Quantum atom
optics is concerned with the statistical properties and
correlations of matter-wave fields. A first step in this area is
the measurement of reduced number fluctuations in a Bose Einstein
condensate partitioned into a series of optical potential wells.
2) The advent of the laser in 1960 began a new era in optics,
eventually leading to numerous technological innovations, from
laser surgery to CD-ROMs. Laser light has a combination of high
coherence and high intensity that had been previously
unattainable. These properties represent a significant difference
from earlier light sources, and new kinds of phenomena became
possible. Among them were nonlinear optical phenomena and the
production of non-classical (that is, quantum) light. The
production of atomic-gas Bose Einstein condensates (BECs)(1,2)
brought a similar change in the optics of matter waves (atom
optics).
3) One of the first qualitatively new experiments to follow the
appearance of the laser was second harmonic generation, or
frequency doubling(3). An intense pulse of red laser light
irradiated a transparent crystal and the emerging pulse included
a small amount of blue light, with twice the frequency (half the
wavelength) of the red light. The blue light arose because the
crystal responded nonlinearly to the electric field of the
incident laser (the index of refraction depends on the light
intensity). This and other nonlinear phenomena have made
nonlinear optics an important and exciting field of research for
the past 40 years4, with applications in physics, chemistry and
biology.
4) The inverse process to second harmonic generation (or sum
frequency generation in the case of two input frequencies) is
parametric down-conversion(5). Here, photons from laser light
incident on a crystal are converted into twin photons whose
frequency and momentum sum to that of the incident photons. The
twins are strongly correlated in that one always accompanies the
other, born simultaneously (within the inverse of their frequency
bandwidth), with complementary frequency and direction. The
number of photons emitted in complementary directions is
identical, representing light beams more alike than any ordinary
beams could ever be. In contrast, a laser beam incident on a
perfect 50/50 beam splitter produces streams of photons whose
numbers are similar only to within the statistical uncertainty of
Poisson counting statistics (the beam splitter "flips a coin" for
each photon that passes through).
References (abridged):
1. Anderson, M. H. et al. Observation of Bose-Einstein
condensation in a dilute atomic vapor. Science 269, 198-201
(1995)
2. Inguscio, M., Stringari, S. & Wieman, C. (eds) Bose-Einstein
Condensation in Atomic Gases(Int. School Phys. "Enrico Fermi"
Course 140) (IOS Press, Amsterdam, 1999)
3. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G.
Generation of optical harmonics. Phys. Rev. Lett. 7, 118-119
(1961)
4. Evans, M. & Kielich, S. Modern Nonlinear Optics Vols 1-3
(Wiley, New York, 1997)
5. Migdall, A. Correlated-photon metrology without absolute
standards. Phys. Today 52, 41-46 (1999)
Nature 2002 416:219
Related Background:
FORMATION OF A MATTER-WAVE BRIGHT SOLITON
L. Khaykovich et al (Ecole Normale Sup‚rieure Paris, FR) discuss
matter waves, the authors making the following points:
1) Solitons are localized waves that travel over long distances
with neither attenuation nor change of shape, as their dispersion
is compensated by nonlinear effects. Soliton research has been
conducted in fields as diverse as particle physics, molecular
biology, geology, oceanography, astrophysics, and nonlinear
optics. Perhaps the most prominent application of solitons is in
high-rate telecommunications with optical fibers (1).
2) The authors report the production of matter-wave solitons in
an ultracold lithium-7 gas. The effective interaction between
atoms in a Bose-Einstein condensate is tuned with a Feshbach
resonance from repulsive to attractive before release in a one-
dimensional optical waveguide. Propagation of the soliton without
dispersion over a macroscopic distance of 1.1 millimeters is
observed. A simple theoretical model explains the stability
region of the soliton. The authors suggest these matter-wave
solitons open possibilities for future applications in coherent
atom optics, atom interferometry, and atom transport (2-5).
References (abridged):
1. See, for example, the recent special issue: Chaos 10, 471
(2000)
2. P. A. Ruprecht, M. J. Holland, K. Burnett, M. Edwards, Phys.
Rev. A 51, 4704 (1995)
3. C. C. Bradley, C. A. Sackett, R. G. Hulet, Phys. Rev. Lett.
78, 985 (1997)
4. J. L. Roberts, et al., Phys. Rev. Lett. 86, 4211 (2001)
5. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972)
Science 2002 296:1290
Related Background:
ON WAVE PHENOMENA IN PHYSICS
The idea of "wave" phenomena, the characterization of certain
phenomena as waves, must rank as one of the most important
concepts in both classical and modern physics. In general, a
"wave" is a time-varying quantity that is also a function of
position, a disturbance either continuous or transient, traveling
through a medium as a result of certain properties of the medium,
the resulting displacements of the medium returning to zero when
the disturbance has passed. The chief parameters of a wave are
its speed of propagation, its frequency, its wavelength, and its
amplitude.
J.A. Scales and R. Sneider (2 installations, US NL) present an
essay on waves in physics, the authors making the following
points:
1) The authors note that when scientists (including physicists)
are asked to define a wave, the answers are often ambiguous.
Students may state that a wave is a solution to the wave
equation; professionals may make some ambiguous statement about
propagation velocity; mathematicians tend to give a formal
characterization based on the hyperbolic character of certain
differential equations. The authors suggest that the term "wave"
be defined as an "organized propagating imbalance", with the
caveat: "Just don't ask us to define 'organized'."
2) The authors state that at the simplest levels, the ubiquity of
(classical) waves can be attributed to the desire of nature for
stable equilibria. Whatever the forces that connect bits of
matter together (e.g., electromagnetic or gravitational), for
small perturbations about a stable equilibrium point, the forces
are approximately linear. A linear restoring force implies
harmonic oscillations, and coupled systems of oscillators support
both propagating and standing disturbances. Linearity also
implies superposition, so that periodic solutions can be added
together to obtain finite wave "packets". Thus, for small
perturbations about an equilibrium state in coupled or decoupled
(extended) systems, waves are the natural consequence of the
stability of simple harmonic motion.
3) Wave propagation is in many situations described by a linear
differential equation. In reality, nonlinearity is of great
importance, and this nonlinearity may destroy the waves. When
this happens, organized wave motion changes into turbulent
motion, and in this process it is impossible to state exactly at
which point the wave ceases to be a wave.
4) Heat is the manifestation of microscopic motion. Computing the
classical resonant frequencies of atoms or molecules in a lattice
gives numbers of the order of 10^(13) Hz, i.e., in the infrared
part of the electromagnetic spectrum, so that when molecules
vibrate they produce heat. These lattice vibrations are called
"phonons", and they have both wave-like and particle-like
character. Lattice vibrations are responsible for the transport
of heat in a lattice, and we know that heat is a diffusive
phenomenon. However, if the lattice is cooled to near absolute
zero, the mean free scattering path of the phonons becomes
comparable to the macroscopic size of the sample, and when this
happens, lattice vibrations no longer behave diffusively but are
actually wave-like. By controlling the temperature of a sample,
one can control the extent to which heat is ballistic (wave-like)
or diffusive.
5) Waves have a central role in quantum mechanics, according to
which theory everything has a wave character. Einstein (1879-
1955) used the relation E = hf (energy equals Planck's constant
times frequency) to connect the wave frequency of light with the
energy of discrete light quanta (photons). De Broglie (1875-1960)
extended this to electrons and other entities of matter. For
classical waves, dissipation generally damps the wave motion, and
ultimately everything appears to come to rest. Quantum mechanics
demonstrates that matter waves do not exhibit dissipation: even
the ground state of a harmonic oscillator is in harmonic motion.
Matter waves never come to rest.
Nature 1999 401:739
Related Background:
NONLINEAR AND QUANTUM ATOM OPTICS
S.L. Rolston and W.D. Phillips (National Institute of Standards
and Technology, US) discuss nonlinear optics, the authors making
the following points:
1) Coherent matter waves in the form of Bose Einstein condensates
have led to the development of nonlinear and quantum atom optics
-- the de Broglie wave analogues of nonlinear and quantum optics
with light. In nonlinear atom optics, four-wave mixing of matter
waves and mixing of combinations of light and matter waves have
been observed; such progress culminated in the demonstration of
phase-coherent matter-wave amplification. Solitons represent
another active area in nonlinear atom optics: these non-
dispersing propagating modes of the equation that governs Bose
Einstein condensates have been created experimentally, and
observed subsequently to break up into vortices. Quantum atom
optics is concerned with the statistical properties and
correlations of matter-wave fields. A first step in this area is
the measurement of reduced number fluctuations in a Bose Einstein
condensate partitioned into a series of optical potential wells.
2) The advent of the laser in 1960 began a new era in optics,
eventually leading to numerous technological innovations, from
laser surgery to CD-ROMs. Laser light has a combination of high
coherence and high intensity that had been previously
unattainable. These properties represent a significant difference
from earlier light sources, and new kinds of phenomena became
possible. Among them were nonlinear optical phenomena and the
production of non-classical (that is, quantum) light. The
production of atomic-gas Bose Einstein condensates (BECs)(1,2)
brought a similar change in the optics of matter waves (atom
optics).
3) One of the first, qualitatively new experiments to follow the
appearance of the laser was second harmonic generation, or
frequency doubling(3). An intense pulse of red laser light
irradiated a transparent crystal and the emerging pulse included
a small amount of blue light, with twice the frequency (half the
wavelength) of the red light. The blue light arose because the
crystal responded nonlinearly to the electric field of the
incident laser (the index of refraction depends on the light
intensity). This and other nonlinear phenomena have made
nonlinear optics an important and exciting field of research for
the past 40 years4, with applications in physics, chemistry and
biology.(4,5)
References (abridged):
1. Anderson, M. H. et al. Observation of Bose-Einstein
condensation in a dilute atomic vapor. Science 269, 198-201
(1995).
2. Inguscio, M., Stringari, S. & Wieman, C. (eds) Bose-Einstein
Condensation in Atomic Gases(Int. School Phys. "Enrico Fermi"
Course 140) (IOS Press, Amsterdam, 1999).
3. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G.
Generation of optical harmonics. Phys. Rev. Lett. 7, 118-119
(1961).
4. Evans, M. & Kielich, S. Modern Nonlinear Optics Vols 1-3
(Wiley, New York, 1997).
5. Migdall, A. Correlated-photon metrology without absolute
standards. Phys. Today 52, 41-46 (1999).
Nature 2002 416:219
Related Background:
FORMATION AND PROPAGATION OF MATTER-WAVE SOLITON TRAINS
K.E. Strecker et al (Rice University, US) discuss matter-wave
solitons, the authors making the following points:
1) Attraction between the atoms of a Bose Einstein condensate
renders it unstable to collapse, although a condensate with a
limited number of atoms(1) can be stabilized(2) by confinement in
an atom trap. However, beyond this number the condensate
collapses(3-5). Condensates constrained to one-dimensional motion
with attractive interactions are predicted to form stable
solitons, in which the attractive forces exactly compensate for
wave-packet dispersion(1).
2) Dispersion and diffraction cause localized wave packets to
spread as they propagate. Solitons may be formed when a nonlinear
interaction produces a self-focusing of the wave packet that
compensates for dispersion. Such localized structures have been
observed in many physical systems including water waves, plasma
waves, sound waves in liquid helium, particle physics, and in
optics. A Bose Einstein condensate can be described by the
nonlinear Schroedinger equation, for which the interaction term
is cubic in the condensate wavefunction. For attractive
interactions, this equation has the same form as the equation for
an optical wave propagating in a medium with a cubic, self-
focusing (Kerr) nonlinearity and, in this sense, bright matter-
wave solitons in one dimension are similar to optical solitons in
optical fibers.
3) The authors report the formation of bright solitons of 7Li
atoms in a quasi-one-dimensional optical trap, by magnetically
tuning the interactions in a stable Bose Einstein condensate from
repulsive to attractive. The solitons are set in motion by
offsetting the optical potential, and are observed to propagate
in the potential for many oscillatory cycles without spreading.
The authors observe a soliton train, containing many solitons;
repulsive interactions between neighboring solitons are inferred
from their motion.
References (abridged):
1. Ruprecht, P. A., Holland, M. J., Burnett, K. & Edwards, M.
Time-dependent solution of the nonlinear Schroedinger equation
for Bose-condensed trapped neutral atoms. Phys. Rev. A 51, 4704-
4711 (1995)
2. Bradley, C. C., Sackett, C. A. & Hulet, R. G. Bose-Einstein
condensation of lithium: observation of limited condensate
number. Phys. Rev. Lett. 78, 985-989 (1997)
3. Sackett, C. A., Gerton, J. M., Welling, M. & Hulet, R. G.
Measurements of collective collapse in a Bose-Einstein condensate
with attractive interactions. Phys. Rev. Lett. 82, 876-879 (1999)
4. Gerton, J. M., Strekalov, D., Prodan, I. & Hulet, R. G. Direct
observation of growth and collapse of a Bose-Einstein condensate
with attractive interactions. Nature 408, 692-695 (2000)
5. Donley, E. A. et al. Dynamics of collapsing and exploding
Bose-Einstein condensates. Nature 412, 295-299 (2001)
Nature 2002 417:150
Related Background:
BOSE-EINSTEIN CONDENSATION ON A MICROELECTRONIC CHIP
W. Haensel et al (Ludwig-Maximilians University, DE) discuss
Bose-Einstein condensates, the authors making the following
points.
Although Bose-Einstein condensates of ultracold atoms have been
experimentally realizable for several years, their formation and
manipulation still impose considerable technical challenges. An
all-optical technique that enables faster production of Bose-
Einstein condensates was recently reported. The authors
demonstrate that the formation of a condensate can be greatly
simplified using a microscopic magnetic trap on a chip. The
authors report they achieve Bose-Einstein condensation inside the
single vapor cell of a magneto-optical trap in as little as 700
milliseconds -- more than a factor of 10 faster than typical
experiments, and a factor of 3 faster than the all-optical
technique. A coherent matter wave is emitted normal to the chip
surface when the trapped atoms are released into free fall.
Alternatively, the authors couple the condensate into an "atomic
conveyor belt", which is used to transport the condensed cloud
nondestructively over a macroscopic distance parallel to the chip
surface. The authors suggest that the possibility of manipulating
laser-like coherent matter waves with such an integrated atom-
optical system holds promise for applications in interferometry,
holography, microscopy, atom lithography, and quantum information
processing.
Nature 2001 413:498
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6. EXCITON CONDENSATES
CONDENSED-MATTER PHYSICS: EXCITON DEVELOPMENTS
Ilias E. Perakis (Vanderbilt University, US) discusses excitons,
the author making the following points:
1) The first Bose Einstein condensate using atomic gases was
created in 1995. This achievement, initially with rubidium, was
made possible by the design of appropriate magnetic traps to hold
the atoms, and the development of sophisticated cooling
techniques(1). Work on producing a new kind of condensate -- this
time, using "excitons" -- has so far produced controversial
results.
2) Excitons are quasiparticles: in semiconductors, electrons can
be excited from the valence band to the conduction band using
optical fields; this conduction electron is attracted, through
the Coulomb interaction, to the positively charged hole left
behind in the valence band. As a result, the electron and hole
form a bound state called an exciton. Like a rubidium atom, this
neutral bound complex can behave as a boson -- a particle with
integer spin which obeys Bose Einstein statistics. When the
temperature of a boson gas drops below a certain value, a large
number of bosons "condense" into a single quantum state -- this
is a Bose Einstein condensate (BEC). All of these bosons then
behave in exactly the same way, and quantum-mechanical effects
become visible at a macroscopic level. Such collective boson
behaviour gives rise to phenomena such as frictionless flow, or
superfluidity, and quantum interference.
3) Several semiconductor systems have been investigated(3) for
evidence of an exciton BEC, with mixed results. Excitons have
much lower mass than the atoms typically used to make BECs. This
means that an exciton BEC can form at higher temperatures
(although still only around the 1 K mark). The problem is that
excitons exist only for a short time, just a few nanoseconds,
before the electron and hole recombine. So it is difficult to
create a "gas" -- a Bose gas -- of excitons that is cold and
dense enough to condense within this short time(4,5).
References (abridged):
1. Pethick, C. J. & Smith, H. Bose-Einstein Condensation in
Dilute Gases (Cambridge Univ. Press, 2002)
2. Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. &
Chemla, D. S. Nature 417, 47-52 (2002)
3. Griffin, A., Snoke, D. W. & Stringari, S. Bose-Einstein
Condensation of Excitons and Biexcitons (Cambridge Univ. Press,
1995)
4. Butov, L. V. et al. Phys. Rev. Lett. 86, 5608-5611 (2001)
5. Trauernicht, D. P., Wolfe, J. P. & Mysyrowicz, A. Phys. Rev. B
34, 2561-2575 (1986)
Nature 2002 417:33
Related Background:
TOWARDS BOSE EINSTEIN CONDENSATION OF EXCITONS IN POTENTIAL TRAPS
L.V. Butov et al (University of California Berkeley, US) discuss
exciton condensation, the authors making the following points:
1) An exciton is an electron hole bound pair in a semiconductor.
In the low-density limit, it is a composite Bose quasi-particle,
akin to the hydrogen atom(1). Just as in dilute atomic
gases(2,3), reducing the temperature or increasing the exciton
density increases the occupation numbers of the low-energy
states, leading to quantum degeneracy and eventually to Bose-
Einstein condensation (BEC)(1). Because the exciton mass is small
-- even smaller than the free electron mass -- exciton BEC should
occur at temperatures of about 1 K, many orders of magnitude
higher than for atoms. However, it is in practice difficult to
reach BEC conditions, as the temperature of excitons can
considerably exceed that of the semiconductor lattice. The search
for exciton BEC has concentrated on long-lived excitons: the
exciton lifetime against electron hole recombination therefore
should exceed the characteristic timescale for the cooling of
initially hot photo-generated excitons(4,5). Until now, all
experiments on atom condensation were performed on atomic gases
confined in the potential traps.
2) The authors report that inspired by these experiments, and
using specially designed semiconductor nanostructures, they have
collected quasi-two-dimensional excitons in an in-plane potential
trap. Their photoluminescence measurements demonstrate that the
quasi-two-dimensional excitons indeed condense at the bottom of
the traps, giving rise to a statistically degenerate Bose gas.
References (abridged):
1. Keldysh, L. V. & Kozlov, A. N. Collective properties of
excitons in semiconductors. Zh. Eksp. Teor. Fiz. 54, 978-993
(1968); Sov. Phys. JETP 27, 521-528 (1968)
2. Anderson, M. N., Ensher, J. R., Matthews, M. R., Wieman, C. E.
& Cornell, E. A. Observation of Bose-Einstein condensation in a
dilute atomic vapor. Science 269, 198-202 (1995)
3. Davis, K. B. et al. Bose-Einstein condensation in a gas of
sodium atoms. Phys. Rev. Lett. 75, 3969-3973 (1995)
4. Snoke, D. W., Wolfe, J. P. & Mysyrowicz, A. Quantum saturation
of a Bose gas: excitons in Cu2O. Phys. Rev. Lett. 59, 827-830
(1987)
5. Lin, J. L. & Wolfe, J. P. Bose-Einstein condensation of
paraexcitons in stressed Cu2O. Phys. Rev. Lett. 71, 1222-1225
(1993)
Nature 2002 417:47
Related Background:
SPONTANEOUS BOSE COHERENCE OF EXCITONS AND POLARITONS
David Snoke (University of Pittsburgh, US) discusses excitons,
the author making the following points:
1) Numerous recent experiments have studied coherence in
semiconductor systems. In most of these experiments, the
coherence is generated from a coherent laser that excites the
system. The laser itself acquires coherence because a selected
optical state is amplified. In the past two decades, however,
several experimenters have pursued the possibility of spontaneous
coherence in semiconductor systems. In such a case, no single
state is selected for amplification. Instead, coherence appears
in a state selected by the system itself by means of a
thermodynamic phase transition.
2) The phase transition that can cause this is Bose-Einstein
condensation (BEC) of excitons or polaritons. In this phase
transition, a macroscopic number of particles enter a single
quantum state, forming a coherent state with definite phase by
the process known as "spontaneous symmetry breaking" (1). The
underlying physics is the same as BEC of atoms, seen in
superfluid helium or, more recently, in alkali atoms in magneto-
optical traps (2,3) and in spin-polarized hydrogen (4). Excitons
and polaritons, quanta of excitation that are integer-spin
bosons, often have an effective mass and a long lifetime, so that
they can be treated theoretically as metastable atom-like
particles. As such, the laws of thermodynamics apply and BEC is
expected at a low temperature, typically a few kelvin. After
initial proposals in the 1960s (5), the theoretical basis for
Bose condensation of excitons was laid down in a number of papers
in the 1970s and 1980s and has continued to attract theoretical
interest.
3) In summary: In the past decade, there has been an increasing
number of experiments on spontaneous Bose coherence of excitons
and polaritons. The author reviews four major areas of research:
three-dimensional excitons in the bulk semiconductor Cu2O, two-
dimensional excitons in coupled quantum wells, Coulomb drag
experiments in coupled two-dimensional electron gases, and
polaritons in semiconductor microcavities. The unifying theory of
all these experiments is the effect of spontaneous symmetry
breaking in the Bose-Einstein condensation phase transition.
References (abridged):
1. For the mathematics of spontaneous symmetry-breaking of pure
bosons, see sections 2.1.1 to 2.1.3 of S. A. Moskalenko, D. W.
Snoke, Bose-Einstein Condensation of Excitons and Biexcitons and
Coherent Nonlinear Optics with Excitons (Cambridge Univ. Press,
Cambridge, 2000).
2. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weimann,
E. A. Cornell, Science 269, 198 (1995).
3. M. R. Andrews, et al., Science 273, 84 (1996)
4. D. G. Fried, et al., Phys. Rev. Lett. 81, 3811 (1998)
5. S. A. Moskalenko, Fiz. Tverd. Tela 4, 276 (1962)
Science 2002 298:1368
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7. ULTRACOLD STATES
QUANTUM ENCOUNTERS OF THE COLD KIND
K. Burnett et al (University of Oxford, UK) discuss ultracold
states, the authors making the following points:
1) Since the introduction of laser-cooling techniques for neutral
atoms in the early 1980s, the study of collisional interactions
between atoms and molecules has been extended to the regime of
ultracold temperatures. With nanokelvin temperatures now
attainable, our ability to probe the interactions, both
experimentally and theoretically, has also progressed.
Understanding of the subtle and often highly quantum-mechanical
effects that are manifest at such low energies has advanced to
the point where new precision measurements are matched by highly
accurate theoretical calculations. Low-energy phenomena such as
Bose Einstein condensation and the photoassociation of atoms into
bound molecules are now accurately described with no free
parameters.
2) The behavior of atoms and their interactions at ultracold
temperatures is a fascinating area of study. These interactions
and their effects distinguish them from those encountered in
collisions at room temperature. The realization that these
interactions would be both subtle and interesting began in the
1970s with studies(1) of spin-polarized hydrogen and long-range
molecules, and expanded as laser cooling(2-4) reached
temperatures in the millikelvin and then microkelvin ranges. With
the advent of evaporative cooling(5) and the production of atomic
Bose Einstein condensates (BECs), we now require a detailed
understanding of atomic interactions at nanokelvin temperatures.
These applications have driven a tremendous growth of interest in
the field.
3) It was realized early on that the quantal nature of ultracold
atomic interactions would have a profound role and provide a
challenge to theorists and experimentalists in the field of
collision dynamics. At the low energies involved, the precise
nature of the interatomic forces -- at ludicrously large
distances from the point of view of "normal molecular physics" --
would have to be determined, requiring new ways to examine them.
It was also evident that nuclear spin dynamics, usually
irrelevant to collision dynamics, would complicate the analysis
enormously. In fact, the term complicated does not do service to
the range of new physics that the hyperfine interactions bring up
in this regime.
References (abridged):
1. Weiner, J., Zilio, S., Bagnato, V. S. & Julienne, P. S.
Experiments and theory in cold and ultracold collisions. Rev.
Mod. Phys. 71, 1-85 (1999)
2. Cohen-Tannoudji, C. Manipulating atoms with photons. Rev. Mod.
Phys. 70, 707-719 (1997)
3. Chu, S. The manipulation of neutral particles. Rev. Mod. Phys.
70, 685-706 (1997)
4. Phillips, W. D. Laser cooling and trapping of neutral atoms.
Rev. Mod. Phys. 70, 721-741 (1997)
5. Ketterle, W. & Van Druten, N. J. Evaporative cooling of
trapped atoms. Adv. At. Mol. Opt. Phys. 37, 181-236 (1996)
Nature 2002 416:225
Related Background:
ULTRACOLD MATTER: SUPERFLUIDITY IN FERMI GASES
L. Pitaevskii and S. Stringari (University of Trento, IT) discuss
superfluidity, the authors making the following points:
1) Over the past decade, studies of ultracold atomic gas clouds
have yielded unprecedented insights into the quantum statistical
properties of matter, with most studies have focused on boson
gases. The elementary constituents of matter can be divided into
fermions and bosons. Fermions are particles whose intrinsic
angular momentum (or spin) is an odd multiple of h/2(pi), where
(h) is the Planck constant. In contrast, the angular momentum of
bosons is an even multiple of h/2(pi). The dramatically different
thermodynamic properties of fermions and bosons at low
temperature are a direct result of quantum statistical effects.
2) The fundamental constituents of atoms (electrons, neutrons,
and protons) are fermions. However, pairs of fermions -- and, in
general, systems composed of an even number of fermions -- behave
like bosons. Because of their bosonic properties, hydrogen and
several alkali elements can be used to study the phenomenon of
Bose-Einstein condensation (2). But some isotopic species of
these alkali atoms, like 6Li and 40K, with an odd number of
fermions, instead exhibit fermionic behavior.
3) The first signatures of quantum statistical effects in atomic
Fermi gases were reported in 1999 (3). An important motivation
for these studies is the search for the transition to the
superfluid phase (4), analogous to the transition exhibited by
superconductors and liquid 3He. According to the standard theory
of fermion superfluidity, this transition should take place at
extremely low temperatures, well below the Fermi temperature T(F)
(the typical temperature where quantum effects show up). Attempts
to reach such temperatures with trapped atomic gases have
encountered major difficulties because the cooling mechanisms
become less and less efficient with decreasing temperature.
4. In contrast to other systems (such as atomic nuclei, liquid
3He, and superconductors), the trapping and interaction
mechanisms in atomic gases can be manipulated in a controlled
manner, allowing the interaction between atoms to be tuned (5).
By changing the strength of the magnetic field, the value and
even the sign of the scattering length can be changed. The
scattering length can be extremely large, much larger than the
average distance between atoms. As a result, the number of
collisions increases dramatically, enhancing the efficiency of
the cooling mechanisms, which are based on evaporation.
References (abridged):
1. K. M. O'Hara, S. L. Hemmer, M. E. Gehm, S. R. Granade, J. E.
Thomas, Science 298, 2179 (2002)
2. M. H. Anderson et al., Science 269, 198 (1995)
3. B. DeMarco, D. S. Jin, Science 285, 1703 (1999)
4, G. Shlyapnikov, in Proceedings of the 19th International
Conference on Atomic Physics, Cambridge, MA (World Scientific
Publishing), in press.
5. S. Inouye et al., Nature 392, 151 (1998)
Science 2002 298:2144
Related Background:
COLLAPSE OF A DEGENERATE FERMI GAS
G. Modugno et al (University of Firenze, IT) discuss degenerate
Fermi gases, the authors making the following points:
1) Experimental research on ultracold atoms has highlighted the
marked differences in basic properties of bosonic and fermionic
dilute quantum gases (1). In the case of a degenerate Fermi gas,
confined in a harmonic external potential, the Pauli exclusion
principle forbids the multiple occupation of a single quantum
state and leads to a strong effective repulsion between the
identical atoms. The fermions are arranged in the trap in a cloud
with relatively large spatial distribution and large kinetic
energy, which can be interpreted as being the result of an
outward "Fermi pressure" (2,3). This is a general property of any
degenerate Fermi system; for instance, it is the mechanism that
stabilizes white dwarfs and neutron stars against gravitational
collapse. As a result of this pressure, a dilute atomic Fermi gas
is only weakly affected by the actual interactions between
particles. Conversely, a Bose-Einstein condensate (BEC) occupies
only the ground state of the trap, with a narrow spatial
distribution, and the presence of interactions can strongly alter
its structure. Indeed, a repulsive interaction broadens the
density distribution, whereas an attractive interaction can lead
to a collapse for a sufficiently large number of atoms, as
observed for lithium (4) and rubidium (5).
2) Another scenario has been opened by the recent production of
degenerate boson-fermion mixtures (3). Here also the interspecies
interactions can play an important role, and, in particular, the
effect of the mutual interaction is predicted to be enhanced for
fermions by the higher density of the bosons. Moreover, as shown
by the early experiments on mixtures of superfluid 3He and 4He,
the presence of an interaction between bosons and fermions can
induce an effective attraction between fermions themselves.
3) In summary: The authors report that a degenerate gas of
identical fermions is brought to collapse by the interaction with
a Bose-Einstein condensate. The authors used an atomic mixture of
fermionic potassium-40 and bosonic rubidium-87, in which the
strong interspecies attraction leads to an instability above a
critical number of particles. The observed phenomenon suggests a
direction for manipulating fermion-fermion interactions on the
route to superfluidity.
References (abridged):
1. See, for example, J. R. Anglin and W. Ketterle, Nature 416,
212 (2002)
2. B. De Marco and D. S. Jin, Science 285, 1703 (1999)
3. A. G. Truscott, K. E. Strecker, W. I. McAlexander, G. B.
Partridge, R. G. Hulet, Science 291, 2570 (2001)
4. C. A. Sackett, J. M. Gerton, M. Welling, R. G. Hulet, Phys.
Rev. Lett. 82, 876 (1999)
5. E. A. Donley, et al., Nature 412, 295 (2001)
Science 2002 297:2240
Related Background:
QUANTUM PHASE TRANSITION FROM A SUPERFLUID TO A MOTT INSULATOR IN
A GAS OF ULTRACOLD ATOMS
M. Greiner et al (Ludwig-Maximilians University Munich, DE)
discuss ultracold atoms, the authors making the following points:
1) A physical system that crosses the boundary between two phases
changes its properties in a fundamental way. It may, for example,
melt or freeze. This macroscopic change is driven by microscopic
fluctuations. When the temperature of the system approaches zero,
all thermal fluctuations die out. This prohibits phase
transitions in classical systems at zero temperature, as their
opportunity to change has vanished. However, their quantum
mechanical counterparts can show fundamentally different
behavior. In a quantum system, fluctuations are present even at
zero temperature, due to Heisenberg's uncertainty relation. These
quantum fluctuations may be strong enough to drive a transition
from one phase to another, bringing about a macroscopic change.
2) A prominent example of such a quantum phase transition is the
change from the superfluid phase to the Mott insulator phase in a
system consisting of bosonic particles with repulsive
interactions hopping through a lattice potential. This system was
first studied theoretically in the context of superfluid-to-
insulator transitions in liquid helium(1). Recently, Jaksch et
al.(2) have proposed that such a transition might be observable
when an ultracold gas of atoms with repulsive interactions is
trapped in a periodic potential.
3) The authors report they observe such a quantum phase
transition in a Bose Einstein condensate with repulsive
interactions, held in a three-dimensional optical lattice
potential. As the potential depth of the lattice is increased, a
transition is observed from a superfluid to a Mott insulator
phase. In the superfluid phase, each atom is spread out over the
entire lattice, with long-range phase coherence. But in the
insulating phase, exact numbers of atoms are localized at
individual lattice sites, with no phase coherence across the
lattice; this phase is characterized by a gap in the excitation
spectrum. We can induce reversible changes between the two ground
states of the system.
References (abridged):
1. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D.
S. Boson localization and the superfluid-insulator transition.
Phys. Rev. B 40, 546-570 (1989)
2. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. &
Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev.
Lett. 81, 3108-3111 (1998)
3. Stringari, S. Bose-Einstein condensation and superfluidity in
trapped atomic gases. C.R. Acad. Sci. 4, 381-397 (2001)
4. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press,
Cambridge, 2001)
5. Sheshadri, K., Krishnamurthy, H. R., Pandit, R. &
Ramakrishnan, T. V. Superfluid and insulating phases in an
interacting-boson model: Mean-field theory and the RPA. Europhys.
Lett. 22, 257-263 (1993)
Nature 2002 415:39
Related Background:
ON ULTRACOLD MOLECULES
At room temperature, a gas of atoms moves with speeds estimated
at 0.6 x 10^(3) meters per second, and slowing an atom down is
equivalent to cooling it. One way to cool atoms is to force a
head-on collision with a laser beam: if the photons of the beam
have the appropriate energy to be absorbed, then conservation of
momentum implies that the atom slows. In 1985, Stephen Chu
devised a successful method based on this idea, the method
involving 3 pairs of lasers aligned along the three optical axes,
with each pair of lasers antiparallel, the consequence a cooling
of essentially trapped atoms. The resulting electromagnetic field
in which the atoms move has been described as "optical molasses".
Atoms that are trapped at low temperatures can be used for a
variety of purposes. For example, trapped atoms can be allowed to
fall freely, and their excitations can be measured as they are
subsequently hit with a series of short laser pulses of different
frequencies. These excitations vary with the motion of the atoms,
due to a Doppler shift determined by their speed. The result is
that the weakening of gravity due to a rise of as little as 3
centimeters has been measured.
At present, a number of laboratories have focused on the cooling
and trapping of molecules, a more formidable challenge.
Barbara Goss Levi (American Institute of Physics, US) presents a
review of current research on ultracold molecules, the author
making the following points:
1) During the past few decades, the cooling of atoms to lower and
lower temperatures has produced exciting and sometimes unforeseen
results in atomic interferometry, precision spectroscopy, Bose-
Einstein condensates, and atomic lasers. Experimenters are now
exploring the domain of ultracold molecules, and a number of
groups are pointed toward the goal of bringing molecules to
submillikelvin temperatures, at which temperatures molecules are
slow enough to be trapped or otherwise manipulated.
2) The latest achievement in this endeavor was recently announced
by H.L. Bethlem et al (Nature 406:491 2000), who have
demonstrated a promising new method for obtaining ultracold
molecules, the method involving cooling and trapping molecules in
a single quantum level with a density of 10^(6) per cubic
centimeter, and at temperatures estimated to be well below 350
millikelvin.
3) The author points out that with trapped molecules, one would
ideally like to achieve three things: a) reduce translational
temperatures to submillikelvin levels; b) cool a large number of
molecules; and c) put the molecules in a single, and preferably
the lowest, rotational-vibrational state. In addition, it would
be important to find a method for achieving these constraints for
any type of molecule. Impressive progress toward some of these
goals has been made during the past few years using several
different methods, with each method possessing its particular
strengths and weaknesses.
4) In general, the research agenda for ultracold molecules is
probably not too different from the agenda for their atomic
counterparts, with the following possibilities: a) precision
spectroscopy, because the spectral lines will be much narrower in
the absence of motional effects; b) the study of the collisions
of ultracold molecules, which should involve a reduced number of
angular momentum states; c) the availability of ultracold
molecules might also facilitate searches for electric dipole
moments of elementary particles; d) the manipulation of molecules
by various types of electromagnetic fields; e) the formation of a
Bose-Einstein condensate of molecules. But perhaps the most
compelling interest is the lure of the unknown.
Physics Today September 2000
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