ScienceWeek

EXPERIMENTAL PHYSICS: ON THE FERMION SUPERFLUID

The following points are made by Tin-Lun Ho (Science 2004 305:1114):

1) All particles are either bosons or fermions. Bosons behave like each other, whereas fermions refuse to act the same. In their lowest energy state, bosons form a Bose-Einstein condensate (BEC) in which all particles behave identically. As a result, quantum phenomena are magnified, becoming observable even at macroscopic length scales. Fermions cannot perform this feat. However, a bound pair of fermions behaves like a boson. A collection of bound fermion pairs should therefore be able to Bose-condense as bosons do. Recent evidence makes a strong case for the realization of such a fermion superfluid in cold atoms.

2) Since the dramatic discovery of Bose-Einstein condensation in 1995, many groups have tried to create fermion superfluids. Recent experimental advances indicated that the realization of a fermion superfluid was imminent (1-3). In January 2004, Greiner et al reported evidence for pair condensation in a Fermi gas of 40K (4). Reports by other groups on similar (5) and related properties in a different Fermi gas (Li-6) soon followed. However, theories for pair condensates are considerably more complex than those for Bose-Einstein condensates. Confirmation of fermion superfluid is therefore less straightforward. Chin et al. (Science 2004 305:1128)) presented direct evidence of a pairing gap in the Fermi gas of Li-6, which is a key property of a pair condensate. Kinnunen et al (Science 2004 305:1131) provided a theoretical explanation for this observation. These results, together with the evidence in (1-5), make the case for a fermion superfluid difficult to challenge.

3) As pointed out by Bardeen, Cooper, and Schrieffer (BCS), the condensation of electron pairs is the origin of superconductivity in solids. The electron pairs (called "Cooper pairs") are very big, with diameters about 100 times the mean distance between electrons. They therefore overlap strongly with each other. The condensates in Fermi gases are generated with "Feshbach resonance", which allows the size of the pairs to be varied from much larger than the mean distance between atoms to about the size of an atom. As a result, a change from a superfluid with large pairs to a BEC of molecules can occur on a continuum.

4) Feshbach resonance works as follows. When two fermion atoms interact in a vacuum, they can jump between a "closed channel" and an "open channel". In the closed channel, they form a small (atomic-scale) molecule, whereas they are unbound in the open channel. The energy difference between the two states can be tuned with a magnetic field. Feshbach resonance occurs when the energy difference is tuned to zero, at which point a bound pair is about to emerge. When the closed channel lies below the open channel, the fermions form a bound pair that includes both closed- and open-channel contributions. As the resonance is approached from below, the closed channel component is reduced. The pair grows in size toward infinity. Above resonance, the fermion pair remains unbound.

References (abridged):

1. S. Jochim et al., Science 302, 2101 (2003)

2. M. Greiner et al., Nature 426, 537 (2003)

3. M. W. Zwierlein et al., Phys. Rev. Lett. 91, 250401 (2003)

4. C. A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004)

5. M. W. Zwierlein et al., Phys. Rev. Lett. 92, 120403 (2004)

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ULTRACOLD MATTER: SUPERFLUIDITY IN FERMI GASES

The following points are made by L. Pitaevskii and S. Stringari (Science 2002 298:2144):

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)

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COLLAPSE OF A DEGENERATE FERMI GAS

The following points are made by G. Modugno et al (Science 2002 297:2240):

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)

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