Condensed-matter physics

Superfluidity in the picture

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Strongly interacting atomic Fermi gases — useful models for many other exotic forms of matter — enter a superfluid state at low temperatures. The first direct observation of that transition has been made.

Fermions are the building-blocks of the Universe. Strongly interacting gases of these particles make up atomic nuclei, the matter in neutron stars and the quark–gluon plasma of the Big Bang. These systems differ greatly in size and energy but have a lot in common; knowledge of one system therefore illuminates our understanding of the others.

On page 54 of this issue, Zwierlein et al.1 present direct observations of a superfluid phase in one such system — a gas of strongly interacting Fermi atoms — and also determine the temperature of the gas directly. Such atomic gases have been the subject of intensive study2,3,4,5, as they are particularly easy to create and control in a laboratory environment. Although it is accepted that these atoms have been cooled down to an intriguing type of superfluid state, a direct observation of this transition, similar to the formation of ice from freezing water, has been elusive.

The classification of fundamental particles into fermions and bosons depends on their internal rotation, or spin. Spin is a quantized property; that is, it can only take on certain discrete values. If a particle's spin is a half-integer multiple of Planck's constant h divided by 2π, it is a fermion. The familiar atomic building-blocks — the electron, neutron and proton — are all fermions. Spin can point ‘up’ or ‘down’, and fermions obey the Pauli exclusion principle, which permits at most one spin-up and one spin-down particle in each quantum energy level. This explains the way in which electrons are observed to fill up the energy levels in atoms, two by two.

Bosons, on the other hand — particles of whole-integer spin — experience no such restriction. Composite particles (atoms, for example) that are built out of an even number of fermions are bosons, while those containing an odd number of fermions are fermions. So whereas a gas of atomic fermions stacks up in the energy levels in a ladder-like fashion, with at most one spin-up and one spin-down atom on each rung, all the atoms in an ultracold gas of bosons can condense into the lowest quantum energy state: the superfluid state of matter known as a Bose–Einstein condensate. For fermions, this is generally not possible, but this situation changes dramatically when spin-up and spin-down particles attract each other. Then, at sufficiently low temperature, fermions of opposite spin can pair to form composite bosonic objects, and a superfluid that flows without friction is also produced in this case.

In metals, the pairing of spin-up and spin-down electrons produces a superconducting superfluid, in which electric current can flow without resistance. If the strength of the pairing between the electrons is weak, and the pairing energy is a small fraction of the electrons' total energy, this superconducting transition occurs at very low temperatures (below the boiling point of helium at 4.22 K), and thus is useful only in a laboratory environment. A strong pairing, by contrast, can produce a transition at high temperature. Super-high-temperature superconductors that would operate at temperatures well above room temperature would enable lossless power transmission, magnetic levitation and more efficient communication. The interest in developing such materials is understandably great.

Remarkably, certain atomic Fermi gases at temperatures of a fraction of a millionth of a degree above absolute zero provide a model system for testing the theory of such high-temperature superconductors, because the pairing energy of their atoms is a large fraction of the fluid's total energy — in fact larger than that in any existing superconductor. Such gases have a feature known as a Feshbach resonance, near which the strength of the interactions between spin-up and spin-down atoms can be tuned over a wide range simply by applying a magnetic field. At resonance, the attractive inter-action between atoms is so strong that the gas flows like a high-temperature superfluid, modelling the movement of electrons in a superconductor that would work even at temperatures of thousands of degrees. Many experiments, including measurements of pair condensation6,7, collective oscillation modes8,9, pairing energy10, heat capacity11 and, most recently, vortices that signal superfluid flow12 have established that the transition to a superfluid phase occurs. But until now, the direct signature of the transition that would be given by a change in shape of the atomic cloud had not been observed.

Zwierlein and colleagues' proof1 of that change comes from a mixture of fermionic lithium-6 atoms in which the number of spin-up and spin-down atoms is unequal13,14 At temperatures above a critical value, the trapped mixture remains homogeneous, with a uniform distribution of both spin-up and spin-down particles across the trapped mixture (Fig. 1a). As the temperature is lowered, however, the gas cloud suddenly makes a transition to an energetically more favourable shape. A higher-density central ‘bump’ forms that contains nominally equal numbers of paired spin-up and spin-down atoms, while the excess of the majority spin component moves to the outside (Fig. 1b).

Figure 1: Changing shape.

a, A homogeneous state of an unequal number of spin-up and spin-down atoms, such as that prepared by Zwierlein et al.1. b, As the gas temperature is lowered past a critical value, a phase transition occurs. A superfluid state forms in the centre of the gas with spin-up and spin-down atoms paired and equal in number, and the excess unpaired atoms move to outside the central core.

This abrupt change is interpreted as a phase transition, analogous to the formation of ice in water when cooled to below its freezing point. When the gas is rotated, vortices form in the central region. Such vortices require perfect hydrodynamic flow, so their appearance is a sure sign that this region is a superfluid.

The majority spin component in the outside region brings an added benefit: it functions as a thermometer for the gas. When the trap initially confining the atoms is turned off, this pure component expands ballistically. That enables precise measurement of the velocity distribution of the atoms, which in turn is a measure of the temperature of the gas. As most thermodynamic quantities depend on temperature, this provides a valuable experimental check on theoretical models.

With precise control of spin populations and precision thermometry, the experiments open up new territory for modelling some of the most fundamental processes in the Universe, including superfluidity in neutron stars, hydrodynamics in a quark–gluon plasma and string-theory predictions of minimum viscosity in any generalized system.


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Thomas, J. Superfluidity in the picture. Nature 442, 32–33 (2006) doi:10.1038/442032a

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