Superfluidity of atomic gases

Central to the understanding of the physics of ultracold gases are the concepts of Bose-Einstein condensation and superfluidity. The former refers to the accumulation of a large fraction of atoms in a single quantum mechanical state, as predicted by Einstein in 1925 and finally directly observed in an atomic gas in 1995. The latter refers to the fascinating ability of the gas to flow without any friction. The two concepts have been conceptually linked ever since the discovery of superfluidity in liquid helium in 1937, but they are nevertheless clearly distinct and their exact quantitative connection is often elusive.


Figure 1 - Superfluidity and condensation. In 1938 Fritz London suggested that helium superfluidity is intimately related to the boson condensation theoretically proposed by Einstein 13 years earlier. Ultracold atomic gases, first condensed in 1995, now offer a versatile playground for testing both phenomena.


In many of the most interesting physical situations the superfluid and the condensate fraction of the gas can be very different. For example, strong interactions between particles can lead to depletion of the condensate without reducing the superfluid density. This is what happens in liquid 4He, where in the low-temperature limit the condensate and the superfluid fraction are believed to be ~10% and 100%, respectively. In the opposite limit, a gas of non-interacting bosons at low temperatures forms a BEC, but is not superfluid. Interacting gases or fluids confined to two-dimensions (2D) can become superfluid without appearance of any condensate fraction. (This unusual phase transition in 2D systems is another topic we are particularly interested in – see here.)


The fundamental physics is often universal, but the experimental methods in different fields of physics are often very different and complementary. In liquid helium the superfluid density is routinely measured, but the condensate density is difficult to extract (in addition to being very different from the superfluid density). On the other hand, ultracold atomic gases are celebrated for the direct observation of Bose- Einstein condensation, and we also know that they show superfluid phenomena, but a general method for measuring their superfluid fraction is still lacking.


Figure 2 - Superfluidity of an atomic gas. If an atomic BEC is mechanically set into rotation, it can take up angular momentum only in the form of quantized vortices, which form an “Abrikosov lattice” analogous to the lattice of magnetic flux lines in a type-II superconductor. This proves that the gas is superfluid, but it doesn’t tell us exactly how much of it is superfluid.


We recently proposed a method for a direct measurement of the superfluid fraction of an atomic gas (see fig. 3) [1], and in the future we plan to implement it experimentally. Our work will open the possibility for the superfluid and condensate densities to be measured and directly compared in a variety of physical situations in the same experimental system.


Figure 3 - Measuring the superfluid fraction of an atomic gas. In our proposal [1], the gas is confined in a ring trap and depending on the transverse confinement it can be 1D, 2D, or 3D. Laser beams which carry angular momentum and couple different internal (hyperfine) atomic states can be used to create an effective vector potential which induces slow rotation of the gas. By the very definition of superfluidity, only the normal (non-superfluid) component of the gas will actually change its angular momentum when a weak vector potential is applied. Since different angular momentum states in this case also have different hyperfine compositions, the superfluid fraction can be measured spectroscopically, which plays to a traditional strength of atomic physics.


[1] N. R. Cooper and Z. Hadzibabic, Measuring the Superfluid Fraction of an Ultracold Atomic Gas, Phys. Rev. Lett. 104, 030401 (2010). (pdf), see also the accompanying Viewpoint by Iacopo Carusotto in Physics.