Superfluids mixing it up

Imagine two fierce competitors tossed into a trap, locked in a struggle with each other for supremacy. The quantum-mechanical match is hardly fair: the first competitor, 50,000 hefty ⁸⁷Rb atoms in a Bose-Einstein condensate (BEC), outweighs the second almost fourfold. The svelte opponent of the rubidium BEC is an equal number of lighter, smaller ²³Na atoms that are also Bose-Einstein condensed. The entire cloud hovers magnetically, a whisper above absolute zero on the temperature scale. New theoretical work by Pu and Bigelow¹ predicts striking properties for such a two-component BEC formed from sodium and rubidium atoms.

In theory^1,2,3,4, a regime might exist in which superfluid condensates interpenetrate like miscible fluids. Depending on the strength of interactions between two unlike atoms, however, a very different phase-separated regime could arise in which the sodium atoms form a shell that encloses the rubidium. In the latter case, a higher-energy metastable state has now been predicted¹, in which the rubidium atoms form a shell around the periphery of an inner sodium cloud. Pu and Bigelow also point out an intriguing experimental possibility: the inner cloud can be intentionally squeezed into a smaller volume, simply by adding more atoms to the outer shell (Fig. 1).

Figure 1: Composite condensates: the distribution of a spherical two-component Bose-Einstein condensate made of ⁸⁷Rb atoms (red) and ²³Na atoms (white), at absolute zero.

Half of the condensate has been cut away to expose the centre. a, Miscible superfluid of 50,000 rubidium and 50,000 sodium atoms, with a rubidium-sodium scattering length A₁₂ = 1.8 nm. b, Immiscible superfluid, with rubidium atoms inside a shell of sodium atoms; A₁₂ = 9.6 nm. c, As b, but the higher-energy metastable state is shown, with the sodium on the inside. d, As b, but now 200,000 sodium atoms compress 50,000 of rubidium into a far smaller volume. These pictures are from our simulations, with parameters the same as those used by Pu and Bigelow¹.

The fun with two-component Bose-Einstein condensates began in 1997, when Myatt et al.⁵ observed a double condensate composed of two clouds of ⁸⁷Rb atoms in different internal spin states. The experiment astonished the BEC community, because it violated an expectation gleaned from a quarter of a century of research into spin-exchange processes: atoms colliding in these states should scatter into different spin states, in which they would be ejected from the trap by magnetic forces. But fortunately, the dastardly spin-exchange process happens to be suppressed in ⁸⁷Rb by nearly two orders of magnitude.

Only this accident permits the Myatt et al. double condensate to form and to persist^6,7,8. So as long as multiple-component condensates are trapped magnetically, they will have to be ⁸⁷Rb — unless another ‘accident’ occurs for a different alkali atom. But Ketterle and colleagues have demonstrated BEC in an optical trap⁹, in which focused light captures the electric dipole moment of each atom rather than its magnetic moment. A trap of this type will hold an atom even after a spin-changing collision; potentially, a richer variety of multiple-component condensates can therefore be studied.

At these ultra-low temperatures, the scattering length A controls the strength of interactions between any two particles. (The Newtonian-minded reader can view A very roughly as the sum of the radii of two colliding billiard ball atoms.) In any bargain-basement condensate with a single component, every atom is identical and there is only one scattering length. For a double condensate, however, three scattering lengths are needed: A₁₁(Rb-Rb, for the system studied by Pu and Bigelow), A₂₂(Na-Na) and A₁₂(Rb-Na). The first two are accurately known, but unfortunately A₁₂(Rb-Na) has never been measured. All we know is that it lies somewhere between plus and minus infinity. (Less uncertainty exists about the properties predicted¹⁰ for a double condensate composed of the two isotopes ⁸⁵Rb and ⁸⁷Rb.)

To cope with this vast uncertainty, Pu and Bigelow solved the problem for many different values of A₁₂. Three phases could occur^1,2,3,4: (i) a miscible, fully interpenetrating phase, if A₁₂(Rb-Na) is between −3.4 nm and +3.4 nm; (ii) an immiscible, phase-separated double condensate if A₁₂ > 3.4 nm; (iii) no condensate at all, if A₁₂ < −3.4 nm. in the last case the interaction is too attractive and the double condensate undergoes a runaway collapse, as it tries to form clusters of sodium and rubidium, or ‘metallic snowflakes’.

Researchers have longed for years to study interpenetrating superfluids, but the only superfluids available — ³He and ⁴He — steadfastly refuse to mix when cooled together. Should the sodium-rubidium interaction A₁₂turn out to be in the right range, this will be the first example of miscible superfluids. Yet interesting science beckons even if A₁₂ > 3.4 nm, because two curious effects can still be explored in this phase.

The first follows from the tendency of the sodium atom cloud to form a shell around the outside of the rubidium atom condensate cloud. Pu and Bigelow¹ suggest that by increasing the sodium cloud size, a higher pressure could be brought to bear on the inner rubidium cloud, causing it to shrink, increasing inelastic collision rates enormously. The second effect possible in this phase follows from the smallness of the energy cost of swapping each sodium atom with a rubidium atom. The swap results in a metastable state with rubidium atoms packed around an inner sodium cloud; it has slightly higher energy than the ground state, and a long lifetime against decay into the true ground state.

This regime may have another peculiar property. The condensate is predicted to be unstable¹, an instability that has been shown to lead to a spontaneous symmetry breaking in other cases¹¹,¹². Our calculations confirm this: the immiscible phase should not possess the spherical symmetry of the trap, but should instead consist of two unmixed superfluids arranged more or less linearly along some axis in space¹².

But the notion that multiple-component BEC experiments are constrained by what nature has handed us, in the way of atom-atom scattering lengths, appears to be far too pessimistic. Just last month, for instance, Wolfgang Ketterle's group reported the ability to tune a sodium-sodium scattering length by varying the magnetic field across a Feshbach resonance¹³. We seem to be at the threshold of a new era of designer multi-condensates.