Producing FFLO states

Nature, 467: 535–536:

Atomic gases cooled down to nanokelvin temperatures and confined in optical or magnetic traps have helped to realize and investigate fundamental many-body quantum phases of matter^{1, 2}. An investigation by Liao et al.³ on page 567 of this issue now shows how such ultracold systems are also moving to centre stage in the quest for an exotic form of superconductivity — the elusive FFLO superconducting state of matter that was proposed more than 40 years ago by Fulde and Ferrell⁴ and Larkin and Ovchinnikov⁵.

In condensed-matter physics, an arbitrarily small attraction between fermions (particles with half-integer spin, such as electrons) of identical but opposing spin and momentum can lead to the formation of bound pairs that have bosonic character (bosons being particles with whole-integer spin). Under specific conditions, such pairs can undergo the phenomenon of Bose–Einstein condensation (BEC), transforming the many-body system into a 'giant matter wave' with spectacular frictionless-flow properties — a superconductor or superfluid is born. This remarkable outcome of pairing, first proposed by Bardeen, Cooper and Schrieffer (BCS), is considered to be the conventional way in which superconductivity emerges in a wide range of materials. In the world of atomic physics, the same pairing mechanism has been studied thoroughly in three dimensions with equal two-component gas mixtures of fermionic neutral atoms^{1, 2}, each component comprising atoms with one of two spin states (up or down). But what happens to such a BCS superfluid state if the two fermionic spin states are not present in equal numbers in the system?

In a solid-state material, such a spin-imbalance condition can be created by applying a magnetic field to the system. In ultracold atomic gases, a simple initial difference in the number of spin-up and spin-down atoms will do the job. Intuitively, one might think that an increasing mismatch in the number of spin-up and spin-down particles would make it harder for the opposing spins to meet each other and pair up, thus hindering superconductivity. And this is indeed what happens in experiments. Put in more technical terms, the Fermi surfaces of the two system components will have different sizes, and this difference will hamper the formation of the pairs and the ensuing BCS superfluid state (the Fermi surface is the boundary in momentum space that separates unoccupied states from occupied ones).

Fulde and Ferrell⁴, as well as Larkin and Ovchinnikov⁵, proposed a clever solution that would still allow a superfluid state to exist under spin-imbalanced conditions. They suggested a paired state in which the pairs are not at rest but instead have a net momentum. This FFLO state can be viewed as a kind of microscale phase separation, containing alternating superfluid regions and normal, non-superfluid regions, in which the extra atoms of the spin species that are in excess squeeze in. Although searches for such an exotically paired FFLO state have been carried out exhaustively in condensed-matter systems, and more recently in ultracold atomic gases, unambiguous experimental evidence has remained elusive. In their study, Liao et al.³ take a major step towards creating an FFLO state using ultracold fermionic atoms.