Superfluidity in two-dimensional imbalanced Fermi gases

Abstract

We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy ǫB, whose variation allows to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance hc after which there is a first-order phase transition to the normal state. We find that hc, the Chandrasekhar-Clogston limit of superfluidity, has the same value as in three dimensional systems. We show that for a fixed ratio ǫB/ǫF , where ǫF is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance mc phase separation is not supported and the normal phase is energetically preferable. The BCS-BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.

Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional imbalanced Fermi gases

“…Additionally, the phase diagrams shown in Figs. 1 and 2 are consistent with earlier work [30,31,34,35,40]. Here, we show that the FFLO phase boundary, and the universal FFLO wavevector, follow from a nonanalytic structure of the integral governing the FFLO gap equation.…”

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

“…The regime of stability of the FFLO state, as a function of parameters such as interaction strength and population imbalance, is theoretically predicted to be strongly dependent on dimensionality, with the regime of stability smallest in three dimensions [9,10], becoming larger for two spatial dimensions [11][12][13][14][15][16][17][18][19][20][21] and largest in one dimension [22,23]. Although many experiments on imbalanced Fermi gases have investigated the threedimensional regime [24][25][26][27][28][29] (finding no evidence of the FFLO state), recent experiments have explored Fermi gases in one [6,30] or two spatial dimensions [31][32][33][34][35][36][37][38] using an appropriate trapping potential.…”

Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases

“…4. The red solid curve shows the 2D polaron model prediction, for the same trap frequency ω ⊥ as used to de- 2D-BCS theory prediction [14,28], where ǫ F = µ + E b /2, the Gibbs-Duhem relation requiresp = 1 for all E F /E b , in contrast to the measurements [29]. We have also measured the central density ratio n 2 /n 1 of the 2D gas as a function of N 2 /N 1 .…”