FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a non-uniform background potential

Abstract

We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1-3 dimensions, considering the possibilities of the FFLO, Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in presence of an additional (harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus on population imbalanced gases, the results are relevant also for the (effective) mass imbalanced case. We demonstrate by LDA calculations that various shell structures such as normal-FFLO-BCS-FFLO-normal, or FFLO-normal, are possible in presence of a background harmonic trap. The phases are reflected in noise correlations: especially in 1D the unpaired atoms leave a clear signature of the FFLO state as a zero-correlation area ("breach") within the Fermi sea. This strong signature occurs both for a 1D lattice as well as for a 1D continuum. We also discuss the effect of Hartree energies and the Gorkov correction on the phase diagrams.

Larkin-Ovchinnikov phases in two-dimensional square lattices

“…It can be seen that q is more or less proportional to h. see for instance Fig.3(a). We find this transition to be a continuous phase transition, in contrast to results obtained with the FF ansatz [36,37].…”

“…Theoretically, it has been predicted that optical lattices enhance the FFLO superfluid pairing, due to nesting of the Fermi surfaces [36,37]. The parameter regime where FFLO states are stable is therefore larger in optical lattices [36][37][38][39][40][41][42], making this promising systems to observe these exotic quantum states of matter.…”

Fulde-Ferrell-Larkin-Ovchinnikov state in the dimensional crossover between one- and three-dimensional lattices

“…This enhancement of the normal state can be understood in light of the fact that including the particle-hole channel was shown to reduce pairing significantly in lattices: 28 DMFT includes full local quantum fluctuations, causing such higher order effects. (2) In 1D lattices, mean-field theory 29 predicted only a 3D-like shell structure with a fully paired center and polarized edges. Polarized superfluid phase at finite temperature.…”

Pair Correlations of a Spin-Imbalanced Fermi Gas on Two-Leg Ladders

“…In particular, in one dimension (1D), where a true condensation is prohibited, the existence of an FFLO-type state with quasi-long range order has been proven by means of analytical [7,8] as well as numerically exact approaches [9][10][11][12]. This also pertains to the experimentally relevant case of a harmonic trap [10][11][12].It is then natural to ask whether such quasi-FFLO states seen in 1D are stable against coupling chains to 2D or 3D ensembles, in order to connect the aforementioned theoretical results for 1D to those available for 2D [6,[13][14][15][16]. For 1D chains weakly coupled to a 3D array, the polarization-interaction phase diagram has recently been derived in Refs.…”