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

Abstract

We study the pair correlations of a spin-imbalanced two-leg ladder with attractive interactions, using the density matrix renormalization group method (DMRG). We identify regions in the phase diagram spanned by the chemical potential and the magnetic field that can harbor Fulde-FerrellLarkin-Ovchinnikov (FFLO)-like physics. Results for the pair structure factor, exhibiting multiple pairing wave-vectors, substantiate the presence of FFLO-like correlations. We further discuss phase separation scenarios induced by a harmonic trap, which differ from the case of isolated chains.The experimental realization of fermionic superfluids in ultracold atom gases under clean conditions and with a great control over interactions has paved the way toward a detailed understanding of the BEC-BCS crossover of spin-balanced, ultracold Fermi gases [1]. Now, the case of a polarized two-component Fermi gas, realized by unequally populating the two lowest hyperfine states, has moved into the focus of current experimental work [2].Intriguing properties such as phase separation in a trap and the transition from superfluidity to a normal state driven by the population imbalance have attracted a great deal of attention, but it is, in particular, the search for exotic superfluids such as the FFLO one [3,4] that drives the current interest in imbalanced Fermi gases. In an FFLO state, the order parameter is spatially inhomogeneous with Cooper pairs with a finite center-of-mass momentum. In recent experiments on three dimensional (3D) ultracold gases, this state remains elusive, and theoretical work indicates that in 3D, the phase space volume of this phase in the interaction-polarization plane is small [5]. Yet, reducing the spatial dimension renders this pairing mechanism more effective as a larger portion of the Fermi surfaces of minority and majority spins can be matched [6]. 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. [6,7,12,17]. Here we present a rigorous and quasi-exact numerical analysis of pairing correlations in two coupled chains, using DMRG [18].The physics of spin [19] and Hubbard ladders [20] has proven to be unique and interesting in itself, due to the emergence of exotic quantum phases -such as spin liquids -driven by strong correlations [19]. The experimentally realization of ladders in optical lattices as arrays of double wells could be an important step toward understanding the experimen...

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model with spin imbalance

“…The effect of integrability breaking can, in experiments, be studied either by using two-leg ladders [90], realized with superlattices [91], in fermionic superfluids with resonant interactions [92,93], or with mass-imbalanced systems, realizable with two-component gases of different fermionic species (see the discussion in [94][95][96][97][98]) or using spin-dependent optical lattices [99]. A recent study [100] discussed quasi-many-body localization in such a system.…”

Pairing in a two-dimensional Fermi gas with population imbalance

“…Another mean-field study of two-dimensional two-orbital Hubbard model with p orbitals and highly unidirectional hopping shows enhancement of the FFLO region in the phase diagram due to the one-dimensional character of the Fermi surface [29]. A DMRG study of population imbalanced Fermi gas on two-leg ladders has found FFLO pair correlations [30].…”

Oscillatory pairing amplitude and magnetic compressible-incompressible transitions in imbalanced fermionic superfluids in optical lattices of elongated tubes

“…However, in three dimensions (3D) the FFLO state has remained elusive, while in lower dimensions it can hardly be sustained due to the lack of superfluid long-range order. Recent attention has turned to an array of one-dimensional (1D) systems [8][9][10][11][12][13], which is expected to have both a wider parameter range for the FFLO (as compared with the 3D case) and stabilized long-range order through the coupling between these systems. In cold-atom experiments, such arrays have been realized as two-dimensional (2D) optical lattices of elongated tube confinements in a global trap [14,15] [as illustrated in Fig.…”