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...
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