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arXiv:0901.4896 · Physical Review A

Quantum phase diagram of fermion mixtures with population imbalance in one-dimensional optical lattices

B. Wang, Han-Dong Chen, S. Das Sarma

Published May 14, 2009• 47 citations
arXivHTMLPDF

Abstract

With a recently developed time-evolving block decimation algorithm, we numerically study the ground-state quantum phase diagram of Fermi mixtures with attractive interspecies interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.

DOI
10.1103/physreva.79.051604

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•Feb 27, 2008•0 citations
With a recently developed time-evolving block decimation algorithm, we numerically study the ground-state quantum phase diagram of Fermi mixtures with attractive interspecies interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices.
The ground state phase diagram of the two-dimensional attractive Hubbard model with population imbalance is explored using a mean field ansatz. A linear programming algorithm is used to identify the blocked states, such that the population imbalance can be imposed exactly. This allows to explore regions of the number-projected phase diagram that can not be obtained with the conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase of pairs with non-zero momentum is found to be the ground state over a wide range of parameters, while phase separation occurs only in a limited region at small population imbalance. Through a particle-hole transformation these results can be related to the underdoped repulsive Hubbard model, where the FFLO phase takes the form of a particle-hole condensate that exhibits a spontaneous restoration of spin symmetry.
In this paper, we study the role of both "spin"(species) and mass imbalance in a mixture of two species of fermionic atoms with attractive interaction in an one-dimensional optical lattice. Using the bosonization approach, quantum phase transitions between a liquid phase and phase separated states are studied under various conditions of interaction, spin imbalance, and mass imbalance. We find that, in the phase-separated region, there exists two kinds of phase separation and a special quantum phase transition might exist between them in the large UUU limit. On the other hand, the singlet superconducting correlation dominates in the liquid phase. The pairing behavior has been also demonstrated that there is oscillating behavior in real space. We find both the spin and mass imbalance are in favor of the formation of Fulde-Ferrell-Larkin-Ovchinnikov state.
We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.
We consider a two-component gas of fermions in optical lattices in the presence of a population imbalance within a mean-field theory. We study phase transitions from a normal gas of unpaired fermions to a superfluid phase of Bose-condensed Cooper pairs. The possibility of Cooper pairs with a nonzero centre-of-mass momentum is included, which corresponds to a so-called Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) state. We find that for population-imbalanced systems such states can form the ground state. The FF and LO state are compared and it is shown that actually the LO state is energetically more favourable. We complete the mean-field phase diagram for the LO phase and show that it is qualitatively in excellent agreement with recent diagrammatic Monte Carlo calculations. Subsequently, we calculate the atomic density modulations in the LO phase.
The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced two-component fermion mixtures in harmonically trapped optical lattices. In the low density limit, the superfluid order parameter has Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type oscillations in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit, while the order parameter has oscillations in the radial direction towards the trap center for low imbalances, it also has oscillations towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalances, but leads to double peaks for intermediate imbalances.