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arXiv:0812.2963 · Physical Review A

Paired states in spin-imbalanced atomic Fermi gases in one dimension

Paata Kakashvili, C. J. Bolech

Published Apr 15, 2009• 68 citations
arXivHTMLPDF

Abstract

A growing expertise to engineer, manipulate, and probe different cold-atom analogs of electronic condensed-matter systems allows to probe properties of exotic pairing. We study paired states of spin-imbalanced ultracold atomic system of fermions with attractive short-range interactions in one-dimensional traps. Calculations are done using the Bethe ansatz technique, and the trap is incorporated into the solution via a local-density approximation. The thermodynamic Bethe ansatz equations are solved numerically and different local-density profiles are calculated for zero and finite temperatures. A procedure to identify the homogeneous-system phase diagram using local-density profiles in the trap is also proposed. Such scheme would be immediately useful for the experiments.

DOI
10.1103/physreva.79.041603

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A growing expertise to engineer, manipulate, and probe different cold-atom analogs of electronic condensed-matter systems allows to probe properties of exotic pairing. We study paired states of spin-imbalanced ultracold atomic system of fermions with attractive short-range interactions in one-dimensional traps. Calculations are done using the Bethe ansatz technique, and the trap is incorporated into the solution via a local-density approximation. The thermodynamic Bethe ansatz equations are solved numerically and different local-density profiles are calculated for zero and finite temperatures. A procedure to identify the homogeneous-system phase diagram using local-density profiles in the trap is also proposed. Such scheme would be immediately useful for the experiments.
We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one-dimensional configurations. The ground state properties are determined with the local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the Fulde-Ferrell-Larkin-Ovchinnikov type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell are calculated as a function of the coupling strength.
Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.
Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.
Fermions in one dimension are vastly different from their higher-dimension counterparts. At the same time, many theoretical models in one dimension have the luxury of being integrable and exactly solvable, which makes them excellent test beds for quantum simulation. In using these test beds, we can understand and improve on the techniques of quantum simulation so that we move towards solving difficult problems that cannot be solved using other methods due to the sheer complexity of these systems. In this work, we prepare one-dimensional fermions using cold atom techniques and probe low-energy excitations in such systems. We do so using the technique of Bragg spectroscopy, which enables us to probe the dynamical structure factor of the system directly, which in turn tells us about the density-density and spin-density correlations in the system. Utilizing the extreme tunability of cold atom experiments, we can study different regimes of these 1D Fermi gases. In particular, moving on from our previous investigations in the repulsive interactions, we investigate the attractive interaction side, where the attraction of the fermions causes bound states to form. The binding energy of these bound states causes a gap in the spin excitation, a hallmark of a new class of model: Luther-Emery liquid. We investigate weakly attractive Fermi gases close to the Luther-Emery limit and observe an inversion of the spin-charge separation hierarchy compared to the repulsive side, confirming expectations from exact Bethe ansatz solutions for the homogeneous gas at zero temperature, in which weakly bound fermion pairs are predicted. The result presented here provides insight into physics in one dimension, an important realm that is well known to host many exciting physics and exotic phases.
We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field H<Hc1H<{H}_{c1}H<Hc1​. A completely ferromagnetic phase without pairing occurs when the external field H>Hc2H>{H}_{c2}H>Hc2​. In the region Hc1<H<Hc2{H}_{c1}<H<{H}_{c2}Hc1​<H<Hc2​, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.
It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.