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arXiv:cond-mat/0607664 · Physical Review A

Superfluid shells for trapped fermions with mass and population imbalance

Guin-Dar Lin, Wei Yi, L.-M. Duan

Published Sep 29, 2006• 45 citations
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Abstract

We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two components. As a unique feature distinctively different from the equal-mass case, we show that the superfluid here forms a shell structure which is not simply connected in space. Different types of normal states occupy the trap regions inside and outside this superfluid shell. We calculate the atomic density profiles, which provide an experimental signature for the superfluid shell structure.

DOI
10.1103/physreva.74.031604

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We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two components. As a unique feature distinctively different from the equal-mass case, we show that the superfluid here forms a shell structure which is not simply connected in space. Different types of normal states occupy the trap regions inside and outside this superfluid shell. We calculate the atomic density profiles, which provide an experimental signature for the superfluid shell structure.
We study equal mass population imbalanced two-component atomic Fermi gas with unequal trap frequencies $({\ensuremath{\omega}}_{\ensuremath{\uparrow}}\ensuremath{\ne}{\ensuremath{\omega}}_{\ensuremath{\downarrow}})$ at zero temperature using the local density approximation (LDA). We consider the strongly attracting Bose-Einstein condensation (BEC) limit where polarized (gapless) superfluid is stable. The system exhibits shell structure: unpolarized superfluid$\ensuremath{\rightarrow}$polarized superfluid$\ensuremath{\rightarrow}$normal state. Compared to the trap symmetric case, when the majority component is tightly confined the gapless superfluid shell grows in size leading to reduced threshold polarization to form a polarized (gapless) superfluid core. In contrast, when the minority component is tightly confined, we find that the superfluid phase is dominated by the unpolarized superfluid phase with the gapless phase forming a narrow shell. The shell radii for various phases as a function of polarization at different values of trap asymmetry are presented and the features are explained using the phase diagram.
We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.
We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.
We study the properties of a trapped interacting three component Fermi gas. We assume that one of the components can have a different mass from the other two. We calculate the different phases of the three component mixture and find a rich variety of different phases corresponding to different pairing channels, and simple ways of tuning the system from one phase to another. In particular, we predict coexistence of several different superfluids in the trap, forming a shell structure, and phase transitions from this mixture of superfluids to a single superfluid when the system parameters or temperature is varied. Such shell structures realize superfluids with a nontrivial spatial topology and leave clear observable signatures in the density profile of the gas.
It is shown by microscopic calculations for trapped imbalanced Fermi superfluids that the gap function always has sign changes, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state, up to a critical imbalance P(c), beyond which normal state becomes stable, at temperature T=0. A temperature-versus-pressure phase diagram is constructed, where the BCS state without sign change is stable only at T not equal to 0. We reproduce the observed bimodality in the density profile to identify its origin and evaluate P(c) as functions of T and the coupling strength. These dependencies match with the recent experiments.
The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS--Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of 6{}^{6}6Li and 40{}^{40}40K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the 6{}^{6}6Li-40{}^{40}40K and other possible Fermi-Fermi mixtures.