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arXiv:1605.01479 · Physical Review A

Two-dimensional spin-imbalanced Fermi gases at nonzero temperature: Phase separation of a noncondensate

Chien‐Te Wu, Rufus Boyack, Kathryn Levin

Published Sep 6, 2016• 3 citations

Abstract

We study a trapped two-dimensional (2D) spin-imbalanced Fermi gas over a range of temperatures. In the moderate-temperature regime, associated with current experiments, we find reasonable semiquantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin-balanced core can be associated with noncondensed fermion pairs. To shed light on the nature of 2D quasicondensation we compute the momentum, $q$, distribution of pairs, called ${n}_{B}(\mathbf{q})$; a pronounced low momentum peak is found, but importantly there is no macroscopic condensate. Following the protocols of Jochim and collaborators, we compute the characteristic temperature at which this peak disappears, thus providing a phase diagram for a quasicondensation onset temperature in the polarized case. Additional information about ${n}_{B}(\mathbf{q})$ is reflected in the behavior of the density profiles when the trap is removed. We show how quasicondensed bosons have a distinctive signature; they evolve relatively slowly under time of flight.

DOI: 10.1103/physreva.94.033604

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We study a trapped two-dimensional (2D) spin-imbalanced Fermi gas over a range of temperatures. In the moderate-temperature regime, associated with current experiments, we find reasonable semiquantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin-balanced core can be associated with noncondensed fermion pairs. To shed light on the nature of 2D quasicondensation we compute the momentum,

q

, distribution of pairs, called

{n}_{B}(\mathbf{q})

; a pronounced low momentum peak is found, but importantly there is no macroscopic condensate. Following the protocols of Jochim and collaborators, we compute the characteristic temperature at which this peak disappears, thus providing a phase diagram for a quasicondensation onset temperature in the polarized case. Additional information about

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is reflected in the behavior of the density profiles when the trap is removed. We show how quasicondensed bosons have a distinctive signature; they evolve relatively slowly under time of flight.

We study a two-component quasi-two-dimensional Fermi gas with imbalanced spin populations. We probe the gas at different interaction strengths and polarizations by measuring the density of each spin component in the trap and the pair momentum distribution after time of flight. For a wide range of experimental parameters, we observe in-trap phase separation characterized by the appearance of a spin-balanced core surrounded by a polarized gas. Our momentum space measurements indicate pair condensation in the imbalanced gas even for large polarizations where phase separation vanishes, pointing to the presence of a polarized pair condensate. Our observation of zero momentum pair condensates in 2D spin-imbalanced gases opens the way to explorations of more exotic superfluid phases that occupy a large part of the phase diagram in lower dimensions.

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. A key signature of quasi-condensation, which contains aspects of Berezinskiĭ-Kosterlitz-Thouless behavior, is a strong zero momentum peak in the pair momentum distribution. Importantly, this peak emerges at a reasonably well defined onset temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS.

We study the finite temperature

T

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We present phase diagrams for population-imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature, and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.

We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of

^{6}\mathrm{Li}

atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the Bardeen-Cooper-Schrieffer and unitary regimes. We disagree with the QMC results in the Bose-Einstein condensate regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states.

The density distributions of the two components of a trapped, ultracold Fermi gas with population imbalance reveal the effect of imbalance on superfluid pairing. We develop a path-integral derivation of the density, that takes into account both fluctuations beyond mean-field and effects of nonzero temperature. The calculated density profiles compare favorably to the measured density profiles, and illustrate the necessity to incorporate both quantum fluctuations and finite temperature effects. The temperature dependence of the density profiles, especially near the superfluid-normal interface, allows for determining the temperature of the superfluid core in current experiments.