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arXiv:1412.6685 · Physical Review Letters

Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases

Willie Ong, Chingyun Cheng, Ilya Arakelyan, John E. Thomas

Published Mar 19, 2015• 83 citations
arXivHTMLPDF

Abstract

We measure the density profiles for a Fermi gas of (6)Li containing N(1) spin-up atoms and N(2) spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N(2)/N(1) and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N(2)/N(1). Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.

DOI
10.1103/physrevlett.114.110403

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We measure the density profiles for a Fermi gas of (6)Li containing N(1) spin-up atoms and N(2) spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N(2)/N(1) and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N(2)/N(1). Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.
We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of 6Li^{6}\mathrm{Li}6Li 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.
Motivated by a recent experiment Revelle et al., [Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of 6Li^{6}\mathrm{Li}6Li atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system by using Hartree-Fock Bogoliubov-de Gennes mean-field theory and compare the results with experimental data. Mean-field theory predicts fully-spin-polarized normal, partially-spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the local density approximation to obtain density profiles of the gas in a harmonic trap. We compare these calculations with experimental measurements in Revelle et al. as well as previously unpublished data. Our calculations qualitatively agree with experimentally measured densities and coordinates of the phase boundaries in the trap and quantitatively agree with experimental measurements at moderate-to-large polarizations. Our calculations also reproduce the experimentally observed universal scaling of the phase boundaries for different scattering lengths at a fixed value of scaled intertube tunneling. However, our calculations have quantitative differences with experimental measurements at low polarization and fail to capture important features of the one- to three-dimensional crossover observed in experiments. These suggest the important role of physics beyond mean-field theory in the experiments. We expect that our numerical results will aid future experiments in narrowing the search for the Fulde-Ferrell-Larkin-Ovchinnikov phase.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.
This thesis presents the experimental study on the two-spin component, strongly interacting 6 Li Fermi gases in 3D and 1D traps. The interaction strength is tuned from the molecular BEC regime to the BCS regime using a Feshbach resonance. The trap dimension can be tuned from 3D to 1D with the implementation of optical lattice. The evaporation of imbalanced Fermi gases in 3D trap is studied. The anisotropic and fast evaporation is the cause of the deformation observed in the 2006 Rice experiment. In a balanced Fermi system, the fraction of correlated states is measured as a function of interaction and temperature. At unitarity, the fraction of correlated states is ∼85% and exists above T c . The one-body-like photoexcitation rate can be related to the contact quantity. Lastly, the spin-imbalance in a one-dimensional Fermi gas is studied. The 1D phase diagram is mapped out. The result agrees well with the 1D theory, in which the partially polarized regime is predicted to be a FFLO phase, an exotic superfluid with pairs carrying finite center-of-mass momentum proposed almost 50 years ago.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean-field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local-density approximation exhibits a shell structure, a superfluid core at the center, and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is in a fully polarized state with a density profile depending only on the global population imbalance. The difermion bound states can survive in the whole highly imbalanced normal phase.
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, qqq, distribution of pairs, called nB(q){n}_{B}(\mathbf{q})nB​(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 nB(q){n}_{B}(\mathbf{q})nB​(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.