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arXiv:2211.01055 · New Journal of Physics

Disordered structures in ultracold spin-imbalanced Fermi gas

Buğra Tüzemen, Tomasz Zawiślak, Gabriel Wlazłowski, Piotr Magierski

Published Mar 1, 2023• 11 citations
arXivHTMLPDF

Abstract

Abstract We investigate properties of spin-imbalanced ultracold Fermi gas in a large range of spin polarizations at low temperatures. We present results of microscopic calculations based on mean-field and density functional theory approaches, with no symmetry constraints. At low polarization values we predict the structure of the system as consisting of several spin-polarized droplets. As the polarization increases, the system self-organizes into a disordered structures similar to liquid crystals, and energetically they can compete with ordered structures such as grid-like domain walls. At higher polarizations the system starts to develop regularities that, in principle, can be called supersolid, where periodic density modulation and pairing correlations coexist. The robustness of the results has been checked with respect to temperature effects, dimensionality, and the presence of a trapping potential. Dynamical stability has also been investigated.

DOI
10.1088/1367-2630/acc26b

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Abstract We investigate properties of spin-imbalanced ultracold Fermi gas in a large range of spin polarizations at low temperatures. We present results of microscopic calculations based on mean-field and density functional theory approaches, with no symmetry constraints. At low polarization values we predict the structure of the system as consisting of several spin-polarized droplets. As the polarization increases, the system self-organizes into a disordered structures similar to liquid crystals, and energetically they can compete with ordered structures such as grid-like domain walls. At higher polarizations the system starts to develop regularities that, in principle, can be called supersolid, where periodic density modulation and pairing correlations coexist. The robustness of the results has been checked with respect to temperature effects, dimensionality, and the presence of a trapping potential. Dynamical stability has also been investigated.
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 analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ density functional theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely, a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and, finally, a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.
Interacting fermions are ubiquitous in nature, and understanding their thermodynamics is an important problem. We measured the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin-imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.
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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, 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.
Ultracold atomic Fermi gases can be tuned to interact strongly, which produces a display of spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned since many thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radio frequency technique with ultracold ^{6}Li gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared to the equivalent value for a noninteracting Fermi gas. At unitarity, we can use the local density approximation to extract the integrated spin susceptibility for the uniform gas as a function of temperature, which at high temperatures is generally less than theoretically predicted. At low temperatures, our data lie within the range of theoretical predictions, although we can also describe the entire curve using a very simple one-parameter mean field model with monotonically increasing spin susceptibility.