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arXiv:1609.00550 · Physical Review A

Pressure profiles of nonuniform two-dimensional atomic Fermi gases

Kirill Martiyanov, Tatiana Barmashova, Vasiliy Makhalov, Andrey V. Turlapov

Published Jun 17, 2016• 15 citations
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Abstract

Spatial profiles of the pressure have been measured in atomic Fermi gases with primarily two-dimensional (2D) kinematics. The in-plane motion of the particles is confined by a Gaussian-shape potential. The two-component deeply degenerate Fermi gases are prepared at different values of the $s$-wave attraction. The pressure profile is found using the force-balance equation, from the measured density profile and the trapping potential. The pressure is compared to zero-temperature models within the local density approximation. In the weakly interacting regime, the pressure lies above a Landau Fermi-liquid theory and below the ideal-Fermi-gas model, whose prediction coincides with that of the Cooper-pair mean-field theory. The values closest to the data are provided by the approach where the mean field of Cooper pairs is supplemented with fluctuations. In the regime of strong interactions, in response to the increasing attraction, the pressure shifts below this model reaching lower values calculated within Monte Carlo methods. Comparison to models shows that interaction-induced departure from 2D kinematics is either small or absent. In particular, comparison with a lattice Monte Carlo suggests that kinematics is two dimensional in the strongly interacting regime.

DOI
10.1103/physreva.93.063622

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Spatial profiles of the pressure have been measured in atomic Fermi gases with primarily two-dimensional (2D) kinematics. The in-plane motion of the particles is confined by a Gaussian-shape potential. The two-component deeply degenerate Fermi gases are prepared at different values of the sss-wave attraction. The pressure profile is found using the force-balance equation, from the measured density profile and the trapping potential. The pressure is compared to zero-temperature models within the local density approximation. In the weakly interacting regime, the pressure lies above a Landau Fermi-liquid theory and below the ideal-Fermi-gas model, whose prediction coincides with that of the Cooper-pair mean-field theory. The values closest to the data are provided by the approach where the mean field of Cooper pairs is supplemented with fluctuations. In the regime of strong interactions, in response to the increasing attraction, the pressure shifts below this model reaching lower values calculated within Monte Carlo methods. Comparison to models shows that interaction-induced departure from 2D kinematics is either small or absent. In particular, comparison with a lattice Monte Carlo suggests that kinematics is two dimensional in the strongly interacting regime.
Using an ultracold gas of atoms, we have realized a quasi-two-dimensional Fermi system with widely tunable s-wave interactions nearly in a ground state. Pressure and density are measured. The experiment covers physically different regimes: weakly and strongly attractive Fermi gases and a Bose gas of tightly bound pairs of fermions. In the Fermi regime of weak interactions, the pressure is systematically above a Fermi-liquid-theory prediction, maybe due to mesoscopic effects. In the opposite Bose regime, the pressure agrees with a bosonic mean-field scaling in a range beyond simplest expectations. In the strongly interacting regime, measurements disagree with a purely 2D model. Reported data may serve for sensitive testing of theoretical methods applicable across different quantum physics disciplines.
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Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0T=0T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.
We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond-mean-field Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local-density approximation, with two different schemes, to model different trapping potentials in the tightly confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly confined transverse direction and describe its behavior as a function of the dimensionality, from two to three dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms.
We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.
Understanding the formation of Cooper pairs and the resulting thermodynamic properties of low-dimensional Fermi gases is an important area of research, which may help build our understanding of other low-dimensional systems, such as high-temperature superconductors. In lower dimensions, quantum fluctuations are expected to play an increasingly important role, and the reliability of strong-coupling theories becomes questionable. Here, we present a comparison of recent thermodynamic measurements and theoretical predictions from different many-body TTT-matrix theories for a two-dimensional strongly interacting Fermi gas in the normal state. We find that the fully self-consistent TTT-matrix theory provides the best description of the experimental data over a wide range of temperatures and interatomic interactions.