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arXiv:1312.1612 · Journal of Physics Conference Series

Quantum Monte Carlo study of strongly interacting Fermi gases

S Gandolfi

Published Aug 14, 2014• 7 citations
arXivHTMLPDF

Abstract

In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li – K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.

DOI
10.1088/1742-6596/529/1/012011

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In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li – K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.
Abstract. In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li−K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas. 1.
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.
In this Thesis we will theoretically address some issues concerning the Physics of ultracold Fermi gases, all of them with experimental relevance. The field of ultracold gases, and more recently of ultracold Fermi gases, is gathering a lot of experimental and theoretical interest for two main reasons: the great control on the relevant parameters of the problem and the relative simplicity of the minimal theory which is able to correctly describe the system. Building upon this solid background, ultracold gases provided an ideal laboratory for testing more refined theories and also for addressing fundamental issues of quantum mechanics as well as for simulating more complex physical systems such as those encountered in condensed matter. Even if the effective hamiltonian of ultracold gases can be simple, due to the diluteness of the system and the low temperature, which imply low energy physics, the solution of the quantum mechanic equations governing the state of these systems is not always simple. For the static properties usually mean-field solutions exist or perturbative expansions can be produced in some regimes. However Quantum Monte Carlo (QMC) techniques provide more accurate results especially in the strongly interacting regimes. For confined systems it is possible to use QMC only for a few particles, so that, for large number of particles, a fruitful combined use of Density Functional Theory (DFT) and QMC is necessary. The study of the dynamics of ultracold gases has received little attention with QMC techniques, due to the intrinsic computational difficulty of the many-body problem, so that general hydrodynamic equations are often used for studying the propagation of smoothly varying perturbations. In this Thesis we use QMC techniques for studying the problem of ferromagnetism in repulsive or effectively repulsive ultracold gases without a lattice and the problem of the Bardeen-Cooper-Schrieffer to Bose-Einstein-Condensation (BCS-BEC) crossover in two dimensions. We use DFT in the Local Density Approximation (LDA) for calculating the density profiles of ultracold Fermi gases in harmonic magneto-optical traps, starting from QMC equations of state. We study the propagation of first and second sound in ultracold Fermi gases in cylindrical geometry, using the hydrodynamic equations of superfluids.
We will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.
The quantum Monte Carlo method for spin-12\frac{1}{2}21​ fermions at finite temperature is formulated for dilute systems with an sss-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature Tc{T}_{c}Tc​ for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where aaa is the sss-wave scattering length and kF{k}_{F}kF​ is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature T0>Tc{T}_{0}>{T}_{c}T0​>Tc​, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc<T<T0{T}_{c}<T<{T}_{0}Tc​<T<T0​ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.
Properties of the ground state of an unpolarized ultracold Fermi gas along the BCS-BEC crossover are investigated by the variational and diffusion Monte Carlo methods. We apply the Wigner-Bethe-Peierls boundary condition in our calculations to avoid any bias from using an interatomic potential with finite effective range. Properties for several values of the scattering length are studied in the range $\ensuremath{-}8\ensuremath{\le}1/a{k}_{F}\ensuremath{\le}4$, including the unitary limit. The contact parameters as a function of scattering length are obtained by fitting the pair distribution functions for particles with different spins. The energies and contact parameters are in very good agreement with experimental data reported in the literature.