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arXiv:1411.3036 · Frontiers of Physics

Many-body theories of density response for a strongly correlated Fermi gas

Hui Hu

Published Nov 4, 2011• 5 citations
arXivHTMLPDF

Abstract

Recent breakthroughs in the creation of ultracold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, hightemperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.

DOI
10.1007/s11467-011-0216-x

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By developing a quantum virial expansion theory, we quantitatively calculate the dynamic density response function of a trapped strongly interacting Fermi gas at high temperatures near unitarity. A clear transition from atomic to molecular responses is identified in the spectra when crossing from the BCS to BEC regimes, in qualitative agreement with recent Bragg spectroscopy observations. Our virial expansion method provides a promising way to solve the challenging strong-coupling problems and is applicable to other dynamical properties of strongly correlated Fermi gases.
Recent breakthroughs in the creation of ultra‐cold atoms in the laboratory have ushered in unprecedented changes in physical science. These enormous changes in the coldest temperatures available in the laboratory mean that many novel experiments are possible. There is unprecedented control and simplicity in these novel systems, meaning that quantum many‐body theory is now facing severe challenges in quantitatively understanding these new results. We discuss some of the new experiments and recently developed theoretical techniques required to predict the results obtained.
We briefly review current research progress in the field of strongly correlated atomic Fermi gases. A deep understanding of strongly correlated quantum gases is plagued by the lack of either exact solutions or a controllable small interaction parameter. In this work, we present a systematic virial expansion method to study the high-temperature thermodynamics of a strongly correlated Fermi gas,where the controllable parameter is given by the fugacity,exp (μkBT),with μ being the chemical potential. A practical way is proposed to obtain the expansion coefficients for both homogeneous and harmonically trapped Fermi gases. We calculate, for the first time accurately, the third-order virial coefficient. The resulting equation of states at high temperatures is compared with a recent thermodynamic measurement and with Monte Carlo simulations.
Universality of strongly interacting fermions is a topic of great interest in diverse fields. Here we investigate theoretically the universal dynamic density response of resonantly interacting ultracold Fermi atoms in the limit of either high temperature or large frequency. At high temperature, we use quantum virial expansion to derive universal, nonperturbative expansion functions of the dynamic structure factor; at large momentum, we conjecture that the second-order expansion function gives the Wilson coefficient used in the operator product expansion method. The dynamic structure factor is therefore determined by its second-order expansion function with an overall normalization factor given by Tan's [S. Tan, Ann. Phys. (NY) 323, 2952 (2008); S. Tan, Ann. Phys. (NY) 323, 2971 (2008); S. Tan, Ann. Phys. (NY) 323, 2987 (2008)] contact parameter. We show that the spin-parallel and -antiparallel dynamic structure factors have, respectively, a tail of the form $\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}^{\ensuremath{-}5/2}$ for $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, decaying slower than the total dynamic structure factor found previously ($\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}7/2}$). Our predictions for the dynamic structure factor at high temperature or large frequency are testable using Bragg spectroscopy for ultracold atomic Fermi gases.
Many-body quantum systems provide an interesting playground for experimentalists and theorists alike. In particular, ultracold atomic gases provide not only a realm of study for which experiments have a high degree of control but also provides theorists with intriguing, yet challenging systems that may be accessed computationally. It is for these reasons that it is here where the majority of our work will focus. We discuss the necessary physics, thermodynamics, and computational methods for carrying out this work, and present several methods for computing coefficients of the quantum virial expansion across dimensions for Fermi gases with zero-range interactions. The techniques discussed are non-perturbative and involve stochastic methods as well as a semi-classical lattice approximation. Through these algorithms, we have computed the interaction dependence (both attractive and repulsive where applicable) of the virial coefficients to a relatively high order as compared to current literature in one, two, and three spatial dimensions. Through one of said methods, we are able to provide a prediction for the radius of convergence of the virial expansion in one spatial dimension.