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arXiv:1201.4035 · Physical Review Letters

Density and Spin Response of a Strongly Interacting Fermi Gas in the Attractive and Quasirepulsive Regime

F. Palestini, P. Pieri, Giancarlo Calvanese Strinati

Published Feb 23, 2012• 50 citations
arXivHTMLPDF

Abstract

Recent experimental advances in ultracold Fermi gases allow for exploring response functions under different dynamical conditions. In particular, the issue of obtaining a "quasirepulsive" regime starting from a Fermi gas with an attractive interparticle interaction while avoiding the formation of the two-body bound state is currently debated. Here, we provide a calculation of the density and spin response for a wide range of temperature and coupling both in the attractive and quasirepulsive regime, whereby the system is assumed to evolve nonadiabatically toward the "upper branch" of the Fermi gas. A comparison is made with the available experimental data for these two quantities.

DOI
10.1103/physrevlett.108.080401

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Comment on “Density and Spin Response of a Strongly Interacting Fermi Gas in the Attractive and Quasirepulsive Regime”

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This is a comment on Phys. Rev. Lett. 108, 080401 (2012) by Palestini et al. We pointed out that the diagrammatic method in that article violates gauge invariance. As a consequence, there will a Meissner effect in the normal phase and the contribution from collective modes are not mentioned in the symmetry-broken phase.

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Recent experimental advances in ultracold Fermi gases allow for exploring response functions under different dynamical conditions. In particular, the issue of obtaining a "quasirepulsive" regime starting from a Fermi gas with an attractive interparticle interaction while avoiding the formation of the two-body bound state is currently debated. Here, we provide a calculation of the density and spin response for a wide range of temperature and coupling both in the attractive and quasirepulsive regime, whereby the system is assumed to evolve nonadiabatically toward the "upper branch" of the Fermi gas. A comparison is made with the available experimental data for these two quantities.
Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance have brought about a number of interesting problems in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a ``quasirepulsive'' regime in the upper branch of the energy spectrum due to the rapid quench is currently being debated, and the Stoner transition has mainly been investigated theoretically by using perturbation theory or at high polarization due to the limited theoretical approaches in the strongly repulsive regime. In this work, we present a nonperturbative theoretical approach to the quasirepulsive upper branch of a Fermi gas near a broad Feshbach resonance, and we determine the finite-temperature phase diagram for the Stoner instability. Our results agree well with the known quantum Monte Carlo simulations at zero temperature, and we recover the known virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the Stoner transition temperature becomes of the order of the Fermi temperature, around which the molecule formation rate becomes vanishingly small. This suggests a feasible way to observe Stoner ferromagnetism in the nondegenerate temperature regime.
We develop a non-Hermitian effective theory for a repulsively interacting Fermi gas in the excited branch. The on-shell TTT-matrix is employed as a complex-valued interaction term, which describes a repulsive interaction between atoms in the excited branch and a two-body inelastic decay to the attractive branch. To see the feature of this model, we have addressed, in the weak coupling regime, the excitation properties of a repulsive Fermi polaron as well as the time-dependent number density. The analytic expressions obtained for these quantities qualitatively show a good agreement with recent experiments. By calculating the dynamical transverse spin susceptibility in the random phase approximation, we show that a ferromagnetic system with nonzero polarization undergoes a dynamical instability and tends towards a heterogeneous phase.
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The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.