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Chapman & Hall/CRC eBooks

The Fermi Gas

Kerson Huang

Published Sep 21, 2009• 0 citations
Publisher

Abstract

F = μ(n, 0) (16.4) are occupied, and all those above are empty. In momentum space the occupied states lie within the Fermi sphere of radius pF , as illustrated in Figure 16.1. Such a condition is called “quantum degeneracy.”
DOI
10.1201/9781439878132-18

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We consider a system of fermions with mass m and model repulsive interaction U(q) = g/\sqrt{q^2 + q_0^2}, where q is the momentum transfer, q_0 the screening constant, and g > 0 the coupling constant. It is shown that at g > g_cr > 3π^2/m the system ground state is changed from fully occupied Fermi sphere to multiconnected Fermi sphere (MFS), consisting in N fully occupied spherical layers (icebergs) separated by empty spacers. An effective description is developed for such states at N >> 1, showing their tendency at N \to \infty to the Fermi condensate (FC) state known for the model U(q) = g/q [Khodel, Shaginyan, JETP Lett., 51, 553, 1990]. At finite temperatures, a crossover is predicted from the Fermi liquid behavior of MFS with effective mass m^* \sim m N/ln(N) to non-Fermi-liquid behavior with m^* \propto 1/T at T > T^* \sim T_F ln(N)/N.
We study theoretically the deformation of the Fermi surface (FS) of a three-dimensional gas of Rydberg-dressed 6Li^{6}\mathrm{Li}6Li atoms. The laser dressing to high-lying Rydberg DDD states results in angle-dependent soft-core-shaped interactions whose anisotropy is described by multiple spherical harmonics. We show that this can drastically modify the shape of the FS and that its deformation depends on the interplay between the Fermi momentum kF{k}_{F}kF​ and the reciprocal momentum k‾\overline{k}k corresponding to the characteristic soft-core radius of the dressing-induced potential. When kF<k‾{k}_{F}<\overline{k}kF​<k, the dressed interaction stretches a spherical FS into an ellipsoid. When ${k}_{F}\ensuremath{\gtrsim}\overline{k}$, complex deformations are encountered which exhibit multipolar characteristics. We analyze the formation of Cooper pairs around the deformed FS and show that they occupy large orbital angular momentum states (p,fp, fp,f, and hhh wave) coherently. Our study demonstrates that Rydberg dressing to high angular momentum states may pave a route toward the investigation of unconventional Fermi gases and multiwave superconductivity.
Fermions in a Fermi gas obey the Pauli exclusion principle restricting any two fermions from occupying the same quantum state. Strong interactions between fermions can completely change the properties of the Fermi gas. In our theoretical study we find an exotic quantum phase in strongly interacting Fermi gases subject to a certain condition imposed on the Fermi surfaces that we call the Fermi surface resonance. The phase is quantum critical in time and space and can be identified by the power-law dependence of the spectral density in frequency and momentum. The linear-response functions are singular in the static limit and at the Kohn anomalies. We analyze the quantum critical state at finite temperatures TTT and finite size LLL of the Fermi gas and provide a qualitative $L\ensuremath{-}T$ phase diagram. The quantum critical phase can be experimentally found in typical semiconductor heterostructures.