Nonzero orbital angular momentum superfluidity in ultracold Fermi gases

TL;DR

This paper investigates the evolution of superfluidity with nonzero orbital angular momentum in ultracold Fermi gases, revealing a quantum phase transition in contrast to the s-wave case, and provides a comprehensive theoretical analysis from low energy scattering to Ginzburg-Landau theory.

Contribution

It presents a detailed theoretical framework for nonzero angular momentum superfluidity, including scattering, ground state properties, and critical temperature behavior, highlighting a quantum phase transition.

Findings

Quantum phase transition for nonzero angular momentum pairing.

Differences between BCS-BEC evolution in s-wave and nonzero angular momentum channels.

Derived Ginzburg-Landau functional and coherence length near critical temperature.

Abstract

We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground state ($T = 0$) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground state energy and low energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a gaussian fluctuation theory near the critical temperature ($T = T_{\rm c}$), and we analyze the number of bound, scattering and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near $T_{\rm c}$, and compare the Ginzburg-Landau coherence length with the zero temperature average Cooper pair size.