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arXiv:1512.00214 · Physical Review A

Finite-temperature vortices in a rotating Fermi gas

Serghei N. Klimin, Jacques Tempere, Nick Verhelst, M. V. Miloševıć

Published Aug 16, 2016• 10 citations
arXivHTMLPDF

Abstract

Vortices and vortex arrays have been used as a hallmark of superfluidity in rotated, ultracold Fermi gases. These superfluids can be described in terms of an effective field theory for a macroscopic wave function representing the field of condensed pairs, analogous to the Ginzburg-Landau theory for superconductors. Here we establish how rotation modifies this effective field theory, by rederiving it starting from the action of Fermi gas in the rotating frame of reference. The rotation leads to the appearance of an effective vector potential, and the coupling strength of this vector potential to the macroscopic wave function depends on the interaction strength between the fermions, due to a renormalization of the pair effective mass in the effective field theory. The mass renormalization derived here is in agreement with results of functional renormalization-group theory. In the extreme Bose-Einstein condensate regime, the pair effective mass tends to twice the fermion mass, in agreement with the physical picture of a weakly interacting Bose gas of molecular pairs. Then we use our macroscopic-wave-function description to study vortices and the critical rotation frequencies to form them. Equilibrium vortex state diagrams are derived and they are in good agreement with available results of the Bogoliubov--de Gennes theory and with experimental data.

DOI
10.1103/physreva.94.023620

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Vortices and vortex arrays have been used as a hallmark of superfluidity in rotated, ultracold Fermi gases. These superfluids can be described in terms of an effective field theory for a macroscopic wave function representing the field of condensed pairs, analogous to the Ginzburg-Landau theory for superconductors. Here we establish how rotation modifies this effective field theory, by rederiving it starting from the action of Fermi gas in the rotating frame of reference. The rotation leads to the appearance of an effective vector potential, and the coupling strength of this vector potential to the macroscopic wave function depends on the interaction strength between the fermions, due to a renormalization of the pair effective mass in the effective field theory. The mass renormalization derived here is in agreement with results of functional renormalization-group theory. In the extreme Bose-Einstein condensate regime, the pair effective mass tends to twice the fermion mass, in agreement with the physical picture of a weakly interacting Bose gas of molecular pairs. Then we use our macroscopic-wave-function description to study vortices and the critical rotation frequencies to form them. Equilibrium vortex state diagrams are derived and they are in good agreement with available results of the Bogoliubov--de Gennes theory and with experimental data.
Dilute atomic gases have become a powerful tool for studying many-body quantum mechanics. The best example of this is the achievement of Bose-Einstein condensation in 1995 in a gas of Bose atoms, a discovery which has invoked a confluence of ideas from condensed matter, atomic and nuclear physics. Now a concerted research effort is focused on creating and studying a BCS superfluid in an atomic Fermi gas. In the work presented here we study in detail pairing superfluidity in a Fermi gas of atoms, by self-consistently solving the Bogoliubov-de Gennes equations, both for bulk systems, and for atoms in a harmonic confining potential. A critical part of this work is the derivation of a regularized theory, which is formulated entirely in terms of physically measurable quantities, such that a quantitative comparison between theory and experiment is possible with no adjustable parameters. The resulting equations form a non-linear problem, and the accurate numerical solution of this poses a formidable challenge. A major component of this thesis is the development of efficient computational approaches to overcome these difficulties. Based on the linear response of the gas to a twisting of the order parameter phase, the superfluid density can be defined as a generalized elasticity of the system. Using finite temperature perturbation theory we calculate the superfluid density in an inhomogeneous system. We investigate the structure and thermodynamic properties of a singly quantized vortex line in a gas of superfluid fermionic atoms, making the first quantitative determination the critical rotation frequency for thermodynamic stability of the vortex state, and study the nature of the bound states in the vortex core. These excitations fill the core, making direct imaging of the vortex unlikely. Instead, we propose an experiment to indirectly probe the vortex density of states with laser fields, in a scheme analogous to Scanning Tunneling Microscopy. Furthermore, it is shown that the vortex state causes a shift of the superfluid transition temperature, which can be understood as a finite size effect.
We report the equilibrium vortex phase diagram of a rotating two-band Fermi gas confined to a cylindrically symmetric parabolic trapping potential, using the recently developed finite-temperature effective field theory (Klimin et al 2016 Phys. Rev. A 94 023620). A non-monotonic resonant dependence of the free energy as a function of the temperature and the rotation frequency is revealed for a two-band superfluid. We particularly focus on novel features that appear as a result of interband interactions and can be experimentally resolved. The resonant dependence of the free energy is directly manifested in vortex phase diagrams, where areas of stability for both integer and fractional vortex states are found. The study embraces the BCS–BEC crossover regime and the entire temperature range below the critical temperature T c . Significantly different behavior of vortex matter as a function of the interband coupling is revealed in the BCS and BEC regimes.
In this article, we review developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single-component atomic Bose gas, which (at least at rest) forms a Bose–Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores, as set by the healing length, start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single-particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. In this article, we describe the equilibrium properties of rapidly rotating atomic Bose gases in both the mean-field and the strongly correlated regimes, and related theoretical developments for Bose gases in lattices, for multi-component Bose gases and for atomic Fermi gases. The current experimental situation and outlook for the future are discussed in light of these theoretical developments.
We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.
The rotation of two-component Fermi gases and the subsequent appearance of vortices have been the subject of numerous experimental and theoretical studies. Recent experimental advances in hyperfine state-dependent potentials and highly degenerate heteronuclear Fermi gases suggest that it would be feasible to create component-dependent rotation potentials in future experiments. In this study, we use an effective field theory for Fermi gases to consider the effects of rotating only one component of the Fermi gas. We find that the superfluid band gap in bulk exists up to higher rotation frequencies because the superfluid at rest, far away from the vortex, has to resist only half of the rotational effects. The vortex remains the energetically favorable state above a critical frequency, but exhibits a larger core size.