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arXiv:1801.10098 · New Journal of Physics

Diversified vortex phase diagram for a rotating trapped two-band Fermi gas in the BCS-BEC crossover

S N Klimin, J Tempere, M. V. Miloševıć

Published Feb 5, 2018• 9 citations
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Abstract

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.

DOI
10.1088/1367-2630/aaaceb

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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.
A two-component Fermi gas with attractive sss-wave interactions forms a superfluid at low temperatures. When this gas is confined in a rotating trap, fermions can unpair at the edges of the gas and vortices can arise beyond certain critical rotation frequencies. We compute these critical rotation frequencies and construct the phase diagram in the plane of scattering length and rotation frequency for different total numbers of particles. We work at zero temperature and consider a cylindrically symmetric harmonic trapping potential. The calculations are performed in the Hartree-Fock-Bogoliubov approximation which implies that our results are quantitatively reliable for weak interactions.
We study a rotating atomic Fermi gas near a narrow sss-wave Feshbach resonance in a uniaxial trap with frequencies ${\ensuremath{\Omega}}_{\ensuremath{\perp}}$, ${\ensuremath{\Omega}}_{z}$. We predict the upper-critical angular velocity, ${\ensuremath{\omega}}_{c2}(\ensuremath{\delta},T)$, as a function of temperature TTT and detuning $\ensuremath{\delta}$ across the BEC-BCS crossover. The suppression of superfluidity at ${\ensuremath{\omega}}_{c2}$ is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low TTT and ${\ensuremath{\Omega}}_{z}\ensuremath{\ll}{\ensuremath{\Omega}}_{\ensuremath{\perp}}$, in the BCS and crossover regimes of $0\ensuremath{\lesssim}\ensuremath{\delta}\ensuremath{\lesssim}{\ensuremath{\delta}}_{c}$, ${\ensuremath{\omega}}_{c2}$ is implicitly given by $\ensuremath{\hbar}\sqrt{{\ensuremath{\omega}}_{c2}^{2}+{\ensuremath{\Omega}}_{\ensuremath{\perp}}^{2}}\ensuremath{\approx}2\ensuremath{\Delta}\sqrt{\ensuremath{\hbar}{\ensuremath{\Omega}}_{\ensuremath{\perp}}/{ϵ}_{F}}$, vanishing as ${\ensuremath{\omega}}_{c2}\ensuremath{\sim}{\ensuremath{\Omega}}_{\ensuremath{\perp}}(1\ensuremath{-}\ensuremath{\delta}/{\ensuremath{\delta}}_{c}{)}^{1/2}$ near ${\ensuremath{\delta}}_{c}\ensuremath{\approx}2{ϵ}_{F}+\frac{\ensuremath{\gamma}}{2}{ϵ}_{F}\mathrm{ln}({ϵ}_{F}/\ensuremath{\hbar}{\ensuremath{\Omega}}_{\ensuremath{\perp}})$ (with $\ensuremath{\Delta}$ the BCS gap and $\ensuremath{\gamma}$ the resonance width), and extending the bulk result $\ensuremath{\hbar}{\ensuremath{\omega}}_{c2}\ensuremath{\approx}2{\ensuremath{\Delta}}^{2}/{ϵ}_{F}$ to a trap. In the BEC regime of $\ensuremath{\delta}<0$ we find ${\ensuremath{\omega}}_{c2}\ensuremath{\rightarrow}{\ensuremath{\Omega}}_{\ensuremath{\perp}}^{\ensuremath{-}}$, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.
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.
We theoretically investigate the superfluid properties of a two-band gas of 173Yb^{173}\mathrm{Yb}173Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by interband and intraband pairing interactions associated with OFR by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, the effects of an experimentally inaccessible deep bound state are removed to model a real 173Yb^{173}\mathrm{Yb}173Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced interband interaction. In addition to these superfluid quantities, we also examine collective modes, such as the Goldstone mode, the Schmid (Higgs) mode, and Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multiband superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, aF,a_{F},aF​, and the effective range parameter, re.r_{\mathrm{e}}.re​. In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances. By matching two-body scattering properties near a Feshbach resonance to a simple renormalized model potential, a broad resonance is characterized by a small effective range and the gas displays a universal BCS-BEC crossover behavior. On the other hand, for a narrow resonance thermodynamic quantities depend the effective range which may be large and negative at resonance. For increasing values of −re-r_{\mathrm{e}}−re​ we find the transition temperature to be suppressed in the crossover region. We furthermore argue for existence of a lower bound of TcT_{c}Tc​ at fixed coupling for increasing −re-r_{\mathrm{e}}−re​ in the crossover region.