Hybrid-pair superfluidity in a strongly driven Fermi gas

TL;DR

This paper introduces a three-component Fermi gas under a continuous RF drive that couples two components into hybridized states interacting with a third. A generalized two-gap BCS framework yields two coupled order parameters Δ1 and Δ2, a two-band quasiparticle spectrum, and a finite-temperature Thouless criterion to predict Tc for ground and excited states. By tuning detuning δ and scattering lengths a13,a23, the authors map detuning-driven crossovers among BCS-BCS, BCS-BEC, and BEC-BEC, including an exotic excited saddle-point state with distinctive magnetization and three-body contact signatures. The results establish the Rabi-driven system as a versatile platform for engineering and probing multi-band superfluid phases with experimentally accessible observables such as magnetization and short-range correlations.

Abstract

We explore the paired superfluid phases of a Fermi gas in the presence of a continuous Rabi drive. We focus on the case where two components are strongly coupled by the drive, forming hybrid superpositions, and interacting with an uncoupled third component. Using a generalized Bardeen- Cooper-Schrieffer (BCS) ansatz, we show that there are two coupled superfluid order parameters, and we obtain the associated free energy and quasiparticle excitation spectrum. We find that we can drive BCS-BCS, BCS-Bose-Einstein condensate (BEC) and BEC-BEC crossovers purely by varying the detuning of the Rabi drive from the bare transition, with the precise crossover depending on the sign of the underlying interactions between the coupled and uncoupled components. We furthermore identify an exotic excited branch which features both normal to BCS superfluid transitions, as well as a BCS-BEC-BCS crossover. Introducing a generalized Thouless criterion, we show that this behavior is reflected in the critical temperature for superfluidity. Our Rabi-coupled scenario also gives possesses additional thermodynamic properties related to the pseudospin of the coupled components, which provide novel signatures of the state of the many-body system. The Rabi-driven Fermi gas thus emerges as a unique platform for engineering and probing a rich array of multi-band superfluid phases.

Figures (12)

• Figure 1: (a) Rabi-dressed atom (purple) that is obtained by driving the transition between state $\ket{1}$ (red) and state $\ket{2}$ (blue). (b) Both states $\ket{1}$ and $\ket{2}$ can interact with a third component (gray) via short range interactions that are characterized by the scattering lengths $a_{13}$ and $a_{23}$, respectively. (c) Illustration of the four different crossovers that can be accessed by the ground state of the Rabi driven Fermi gas when varying the detuning $\delta$, depending on the signs of the scattering lengths. The hues of the Rabi-dressed atoms indicate their spin composition.
• Figure 2: Colormaps of the zero-temperature free energy \ref{['eq:minGP1323']} as a function of the two order parameters. (a,b) The free energy at zero detunings for $(a_{13}^{-1},a_{23}^{-1})/\sqrt{2 m_r \Omega}=(1.1,1.3)$, and $(a_{13}^{-1},a_{23}^{-1})/\sqrt{2 m_r \Omega}=(0.55,0.65)$, respectively. (c,d) Free energy for $(a_{13}^{-1},a_{23}^{-1})/\sqrt{2 m_r \Omega}=(1.1,1.3)$ at $\delta/\Omega=\mp 2$. In all panels, we fixed the chemical potentials to be $(\mu+\mu_3-\epsilon_{-})/2=0.25\Omega$. The white dots highlight the minima, while the white stars in panel (a) show the saddle points.
• Figure 3: (a) Critical temperature $T^*$ and (b) corresponding total chemical potential versus detuning for $\Omega/E_F=4$, $(a_{13}^{-1},a_{23}^{-1})/\sqrt{2 m_r \Omega}=(1.1,1.3)$ (same scattering lengths as in Fig. 2(a,c,d)), and equal masses $m=m_3$. We show the results for the ground and excited states as solid and dashed lines, respectively.
• Figure 4: (a) Critical temperature $T^*$ and (b) corresponding total chemical potential versus detuning for $\Omega/E_F=4$, $(a_{13}^{-1},a_{23}^{-1})/\sqrt{2 m_r \Omega}=(-1.1,-1.3)$, and equal masses $m=m_3$. The dashed red line in panel (a) shows Eq. \ref{['eq:TcBCS_Rabi']} with $F= \frac{\pi}{2k_Fa_{-}}$.
• Figure 5: BEC-BCS crossover with Rabi-coupled fermions. (a) Effective scattering length, (b) BCS order parameter, (c) total chemical potential measured from the (Rabi-shifted) continuum. The results are plotted for parameters $1/k_F a_{13} =1$, $a_{23}=0$, and $\Omega/E_F=1,2,3$ (solid, dashed, and dotted lines). The inset in (b) shows the analytical order parameter in the BCS regime, Eq. \ref{['eq:analyticorder']}.