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arXiv:2503.10980 · Physical Review A

Hybrid-pair superfluidity in a strongly driven Fermi gas

Brendan C. Mulkerin, O. Bleu, Cesar R. Cabrera, Meera M. Parish, Jesper Levinsen

Published Jun 23, 2025• 2 citations
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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.

DOI
10.1103/xtfy-8nrt

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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.
We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozi\`eres-Schmitt-Rink approach to a two-band system. In comparison with the single-band case, we find a strong enhancement of the critical temperature, a significant reduction of the preformed pair region where pseudogap effects are expected, and the entanglement of two kinds of composite bosons in the strong-coupling BEC regime.
Abstract We present a theoretical review of the recent progress in non-equilibrium BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover physics. As a paradigmatic example, we consider a strongly interacting driven-dissipative two-component Fermi gas where the non-equilibrium steady state is tuned by adjusting the chemical potential difference between two reservoirs that are coupled with the system. As a powerful theoretical tool to deal with this system, we employ the Schwinger-Keldysh Green’s function technique. We systematically evaluate the superfluid transition, as well as the single-particle properties, in the non-equilibrium BCS-BEC crossover region, by adjusting the chemical potential difference between the reservoirs and the strength of an s-wave pairing interaction associated with a Feshbach resonance. In the weak-coupling BCS side, the chemical potential difference is shown to imprint a two-step structure on the particle momentum distribution, leading to an anomalous enhancement of pseudogap, as well as the emergence of exotic Fulde-Ferrell-Larkin-Ovchinnikov-type superfluid instability. Since various non-equilibrium situations have recently been realized in ultracold Fermi gases, the theoretical understanding of non-equilibrium BCS-BEC crossover physics would become increasingly important in this research field.
We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective sss-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.
We investigate the possibility of using a Rabi drive to tune the interactions in an atomic Fermi gas. Specifically, we consider the scenario where two fermion species (spins) are Rabi coupled and interacting with a third uncoupled species. Using an exact calculation within a minimal low-energy model, we derive analytical expressions for the effective scattering length and effective range that characterize the collisions between a Rabi-dressed atom and an atom from the third species. In particular, we find that new scattering resonances emerge in the Rabi-coupled system, which we demonstrate are linked to the existence of hybrid two-body bound states. Furthermore, we show via a generalized Thouless criterion that the scattering properties have a direct impact on the superfluid transitions in the Rabi-coupled Fermi gas. The presence of Rabi-induced resonances thus has implications for the investigation of many-body physics with driven atomic gases.
We investigate the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation crossover in a two-band superfluid Fermi gas with an energy shift between the bands. When the intraband coupling in the cold (first) band is fixed as weak, we find that in the case of vanishing pair-exchange interband coupling and in the strong-coupling limit of the hot (second) band the system undergoes a transition to a single-component configuration with a full suppression of the first energy gap and a full redistribution of particles between bands. For nonvanishing pair-exchange interband coupling we reveal a nonmonotonic dependence of the energy gap in the first band vs intraband coupling in the second band, with the presence of a hump. In the case of weak interband coupling, the system shows a significant amplification of the intrapair correlation length of the condensate in the first band in the strong-coupling regime of the second band, which clearly indicates the coexistence of giant Cooper pairs and a bosonic condensate even for nonzero temperatures. This can lead to a nonmonotonic temperature dependence of the second energy gap with a peak. The here predicted coexistence of giant Cooper pairs and bosonic molecules can be verified by means of the visualization of vortex cores in two-component atomic condensates as well as in some iron-based superconductors.
We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.