Scattering resonances and pairing in a Rabi-coupled Fermi gas

TL;DR

The paper demonstrates that a coherent Rabi drive between two hyperfine states in a three-component ultracold Fermi gas can qualitatively alter interspecies scattering with a third component. By formulating a minimal low-energy model and deriving a driven two-channel T-matrix, they show that the effective dressed scattering length $a_{-}$ and, in general, an effective range $r_{\text{eff}}$ can exhibit resonances arising from hybrid bound states, controlled purely by the drive parameters $δ$ and $Ω$. Extending to finite density via a generalized Thouless criterion, they predict a drive-tunable crossover between pairing channels and even an excited many-body superfluid branch, linking few-body bound-state structure to many-body superfluid transitions. The results provide a versatile route to explore drive-controlled BCS-BEC physics and related phenomena in driven, three-component ultracold gases, with implications for Efimov physics and spin-imbalanced systems.

Abstract

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.

Figures (5)

• Figure 1: (a) Sketch of the system considered. A coherent drive of strength $\Omega$ couples two atomic species (blue and red), which gives rise to dressed particles (purple). Both of the Rabi coupled species can interact with a third component (gray) via short range interactions that are characterized by the scattering lengths $a_{13}$ and $a_{23}$. The resulting effective scattering length $a_-$ for the lowest energy dressed particle can exhibit resonances. (b) Existence diagram of the dressed Feshbach resonances. The purple-shaded area indicates where a single resonance exists when varying the detuning of the Rabi drive, while in the gray area two resonances exist. By contrast, no resonances exist in the white areas, including along the diagonal where $a_{13}=a_{23}$. Here, $m_r$ is the reduced mass of the coupled and uncoupled components.
• Figure 2: (a) Diagonal $G_{\sigma\sigma}$ and (b) off-diagonal $G_{\sigma\bar{\sigma}}$$(\bar{\sigma}\neq\sigma)$ single-particle Green's functions for species $\sigma=\{1,2\}$ in the presence of a Rabi drive. The thin solid lines represent the bare Green's functions in the absence of Rabi drive, the vertical dotted lines illustrate the Rabi coupling between species 1 and 2, and the double lines represent the Rabi-dressed Green's functions. (c) Diagrammatic representation of the $T$-matrix equation, where the circle represents the interaction vertex $g_{\sigma 3}\delta_{\sigma\sigma'}$, and the thin blue line is the Green's function of a particle from species 3.
• Figure 3: Rabi-dressed Feshbach resonances and hybrid bound states as a function of detuning $\delta/\Omega$. (a) Dressed scattering length for three sets of bare scattering lengths ($a_{13},a_{23}$) corresponding to the points marked by ($\bullet,\blacklozenge,\blacksquare$) symbols in Fig. \ref{['fig:sketch&exist']}(b). (b,c) Energy spectrum for $(a_{13},a_{23})\sqrt{2m_r\Omega}=(-0.3,0.8)$ in (b), and $(a_{13},a_{23})\sqrt{2m_r\Omega}=(0.6,0.8)$ in (c). We show the hybrid bound states (black lines), with the dashed red and blue lines corresponding to the bare 1-3 and 2-3 bound states. The purple lines show the dressed single-particle energies $\epsilon_{\pm}$ and the shaded area highlights the scattering continuum of the driven system.
• Figure 4: (a) Critical temperatures $T^*$ for pairing at equal densities $n_1 + n_2 = n_3$, and (b) associated average chemical potentials versus detuning for $(a_{13},a_{23})\sqrt{2m_r\Omega}=(0.6,0.8)$, $\Omega/E_F=1$ and equal masses $m_3=m$. The black solid (dashed) lines correspond to ground (excited) state solutions. The purple line in (b) marks the edge of the dressed many-body continuum, given by $2E_F+\epsilon_{-}$.
• Figure S1: Properties of the hybrid bound states. (a) Ratio $R$ versus detuning for the ground (solid line) and excited states (dashed line). (b) Magnetization vector component $\mathcal{S}_z$ (red) and $\mathcal{S}_x$ (blue) for the ground (solid line) and excited states (dashed line). The dotted-black lines show the magnetization obtained from the effective Hamiltonian \ref{['eq:Heff']}. The bare scattering lengths are $(a_{13},a_{23})\sqrt{2m_r\Omega}=(0.6,0.8)$ as in Fig. 3(c) of the main text.