Confinement-Induced Resonances in Rabi-Coupled Bosonic Mixtures

Abstract

We consider coherently-coupled bosonic mixtures scattering at low energies in the presence of an external confinement along either one or two directions. We exactly solve the two-body scattering problem, showing that for large Rabi coupling the confinement-induced resonance can be displaced towards scattering lengths values much smaller than the oscillator length. Our results make the observation of confinement-induced resonances more tunable and accessible, offering yet another handle for the efficient control of strong interactions in ultracold quantum gases.

Figures (3)

• Figure 1: Energy scheme representing the scattering process modeled in this paper. Physically, two $\ket{-}$ atoms scatter at the relative collisional energy $\epsilon$ and, as a result, can be virtually excited to the spin states $\ket{+-}$ or $\ket{++}$, in which their energies $\epsilon_1$ and $\epsilon_2$ are negative, and therefore correspond to bound states. If the atoms are confined in quasi low-dimensional geometries, the energies includes the zero-point oscillator energy $E_0$, defined in the main text. We measure energies with respect to the one of two non-trapped atoms with zero relative kinetic energy.
• Figure 2: Effective one-dimensional interaction strength versus the scattering length $a_{\uparrow\uparrow}$, obtained by evaluating Eq. \ref{['g1Dmixture']} for parameters similar to those of Ref. lavoine2021: $\epsilon = 0^{+}$, $a_{\uparrow\downarrow} = a_{\downarrow\downarrow} = 0.01$, $\delta = 2$. The dashed line represents the interaction strength in a quasi-1D single-species calculated in Ref. olshanii1998, i.e. Eq. \ref{['g1DOlshanii']} for $\sigma = \uparrow$, and it is reproduced for small Rabi frequency $\Omega \ll |\delta|$. Note that one can conveniently shift the resonance position towards smaller scattering lengths by increasing $\Omega$, reaching for $\Omega \to \infty$ the red vertical line [corresponding to $1/\bar{a}_+=-\zeta(1/2,1)/\sqrt{2}$]. Inset: magnification around the point where all scattering lengths are equal, where Eq. \ref{['g1DOlshanii']} is exact irrespectively of $\Omega$.
• Figure 3: Two-dimensional s-wave scattering amplitude versus the scattering length, evaluated at the scattering energy $\epsilon = 0.05$ and setting the other parameters as in Fig. \ref{['fig2']}. The dashed line is Eq. \ref{['Petrovf0']}, obtained for a single-species gas, and it is reproduced for small Rabi frequency $\Omega \ll |\delta|$. Inset: plot magnification around the region where all scattering lengths are equal, where Eq. \ref{['Petrovf0']} holds independent of $\Omega$.