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.
A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these inelastic confinement-induced resonances are of interest since they can lead to coherent molecule formation, losses, and heating in ultracold atomic gases. A perturbative model is introduced to describe the resonance positions and the coupling strengths. The validity of the model and the behavior of the resonances for different confinement geometries are analyzed in comparison with exact numerical ab initio calculations. While such resonances have so far only been detected for large positive values of the
s-wave scattering length, it is found that they are present also for negative
s-wave scattering lengths, i.e., for attractive interactions. The possibility to coherently tune the resonances by a variation of the external confinement geometry might pave the way for coherent molecule association where magnetic Feshbach resonances are inaccessible.
The two-body scattering is greatly modified in reduced dimensions. With ultracold atoms, low dimensional configurations are routinely accessible thanks to the use of optical lattices which allow confinements sufficiently strong to freeze the motion along chosen directions. With two different atomic species, we use a species-selective optical potential, in the form of a standing wave, to confine only one species in 2D disks and study the scattering between particles existing in different dimensions, i.e., we realize a 2D-3D mix-dimensional configuration , reminiscent of a brane world. We review the scattering theory specific to this configuration and derive an effective scattering length α eff in terms of the free-space scattering length α and the confinement parameters. We detect experimentally the enhancement of inelastic collisions arising at particular values of α and relate these values to the divergences of α eff . Unlike the confinement-induced resonances predicted and observed for identical particles, our mixed-dimensional resonances occur in a series of several resonances, because the relative and centre-of-mass motion are coupled.
We study the three-body problem of two ultracold identical bosonic atoms (denoted by
B) and one extra atom (denoted by
X), where the scattering length
aBX between each bosonic atom and atom
X is resonantly large and positive. We calculate the scattering length
aad between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom
X, and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length
aBB is of the same order of the van der Waals length
rvdW or even smaller), it can still induce a significant effect for the atom-dimer scattering length
aad. Explicitly, an atom-dimer scattering resonance can always occur when the value of
aBB varies in the region with $|{a}_{BB}|\ensuremath{\lesssim}{r}_{\mathrm{vdW}}$. As a result, both the sign and the absolute value of
aad, as well as the behavior of the ${a}_{\mathrm{ad}}\text{\ensuremath{-}}{a}_{BX}$ function, depends sensitively on the exact value of
aBB. Our results show that, for a good quantitative theory, the intraspecies interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.
We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional (1D) trapping potentials, allowing for two different atom species. As a consequence, the centre-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.
We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal (
z-) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (CoM) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length
a2D, the 2D effective range parameter
R2D, and the bound-state energies, as functions of the
s-wave scattering length and effective range of the two atoms in free three-dimensional (3D) space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion. Around these resonances,
a2D varies rapidly with the 3D scattering parameters, while
R2D is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by i.e., the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.