Asymptotic model for shape resonance control of diatomics by intense non-resonant light: universality in the single-channel approximation

Abstract

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

Controlling thes-wave scattering length with nonresonant light: Predictions of an asymptotic model

“…Collisions at very low temperature are essentially governed by the long-range part of the inter-particle interaction. The scattering properties are therefore very well described by asymptotic models, which account only for the asymptotic part of the interaction potential [16][17][18][19][20][21][22][23]. The asymptotic Hamiltonian describing non-resonant light control of a pair of atoms [22,23] is identical to that found for DC electric field control of the atom-atom interaction [24] as well as that for ultracold collisions of polar molecules [25,26].…”

“…The scattering properties are therefore very well described by asymptotic models, which account only for the asymptotic part of the interaction potential [16][17][18][19][20][21][22][23]. The asymptotic Hamiltonian describing non-resonant light control of a pair of atoms [22,23] is identical to that found for DC electric field control of the atom-atom interaction [24] as well as that for ultracold collisions of polar molecules [25,26]. All of these problems are governed by the anisotropic dipole-dipole interaction, which decreases as 1/R 3 (where R is the inter-particle separation) and which introduces a coupling between partial waves of the same parity.…”

“…Here we investigate non-resonant light control of the scattering length. We show that the asymptotic model together with the nodal line technique [29,30], previously developed to study non-resonant light control of shape resonances [22,23], can be extended to the control of the field-dressed s-wave scattering length a. To predict the dependence of the field-dressed scattering length on the non-resonant field intensity, the asymptotic model only requires knowledge of the reduced mass, atomic polarizability and field-free s-wave scattering length.…”

Asymptotic model for shape resonance control of diatomics by intense non-resonant light

“…Otherwise the slopes of the positions' intensity dependence in the asymptotic model differ by a factor of about 1.75 from those of the full Hamiltonian. A similar factor appears in a single channel approximation to the asymptotic model when intensity-independent nodal lines are considered [44]. The node positions are assumed to depend separately on energy, rotational quantum number and non-resonant field intensity.…”

“…This suggests the use of perturbation theory based on field-free properties only, i.e., a single-channel model. A detailed discussion of such an approach will be presented in [44].…”