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arXiv:1412.7315 · New Journal of Physics

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

A. Crubellier, Rosario González‐Férez, Christiane P. Koch, Eliane Luc-Koenig

Published Apr 27, 2015• 6 citations
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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.

DOI
10.1088/1367-2630/17/4/045022

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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.
We derive a universal model for atom pairs interacting with non-resonant light via the polarizability anisotropy, based on the long range properties of the scattering. The corresponding dynamics can be obtained using a nodal line technique to solve the asymptotic Schrödinger equation. It consists of imposing physical boundary conditions at long range and vanishing the wavefunction at a position separating the inner zone and the asymptotic region. We show that nodal lines which depend on the intensity of the non-resonant light can satisfactorily account for the effect of the polarizability at short range. The approach allows to determine the resonance structure, energy, width, channel mixing and hybridization even for narrow resonances.
The presence of shape resonances due to tunneling through the centrifugal barrier modifies strongly the dynamics of cold atom scattering. As shown on the example of the ground and lowest triplet electronic states of the 85Rb^{85}\mathrm{Rb}85Rb133Cs^{133}\mathrm{Cs}133Cs molecule, the crucial parameter is, as usual for cold collisions, the scattering length. A general description of shape resonances of diatomic molecules is given from three simple single channel asymptotic models, whose respective performances are discussed. The first model, which consists of a ${R}^{\ensuremath{-}6}$ potential limited at short range by a repulsive wall, positioned to reproduce the sss-wave scattering length, accounts satisfactorily for the main system-independent properties of shape resonances. Introduction in the model of energy- and angular-momentum-dependent nodal lines specific to the inner part of the potential greatly improves its efficiency. When the energy and angular momentum dependence of the nodal lines cannot be deduced from full potential calculations or from experiment, a rough, but universal, estimate of these properties is obtained by extending the ${R}^{\ensuremath{-}6}$ behavior of the potential up to the origin.
A pair of atoms interacts with nonresonant light via its anisotropic polarizability. This effect can be used to tune the scattering properties of the atoms. Although the light-atom interaction varies with interatomic separation as 1/R31/{R}^{3}1/R3, the effective sss-wave potential decreases more rapidly as 1/R41/{R}^{4}1/R4 such that the field-dressed scattering length can be determined without any formal difficulty. The scattering dynamics are essentially governed by the long-range part of the interatomic interaction and can thus be accurately described by an asymptotic model [A. Crubellier et al., New J. Phys. 17, 045020 (2015)]. Here we use the asymptotic model to determine the field-dressed scattering length from the sss-wave radial component of a particular threshold wave function. Applying our theory to the scattering of two strontium isotopes, we calculate the variation of the scattering length with the intensity of the nonresonant light. Moreover, we predict the intensities at which the scattering length becomes infinite for any pair of atoms.
A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to 5×1095\times 10^{9}5×109 W/cm2^22 the pair density is increased by one order of magnitude for 87^{87}87Rb atoms at 100μ100 μ100μK and by two orders of magnitude for 88^{88}88Sr atoms at 20μ20 μ20μK.
Interactions in a spin-polarized ultracold Fermi gas are governed by ppp-wave collisions and can be characterized by the ppp-wave scattering volume. Control of these collisions by Feshbach resonances is hampered by huge inelastic losses. Here, we suggest nonresonant light control of ppp-wave collisions, exploiting the anisotropic coupling of nonresonant light to the polarizability of the atoms. The ppp-wave scattering volume can be controlled by strong nonresonant light, in close analogy to the sss-wave scattering length. For collision partners that are tightly trapped, the nonresonant light induces an energy shift directly related to the scattering volume (as defined by A. Crubellier, R. Gonz\'alez-F\'erez, C. P. Koch, and E. Luc-Koenig, preceding paper, Phys. Rev. A 99, 032709 (2019). This effect could be used to climb the ladder of the trap. We also show that controlling the scattering volume implies control, at least roughly, over the orientation at short interatomic distances of the interparticle axis relative to the polarization direction of the light. Our proposal is based on an asymptotic model that explicitly accounts for the anisotropic dipole-dipole interaction which governs the ultracold collision dynamics at long range.
We derive ultracold atom-atom photoassociation line shapes valid for intense light fields and investigate laser power effects in sodium and rubidium photoassociation to the purely long-range ${0}_{g}^{\ensuremath{-}}$ symmetry state. We consider intensities up to a few hundreds W/cm2,{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2},W/cm2, a strongly saturating intensity for typical transitions of experimental interest. For these intensities the ${0}_{g}^{\ensuremath{-}}$ rotational spectrum is still well resolved; however, it is essential to couple the photoassociation resonance to both s- and d-wave ground-state channels. A low-energy d-wave shape resonance can have a profound effect on the line shape. Understanding the line shape is essential for precision spectroscopic analysis and could improve the extraction of ground-state scattering properties such as scattering lengths.