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arXiv:1611.07229 · Physical Review A

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

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

Published Feb 8, 2017• 9 citations
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Abstract

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 $1/{R}^{3}$, the effective $s$-wave potential decreases more rapidly as $1/{R}^{4}$ 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 $s$-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.

DOI
10.1103/physreva.95.023405

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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.
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 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.
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.
The interaction between atoms behaves as $\ensuremath{-}\ensuremath{\alpha}{/r}^{n}$ at large distances and, owing to the large reduced mass \ensuremath{\mu} of the collision pair, allows a semiclassical treatment within the potential well. As a result, the low-energy scattering is governed by two large parameters: the asymptotic parameter $\ensuremath{\gamma}=\sqrt{2\ensuremath{\mu}\ensuremath{\alpha}}/\ensuremath{\Elzxh}\ensuremath{\gg}{a}_{0}^{(n\ensuremath{-}2)/2}$ (a0{a}_{0}a0​ is the Bohr radius) and the semiclassical zero-energy phase $\ensuremath{\Phi}\ensuremath{\gg}1.$ In our previous work [Phys. Rev. A 48, 546 (1993)] we obtained an analytical expression for the scattering length a,a,a, which showed that it has 75% preference for positive values for n=6,n=6,n=6, characteristic of collisions between ground-state neutral atoms. In this paper we calculate the effective range and show that it is a function of a,a,a, ${r}_{e}{=F}_{n}\ensuremath{-}{G}_{n}{/a+H}_{n}{/a}^{2},$ where Fn,{F}_{n},Fn​, Gn,{G}_{n},Gn​, and Hn{H}_{n}Hn​ depend only on \ensuremath{\gamma}. Thus, we know the sss-phase shift at low momenta $k\ensuremath{\ll}{\ensuremath{\gamma}}^{\ensuremath{-}2/(n\ensuremath{-}2)}$ from the expansion $k\mathrm{cot}{\ensuremath{\delta}}_{0}\ensuremath{\simeq}\ensuremath{-}1/a+\frac{1}{2}{r}_{e}{k}^{2}.$ At $k\ensuremath{\gg}{\ensuremath{\gamma}}^{\ensuremath{-}2/(n\ensuremath{-}2)}$ the phase shift is obtained semiclassically as ${\ensuremath{\delta}}_{0}=\ensuremath{\Phi}+\ensuremath{\pi}/4\ensuremath{-}{I}_{n}{\ensuremath{\gamma}}^{2/n}{k}^{(n\ensuremath{-}2)/n},$ where ${I}_{n}=[n/(n\ensuremath{-}2)]\ensuremath{\Gamma}((n\ensuremath{-}1)/n)\ensuremath{\Gamma}((n+2)/2n)/\sqrt{\ensuremath{\pi}}.$ Therefore, \ensuremath{\gamma} and \ensuremath{\Phi} determine the sss-wave atomic scattering in a wide range of momenta, as well as the positions of upper bound states of the diatomic molecule.
By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the sss-wave scattering lengths of all 28 pairs of the seven stable isotopes. The sss-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for 168Yb^{168}\text{Y}\text{b}168Yb, 3.38(11) nm for 170Yb^{170}\text{Y}\text{b}170Yb, $\ensuremath{-}0.15(19)\text{ }\text{nm}$ for 171Yb^{171}\text{Y}\text{b}171Yb, $\ensuremath{-}31.7(3.4)\text{ }\text{nm}$ for 172Yb^{172}\text{Y}\text{b}172Yb, 10.55(11) nm for 173Yb^{173}\text{Y}\text{b}173Yb, 5.55(8) nm for 174Yb^{174}\text{Y}\text{b}174Yb, and $\ensuremath{-}1.28(23)\text{ }\text{nm}$ for 176Yb^{176}\text{Y}\text{b}176Yb. The coefficient of the lead term of the long-range van der Waals potential of the Yb2{\text{Yb}}_{2}Yb2​ molecule is C6=1932(30){C}_{6}=1932(30)C6​=1932(30) atomic units $({E}_{h}{a}_{0}^{6}\ensuremath{\approx}9.573\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{J}\text{ }{\text{nm}}^{6})$.
The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic n=2n=2n=2 singlet and triplet states, respectively, He(21S)\mathrm{He}(2{}^{1}S)He(21S) and He(23S)\mathrm{He}(2{}^{3}S)He(23S). The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two He(21S)\mathrm{He}(2{}^{1}S)He(21S) or two He(23S)\mathrm{He}(2{}^{3}S)He(23S) atoms and for the atom-surface interaction potentials of a He(21S)\mathrm{He}(2{}^{1}S)He(21S) or a He(23S)\mathrm{He}(2{}^{3}S)He(23S) atom with a perfectly conducting or a dielectric wall.