Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Observation of a Shape Resonance in Cold-Atom Scattering by Pulsed Photoassociation

H. M. J. M. Boesten, Chin‐Chun Tsai, BOUDEWIJN J. VERHAAR, Daniel J. Heinzen

Published Dec 23, 1996• 96 citations
Publisher

Abstract

We observe the time dependence of a cold-atom collision in a pulsed photoassociation experiment. For a $g$-wave shape resonance in the ${}^{85}\mathrm{Rb}{+}^{85}\mathrm{Rb}$ system we measure the time needed to build up the resonant state by tunneling through the centrifugal barrier. Combining this with time-independent ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ photoassociation we determine the resonance energy and find evidence for the decay of the shape resonance into inelastic channels. We also determine the ${}^{85}\mathrm{Rb}+{}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}{+}^{87}\mathrm{Rb}$ ${C}_{6}$ coefficient and triplet scattering lengths without relying on ab initio calculations.

DOI
10.1103/physrevlett.77.5194

Related papers

Observation of a shape resonance in the collision of two cold Rb87 atoms

H. M. J. M. Boesten, Chin‐Chun Tsai, Jamie Ryan Gardner +2 more

We observe a shape resonance in the scattering of two ultracold $^{87}\mathrm{Rb}$ atoms, causing the colliding atoms to form a long-living compound system inside an l=2 centrifugal barrier. Its existence follows from a photoassociation experiment in a gas sample of doubly polarized $^{87}\mathrm{Rb}$ atoms. Using it we are able to carry out direct determinations of the triplet scattering length for $^{87}\mathrm{Rb}$, relevant to Bose-Einstein condensation experiments, and of the Rb+Rb ${\mathrm{C}}_{6}$ dispersion coefficient. Consequences for the $^{85}\mathrm{Rb}$ scattering length are discussed.

Physical Review A•Jan 1, 1997•127 citations

Time-independent and time-dependent photoassociation of spin-polarized rubidium

H. M. J. M. Boesten, Chin‐Chun Tsai, Daniel J. Heinzen +2 more

We extract information about collisions of ultra-cold ground-state rubidium atoms from observations of a g-wave shape resonance in the 85Rb + 85Rb system via time-independent and time-dependent photoassociation. The shape resonance arises from a quasi-bound state inside a centrifugal barrier that enhances the excitation to the bound electronically excited state by the photoassociation laser in the time-independent experiment. The shape resonance is sufficiently long-lived that its build-up through the barrier can be observed by first depleting it via a photoassociation laser pulse and then measuring the rate of photoassociation by a second laser pulse with a variable delay time. A combined method of analysis of the time-independent and time-dependent experiments is presented. We discuss the spectroscopy of states of two particles with spin trapped inside a centrifugal barrier, interacting via direct and indirect spin-spin interactions.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 1, 1999•20 citations

Shape resonances in ground-state diatomic molecules: General trends and the example of RbCs

B. E. Londoño, Jorge Mahecha, Eliane Luc-Koenig +1 more

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 $^{85}\mathrm{Rb}$$^{133}\mathrm{Cs}$ 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 $s$-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.

Physical Review A•Jul 29, 2010•30 citations

Determination of 39K scattering lengths using photoassociation spectroscopy of the 0g− state

James P. Burke, Chris H. Greene, John L. Bohn +3 more

Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u., ${C}_{6}=3800$ a.u.

Physical Review A•Dec 1, 1999•35 citations

Effect of Rotations and Shape Resonances on Photoassociation and Photoacceleration by Short Infrared Laser Pulses

Peter Backhaus, Jörn Manz, Burkhard Schmidt

A quantum dynamical description of an atomic collision pair interacting with the electric field of a short infrared laser pulse is developed. Inelastic processes in the electronic ground state are due to stimulated emission resulting in photoassociation, or absorption leading to photoacceleration. A perturbative approach based on a state space representation is compared with a numerical treatment using a grid representation in coordinate space. Special emphasis is on the role of rotations and, in particular, of shape resonances. It is shown that these quasibound states which are supported by the centrifugal barrier (for J ≠ 0) can be used as initial states to effectively populate a selected bound state with specific vibrational and rotational quantum number (photoassociation), or a partial wave of a scattering state with defined energy and rotational quantum number (photoacceleration). Simulations are carried out for the prototype H + Cl collision pair. Also the effect of averaging over initial conditions (velocity, angular momenta) is investigated for a supersonic beam experiment. For a narrow velocity distribution, we predict the presence of a resonance structure of the association and acceleration probability as a function of the mean collision energy.

The Journal of Physical Chemistry A•Feb 12, 1998•14 citations

Photoassociative Spectroscopy as a Self-Sufficient Tool for the Determination of the Cs Triplet Scattering Length

Cyril Drag, B. Laburthe-Tolra, B. T'Jampens +4 more

In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the $s$-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel $f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$, ${m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$. We analyzed the intensities of the lines associated with the ${\mathrm{Cs}}_{2}$ ${0}_{g}^{\ensuremath{-}}$ state dissociating to the ${6s}_{1/2}{+6p}_{3/2}$ asymptote. This yields a value of the Cs triplet state scattering length, ${a}_{T}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}530a}_{0}$, while consistency requirements impose a value of the multipole ground state molecular coefficient, ${C}_{6}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6510$ a.u.

Physical Review Letters•Aug 14, 2000•40 citations
We observe the time dependence of a cold-atom collision in a pulsed photoassociation experiment. For a ggg-wave shape resonance in the 85Rb+85Rb{}^{85}\mathrm{Rb}{+}^{85}\mathrm{Rb}85Rb+85Rb system we measure the time needed to build up the resonant state by tunneling through the centrifugal barrier. Combining this with time-independent 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb{}^{87}\mathrm{Rb}87Rb photoassociation we determine the resonance energy and find evidence for the decay of the shape resonance into inelastic channels. We also determine the 85Rb+85Rb{}^{85}\mathrm{Rb}+{}^{85}\mathrm{Rb}85Rb+85Rb and 87Rb+87Rb{}^{87}\mathrm{Rb}{+}^{87}\mathrm{Rb}87Rb+87Rb C6{C}_{6}C6​ coefficient and triplet scattering lengths without relying on ab initio calculations.
We observe a shape resonance in the scattering of two ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms, causing the colliding atoms to form a long-living compound system inside an l=2 centrifugal barrier. Its existence follows from a photoassociation experiment in a gas sample of doubly polarized 87Rb^{87}\mathrm{Rb}87Rb atoms. Using it we are able to carry out direct determinations of the triplet scattering length for 87Rb^{87}\mathrm{Rb}87Rb, relevant to Bose-Einstein condensation experiments, and of the Rb+Rb C6{\mathrm{C}}_{6}C6​ dispersion coefficient. Consequences for the 85Rb^{85}\mathrm{Rb}85Rb scattering length are discussed.
We extract information about collisions of ultra-cold ground-state rubidium atoms from observations of a g-wave shape resonance in the 85Rb + 85Rb system via time-independent and time-dependent photoassociation. The shape resonance arises from a quasi-bound state inside a centrifugal barrier that enhances the excitation to the bound electronically excited state by the photoassociation laser in the time-independent experiment. The shape resonance is sufficiently long-lived that its build-up through the barrier can be observed by first depleting it via a photoassociation laser pulse and then measuring the rate of photoassociation by a second laser pulse with a variable delay time. A combined method of analysis of the time-independent and time-dependent experiments is presented. We discuss the spectroscopy of states of two particles with spin trapped inside a centrifugal barrier, interacting via direct and indirect spin-spin interactions.
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.
Threshold scattering properties of 39K{}^{39}\mathrm{K}39K atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u., C6=3800{C}_{6}=3800C6​=3800 a.u.
A quantum dynamical description of an atomic collision pair interacting with the electric field of a short infrared laser pulse is developed. Inelastic processes in the electronic ground state are due to stimulated emission resulting in photoassociation, or absorption leading to photoacceleration. A perturbative approach based on a state space representation is compared with a numerical treatment using a grid representation in coordinate space. Special emphasis is on the role of rotations and, in particular, of shape resonances. It is shown that these quasibound states which are supported by the centrifugal barrier (for J ≠ 0) can be used as initial states to effectively populate a selected bound state with specific vibrational and rotational quantum number (photoassociation), or a partial wave of a scattering state with defined energy and rotational quantum number (photoacceleration). Simulations are carried out for the prototype H + Cl collision pair. Also the effect of averaging over initial conditions (velocity, angular momenta) is investigated for a supersonic beam experiment. For a narrow velocity distribution, we predict the presence of a resonance structure of the association and acceleration probability as a function of the mean collision energy.
In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the sss-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f=4f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4f=4, mf=4{m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4mf​=4. We analyzed the intensities of the lines associated with the Cs2{\mathrm{Cs}}_{2}Cs2​ ${0}_{g}^{\ensuremath{-}}$ state dissociating to the 6s1/2+6p3/2{6s}_{1/2}{+6p}_{3/2}6s1/2​+6p3/2​ asymptote. This yields a value of the Cs triplet state scattering length, ${a}_{T}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}530a}_{0}$, while consistency requirements impose a value of the multipole ground state molecular coefficient, C6=6510{C}_{6}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6510C6​=6510 a.u.