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Physical Review A

Chirped fields for Rb+Cs photoassociation

A. Homer, Gareth O. Roberts

Published Nov 11, 2008• 8 citations
Publisher

Abstract

This paper presents model numerical simulations of photoassociation and ionization of cold $\mathrm{Rb}+\mathrm{Cs}$ atoms steered by broadband optical pulses operating within the weak-field limit over a picosecond time scale. The primary focus of the work is on generation of RbCs molecules in bound levels of the $(1){0}^{+}$ $(X^{1}\ensuremath{\Sigma}^{+})$ electronic ground state through a sequence of pump-dump transitions between $(1){0}^{+}$ and $(4){0}^{+}$ states driven by a field centered at $811\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with different phase modulations. It is found that chirped fields generate substantially bound oscillator levels of the $X^{1}\ensuremath{\Sigma}^{+}$ state by avoiding promotion of amplitude to vibrational levels in the upper state whose Franck-Condon factors for stimulated emission to levels in the $X^{1}\ensuremath{\Sigma}^{+}$ state are detrimentally low, but which otherwise come into play when the driving field is transform limited. Optimal generation of molecules in the electronic ground state irrespective of vibrational level selectivity is calculated to occur when the temporal phase of the driving field is modulated by the classical energy difference for promotion of $(4){0}^{+}\ensuremath{\leftarrow}(1){0}^{+}$ photon absorption. Conversely, generation of deeply bound vibrational eigenlevels of the $X^{1}\ensuremath{\Sigma}^{+}$ state is optimally promoted by a field whose temporal phase enhances $(4){0}^{+}\ensuremath{\rightarrow}(1){0}^{+}$ stimulated emission. Driving fields phase modulated by the classical difference potential or linearly down-chirped enhance molecule formation vis-\`a-vis the thermal collision; fields whose temporal phase is modulated according to the shape of the $(1){0}^{+}$ potential energy curve or which are linearly up-chirped suppress molecule formation relative to the thermal probability, but generate deeply bound $X^{1}\ensuremath{\Sigma}^{+}$ vibrational levels. Application of a bichromatic field comprising temporally overlapped components centered 811 and $622\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ also improves the probability of generating deeply bound vibrational levels, but at the expense of increased ionization. Model calculations of transition probabilities between neutral and ionic states of the collision lead to the conclusions that: transitions to individual vibrational levels of the $X^{1}\ensuremath{\Sigma}^{+}$ state occur with a higher probability than resonant three-photon ionization prompted by a single-color field at $811\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$; and application of bichromatic light at 811 and $622\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ preferentially ionizes the incipient molecule via a two-color two-photon absorption, the likelihood of which masks the occupation of deeply bound $X^{1}\ensuremath{\Sigma}^{+}$ oscillator levels.

DOI
10.1103/physreva.78.053404

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This paper presents model numerical simulations of photoassociation and ionization of cold Rb+Cs atoms steered by broadband optical pulses operating within the weak-field limit over a picosecond time scale. The primary focus of the work is on generation of RbCs molecules in bound levels of the (1)0(+) (X-1 Sigma(+)) electronic ground state through a sequence of pump-dump transitions between (1)0(+) and (4)0(+) states driven by a field centered at 811 nm with different phase modulations. It is found that chirped fields generate substantially bound oscillator levels of the X-1 Sigma(+) state by avoiding promotion of amplitude to vibrational levels in the upper state whose Franck-Condon factors for stimulated emission to levels in the X-1 Sigma(+) state are detrimentally low, but which otherwise come into play when the driving field is transform limited. Optimal generation of molecules in the electronic ground state irrespective of vibrational level selectivity is calculated to occur when the temporal phase of the driving field is modulated by the classical energy difference for promotion of (4)0(+)(1)0(+) stimulated emission. Driving fields phase modulated by the classical difference potential or linearly down-chirped enhance molecule formation vis-a-vis the thermal collision; fields whose temporal phase is modulated according to the shape of the (1)0(+) potential energy curve or which are linearly up-chirped suppress molecule formation relative to the thermal probability, but generate deeply bound X-1 Sigma(+) vibrational levels. Application of a bichromatic field comprising temporally overlapped components centered 811 and 622 nm also improves the probability of generating deeply bound vibrational levels, but at the expense of increased ionization. Model calculations of transition probabilities between neutral and ionic states of the collision lead to the conclusions that: transitions to individual vibrational levels of the X-1 Sigma(+) state occur with a higher probability than resonant three-photon ionization prompted by a single-color field at 811 nm; and application of bichromatic light at 811 and 622 nm preferentially ionizes the incipient molecule via a two-color two-photon absorption, the likelihood of which masks the occupation of deeply bound X-1 Sigma(+) oscillator levels.
The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the 85 Rb(5S 1/2 ) + 133 Cs(6P 3/2 ) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0 + or the 4th 0 − electronic states correlated to the Rb(5P 1/2, 3/2 ) + Cs(6S 1/2 ) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state.
We investigate the dynamics of molecular photoexcitation by unchirped femtosecond laser pulses using RbCs as a model system. This study is motivated by a goal of optimizing a two-color scheme of transferring vibrationally excited ultracold molecules to their absolute ground state. In this scheme the molecules are initially produced by photoassociation or magnetoassociation in bound vibrational levels close to the first dissociation threshold. We analyze here the first step of the two-color path as a function of pulse intensity from the low-field to the high-field regime. We use two different approaches, a global one, the ``wave-packet'' method, and a restricted one, the ``level-by-level'' method, where the number of vibrational levels is limited to a small subset. The comparison between the results of the two approaches allows one to gain qualitative insights into the complex dynamics of the high-field regime. In particular, we emphasize the nontrivial and important role of far-from-resonance levels which are adiabatically excited through ``vertical'' transitions with a large Franck-Condon factor. We also point out the spectacular excitation blockade due to the presence of a quasidegenerate level in the lower electronic state. We conclude that selective transfer with femtosecond pulses is possible in the low-field regime only. Finally, we extend our single-pulse analysis and examine population transfer induced by coherent trains of low-intensity femtosecond pulses.
The formations of 85Rb2{}^{85}{\text{Rb}}_{2}85Rb2​ molecules via photoassociation (PA) steered by two-color laser fields are explored theoretically in order to find an efficient and robust PA scheme. The PA processes steered by the PA pulses modulated by two Gaussian pulses and by two chirped pulses are discussed and compared in detail. The two pulses are coherent in the picosecond range and reach their maxima at the same time. The influences of the linear chirp rate, the frequency difference between two pulses, and the phase shift of the modulated envelope with respect to the maximum of the Gaussian envelope on the PA process are investigated. The yield of photoassociated molecules on vibrational levels with a binding energy of $>1.0cm1.0 cm1.0cm{}^{\ensuremath{-}1}$ with respect to the 5S+5P1/25S+5{P}_{1/2}5S+5P1/2​ dissociation limit can apparently be enhanced by choosing proper pulse parameters. Especially, the two-color laser field modulated by two chirped pulses can raise the PA efficiency on one side, and weaken the dependence of the PA process on phase shift on the other side.
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We have produced ultracold, polar RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound $X\text{ }^{1}\ensuremath{\Sigma}^{+}$ ground-state RbCs vibrational levels as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.