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Laser Physics

Photoassociation dynamics driven by second- and third-order phase-modulated laser fields

Meng Wang, Maodu Chen, Xue‐Jin Hu, Jing-Lun Li, Shu‐Lin Cong

Published Apr 11, 2016• 2 citations
Publisher

Abstract

Abstract We investigate theoretically the photoassociation dynamics of ultracold 85 Rb atoms driven by second- and third-order phase-modulated laser fields. The interplay between the second-order and third-order terms of the phase-modulated pulse has an obvious influence on photoassociation dynamics. The different combinations of the second-order and third-order phase coefficients lead to different pulse shapes. Most of the molecular population in the excited electronic state driven only by the third-order phase pulses can be distributed in a single vibrational level. The second-order term of the phase-modulated pulse can change the instantaneous frequency, and therefore the final population is distributed on several resonant vibrational levels, instead of concentrating on a single level. Although the second- and third-order phase-modulated pulse covers more resonant vibrational levels, the total population on the resonant vibrational levels is much smaller than that controlled only by the third-order phase pulse. In particular, the third-order term of the phase-modulated pulse can weaken the ‘multiple interaction’ to some degree.

DOI
10.1088/1054-660x/26/5/055005

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Abstract We investigate theoretically the photoassociation dynamics of ultracold 85 Rb atoms driven by second- and third-order phase-modulated laser fields. The interplay between the second-order and third-order terms of the phase-modulated pulse has an obvious influence on photoassociation dynamics. The different combinations of the second-order and third-order phase coefficients lead to different pulse shapes. Most of the molecular population in the excited electronic state driven only by the third-order phase pulses can be distributed in a single vibrational level. The second-order term of the phase-modulated pulse can change the instantaneous frequency, and therefore the final population is distributed on several resonant vibrational levels, instead of concentrating on a single level. Although the second- and third-order phase-modulated pulse covers more resonant vibrational levels, the total population on the resonant vibrational levels is much smaller than that controlled only by the third-order phase pulse. In particular, the third-order term of the phase-modulated pulse can weaken the ‘multiple interaction’ to some degree.
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.
Photoassociation (PA) dynamics of ultracold cesium atoms steered by a modulated two-color laser field $\phantom{\rule{4pt}{0ex}}E(t)={E}_{0}f(t)\mathrm{cos}(\frac{2\ensuremath{\pi}}{{T}_{p}}\ensuremath{-}\ensuremath{\varphi})\mathrm{cos}({\ensuremath{\omega}}_{L}t)$ is investigated theoretically by numerically solving the time-dependent Schr\"odinger equation. The PA dynamics is sensitive to the phase of envelope (POE) $\ensuremath{\varphi}$ and the period of the envelope Tp{T}_{p}Tp​, which indicates that it can be controlled by varying POE $\ensuremath{\varphi}$ and period Tp{T}_{p}Tp​. Moreover, we introduce the time- and frequency-resolved spectrum to illustrate how the POE $\ensuremath{\varphi}$ and the period Tp{T}_{p}Tp​ influence the intensity distribution of the modulated laser pulse and hence change the time-dependent population distribution of photoassociated molecules. When the Gaussian envelope contains a few oscillations, the PA efficiency is also dependent on POE $\ensuremath{\varphi}$. The modulated two-color laser field is available in the current experiment based on laser mode-lock technology.
Photoassociation of ultracold atoms with pulsed laser light is shown to lead to alignment of the product molecules along the excitation laser polarization axis. We theoretically investigate pulsed two-photon photoassociation of 87Rb^{87}\mathrm{Rb}87Rb atoms into a specific weakly bound level of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ metastable electronic state and find both stationary and time-dependent field-free alignment. Although a transform-limited pulse yields significant alignment, a frequency-chirped pulse dramatically enhances the ultracold molecular formation rate at the cost of a slight decrease in the alignment. Employing multiple pulses synchronized with the vibrational and rotational periods leads to coherent enhancement of both population and alignment of the target state. Inclusion of the rotational degree of freedom in the model gives rise to processes with multiple quantum paths, which lead to quantum effects such as interference and coherence revivals.
Photoassociation of ultracold rubidium atoms with femtosecond laser pulses is studied theoretically. The spectrum of the pulses is cut off in order to suppress pulse amplitude at and close to the atomic resonance frequency. This leads to long tails of the laser pulse as a function of time giving rise to coherent transients in the photoassociation dynamics. They are studied as a function of cut-off position and chirp of the pulse. Molecule formation in the electronically excited state is attributed to off-resonant excitation in the strong-field regime.
This paper presents calculation results for the photoassociation of a NaK molecule with a two-color modulated laser and gives a detailed analysis about them. For the two-step photoassociation process in intense fields, the effect of two-color modulated laser parameters, such as relative phase, envelope period, and laser intensity, on the population of the molecular electronic state can be obtained by solving the time-dependent Schrödinger equation through the quantum wave packet method. The numerical simulation shows not only that the influence of laser parameters on the vibrational distribution presents some regularity, but also that a higher population in the ground electronic state can be realized through adjusting these laser parameters.
This theoretical paper presents numerical calculations for the photoassociation of ultracold cesium atoms with a chirped laser pulse and a detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wave function. In the chosen example, it is shown that an important population transfer is achieved to $\ensuremath{\approx}15$ vibrational levels in the vicinity of the v=98v=98v=98 bound level in the external well of the ${0}_{g}^{\ensuremath{-}}(6s+6{p}_{3∕2})$ potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a ``photoassociation window.'' Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\sum}_{u}^{+}(6\mathrm{s}+6\mathrm{s})$ state is significant, making stable molecules. The results are interpreted in the framework of a two-state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating in the excited state a vibrational wave packet that is focusing at the barrier of the double-well potential.