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arXiv:physics/0404028 · Physical Review A

Photoassociation of cold atoms with chirped laser pulses: Time-dependent calculations and analysis of the adiabatic transfer within a two-state model

Eliane Luc-Koenig, Ronnie Kosloff, Françoise Masnou-Seeuws, Mihaela Vatasescu

Published Sep 27, 2004• 107 citations
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Abstract

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 $v=98$ 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.

DOI
10.1103/physreva.70.033414

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Journal of Theoretical and Computational Chemistry•Dec 1, 2012•7 citations
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≈15\ensuremath{\approx}15\ensuremath≈15 vibrational levels in the vicinity of the v=98v=98v=98 bound level in the external well of the 0g\ensuremath−(6s+6p3∕2){0}_{g}^{\ensuremath{-}}(6s+6{p}_{3∕2})0g\ensuremath−​(6s+6p3∕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 a3\ensuremath∑u+(6s+6s)a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\sum}_{u}^{+}(6\mathrm{s}+6\mathrm{s})a3\ensuremath∑u+​(6s+6s) 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.
Enhancement of the production of cold molecules via photoassociation is considered for the Cs2{\mathrm{Cs}}_{2}Cs2​ system. The employment of chirped picosecond pulses is proposed and studied theoretically. The analysis is based on the ability to achieve impulsive excitation which is given by the ultracold initial conditions where the nuclei are effectively stationary during the interaction with a field. The appropriate theoretical framework is the coordinate-dependent two-level system. Matching the pulse parameters to the potentials and initial conditions results in full Rabi cycling between the electronic potentials. By chirping the laser pulse, adiabatic transfer leading to the population inversion from the ground to the excited state is possible in a broad and tunable range of internuclear distance. Numerical simulations based on solving the time-dependent Schr\"odinger equation (TDSE) were performed. The simulation of the photoassociation of Cs2{\mathrm{Cs}}_{2}Cs2​ from the ground ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ to the excited ${0}_{g}^{\ensuremath{-}}$ state under ultracold conditions verifies the qualitative picture. The ability to control the population transfer is employed to optimize molecular formation. Transfer of population to the excited ${0}_{g}^{\ensuremath{-}}$ surface leaves a void in the nuclear density of the ground ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ surface. This void is either filled by thermal motion or by quantum ``pressure'' and it is the rate-determining step in the photoassociation. The spontaneous-emission process leading to cold-molecules is simulated by including an optical potential in the TDSE. Consequently, the rate of cold molecule formation in a pulsed mode is found to be larger than that obtained in a continuous-wave mode.
This dissertation presents the study of how two laser pulses can bind sodium and cesium atoms at ultracold temperature (T=200muKT=200\\mu KT=200muK) into an ultracold, polar, diatomic molecule with a definite quantum state. \nA single-channel scattering model represents the initial continuum state, and two different models represent the intermediate state: one excluding spin-orbit coupling effects in the intermediate state, the other accounting for such effects. \nWe calculate the A1Sigma+−b3PiA^1\\Sigma^+-b^3\\PiA1Sigma+−b3Pi spin-orbit coupled wave functions using a basis expansion technique, and validate the results by comparing to experimentally obtained, spin-orbit coupled energy levels. \nThe computation of photoassociation rates between the continuum state and the intermediate states reveals the crucial importance of spin-orbit coupling. \nFurthermore, this study shows how the spectral bandwidth (narrow \\vs broad), the chirping (chirped vs. unchirped), the detunings, the intensities, and the pulse delay (intuitive \\vs counter-intuitive sequence) of the lasers affect the transfer of population from the continuum scattering state to a comparatively low-lying (vX=32,JX=0v_X=32, J_X=0vX​=32,JX​=0) rovibrational state of the X1Sigma+X^1\\Sigma^+X1Sigma+ ground electronic state of NaCs. \nThe transfer process relies either on a sequence of pi\\pipi-pulses, or uses stimulated Raman adiabatic passage (STIRAP). \nLasers with narrow spectral bandwidth (0.5GHz0.5\\GHz0.5GHz) always yield a final population in ketX1Sigma+,vX=32,JX=0\\ket{X^1\\Sigma^+, v_X=32, J_X=0}ketX1Sigma+,vX​=32,JX​=0 higher than 95\\% in less than 4 ns.
This theoretical paper investigates the formation of ground state molecules from ultracold cesium atoms in a two-color scheme. Following previous work on photoassociation with chirped picosecond pulses [Luc-Koenig et al., Phys. Rev. A, 70, 033414 (2004)], we investigate stabilization by a second (dump) pulse. By appropriately choosing the dump pulse parameters and time delay with respect to the photoassociation pulse, we show that a large number of deeply bound molecules are created in the ground triplet state. We discuss (i) broad-bandwidth dump pulses which maximize the probability to form molecules while creating a broad vibrational distribution as well as (ii) narrow-bandwidth pulses populating a single vibrational ground state level, bound by $113\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The use of chirped pulses makes the two-color scheme robust, simple, and efficient.
Photoassociation of a pair of cold atoms by excitation with a short chirped laser pulse creates a dynamical hole in the initial continuum wave function. This hole is manifested by a void in the pair wave function and a momentum kick. Photoassociation into loosely bound levels of the external well in ${\mathrm{Cs}}_{2}\phantom{\rule{0.3em}{0ex}}{0}_{g}^{\ensuremath{-}}(6S+6{P}_{3∕2})$ is considered as a case study. After the pulse, the free evolution of the ground triplet state $a^{3}\ensuremath{\Sigma}_{u}^{+}$ wave packet is analyzed. Due to a negative momentum kick, motion to small distances is manifested and a compression effect is pointed out, markedly increasing the density of atom pairs at short distance. A consequence of the hole is the redistribution of the vibrational population in the $a^{3}\ensuremath{\Sigma}_{u}^{+}$ state, with population of the last bound level and creation of pairs of hot atoms. The physical interpretation makes use of the time dependence of the mass current and population on each channel to understand the role of the parameters of the photoassociation pulse. By varying such parameters, optimization of the compression effect in the ground-state wave packet is demonstrated. Due to an increase of the short-range probability density by more than two orders of magnitude, we predict significant gain in the photoassociation rates into deeply bound levels of the excited state by a second pulse, red-detuned relative to the first one, and conveniently delayed.
We investigate theoretically the preparation of ultracold photoassociated Cs 2 molecules in the lowest vibrational level of the ground electronic state via the stimulated Raman adiabatic passage (STIRAP) by solving the time-dependent Schrödinger equation using the mapped Fourier grid method. A negative chirped laser pulse is used to produce the unstable photoassociated molecules in the excited electronic state. A dump pulse is utilized to transfer a partial population of the unstable photoassociated molecules to the vibrational v″ = 18 level of the ground electronic state. This part of population is then transferred to the v″ = 0 level of the ground electronic state by the pump and Stokes laser pulses via an intermediate state which is taken to be the v′ = 7 level of the excited electronic state, forming the stable photoassociated molecules. The population transfer efficiency from v″ = 18 to v″ = 0 in the ground electronic state reaches 96.2% via the STIRAP.