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Laser Physics

Creation of ultracold Cs2molecules via two-step photoassociation with Gaussian and chirped pulses

Yin Hui Huang, Ting Xie, Gao‐Ren Wang, Wei Zhang, Shu‐Lin Cong

Published Mar 18, 2014• 8 citations
Publisher

Abstract

An efficient two-step photoassociation (PA) scheme is used to produce ultracold Cs 2 molecules in the excited electronic state. By using the compression effect of the wavepacket in the ground electronic state induced by the Gaussian pulse L 1 , the PA efficiency P L of forming ultracold molecules in the excited electronic state with binding energies greater than 3.0 cm −1 steered by the pulse L 2 can be efficiently enhanced. The influences of temporal width, electric field amplitude and chirp rate on the PA dynamics are analyzed. Moreover, the total PA efficiency is also estimated when the thermal distribution is taken into account.

DOI
10.1088/1054-660x/24/4/046001

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An efficient two-step photoassociation (PA) scheme is used to produce ultracold Cs 2 molecules in the excited electronic state. By using the compression effect of the wavepacket in the ground electronic state induced by the Gaussian pulse L 1 , the PA efficiency P L of forming ultracold molecules in the excited electronic state with binding energies greater than 3.0 cm −1 steered by the pulse L 2 can be efficiently enhanced. The influences of temporal width, electric field amplitude and chirp rate on the PA dynamics are analyzed. Moreover, the total PA efficiency is also estimated when the thermal distribution is taken into account.
We investigate theoretically the formation of ultracold Cs2 molecules via photoassociation (PA) with three kinds of pulses (the Gaussian pulse, the asymmetric shaped laser pulse SL1 with a large rising time and a small falling time and the asymmetric shaped laser pulse SL2 with a small rising time and a large falling time). For the three kinds of pulses, the final population on vibrational levels from v′ = 120 to 175 of the excited state displays a regular oscillation change with pulse width and interaction strength, and a high PA efficiency can be achieved with optimised parameters. The PA efficiency in the excited state steered by the SL1-pulse (SL2-pulse) train with optimised parameters which is composed of four SL1 (SL2) pulses is 1.74 times as much as that by the single SL1 (SL2) pulse due to the population accumulation effect. Moreover, a dump laser is employed to transfer the excited molecules from the excited state to the vibrational level v″ = 12 of the ground state to obtain stable molecules.
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.
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.
We present results on the effects of nanosecond-timescale frequency-chirped laser light on the formation of 87Rb2 ultracold ground-state molecules. We investigate these effects through photoassociation (PA) experiments and quantum mechanical simulations. The PA experiments show that at higher intensities, the positive chirps have a higher formation rate than the unchirped or negative linear chirps. The quantum mechanical simulations reveal the mechanism responsible for this enhancement. Contributions from stimulated emission cause the positive chirp to be the most efficient for molecule formation.
The formation of ultracold Cs 2 molecules via photoassociation (PA) with a spectral π-jump laser pulse is theoretically investigated by solving the time-dependent Schrödinger equation using the mapped Fourier grid method. Numerical calculations show that the population distributions of associated molecules mainly result from the off-resonant excitation of the π-jump laser pulse. Compared with the transform-limited pulse, an efficient population accumulation in the PA process is achieved with the π-jump pulse. An oscillation pattern appears in the population on the vibrational levels of the state owing to the action of the post-half-pulse in the π-jump pulse. The PA efficiency is related to the Rabi angle of the laser pulse. A π-jump pulse can be used to enhance more effectively the PA efficiency than a transform-limited pulse with the same Rabi angle.
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.