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Chinese Physics B

Stabilizing photoassociated Cs2molecules by optimal control

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

Published Jan 1, 2013• 13 citations
Publisher

Abstract

We demonstrate theoretically that photoassociated molecules can be stabilized to deeply bound states. This process is achieved by transferring the population from the outer well to the inner well using the optimal control theory, the Cs 2 molecule is taken as an example. Numerical calculations show that weakly bound molecules formed in the outer well by a pump pulse can be compressed to the inner well via a vibrational level of the ground electronic state as an intermediary by an additionally optimized laser pulse. The positively chirped pulse can enhance the population of the target state. With a transform-limited dump pulse, nearly all the photoassociated molecules in the inner well of the excited electronic state can be transferred to the deeply vibrational level of the ground electronic state.

DOI
10.1088/1674-1056/22/1/013301

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We demonstrate theoretically that photoassociated molecules can be stabilized to deeply bound states. This process is achieved by transferring the population from the outer well to the inner well using the optimal control theory, the Cs 2 molecule is taken as an example. Numerical calculations show that weakly bound molecules formed in the outer well by a pump pulse can be compressed to the inner well via a vibrational level of the ground electronic state as an intermediary by an additionally optimized laser pulse. The positively chirped pulse can enhance the population of the target state. With a transform-limited dump pulse, nearly all the photoassociated molecules in the inner well of the excited electronic state can be transferred to the deeply vibrational level of the ground electronic state.
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.
We investigate the use of chirped laser pulses to control the tunneling dynamics in the 0g−(6s,6p3/2) double well of Cs2 coupled with other electronic surfaces. The possibility to manipulate the tunneling dynamics appears in a pump-dump scheme designed to form deeply bound cold molecules by photoassociation of two cold cesium atoms in the 0g−(6s,6p3/2) electronic state coupled with a3Σu+ (6s,6s) electronic state. The dump pulse is acting on the 0g−(6s,6p3/2) barrier and can be used to control the tunneling and to capture population in the inner well in deep vibrational levels out of tunneling resonances.
We consider the formation of cold ground-state polar molecules in a low vibrational level by laser fields. Starting from a pair of cold colliding atoms of dissimilar species, we propose a strategy consisting of three steps. In the first step, a pump pulse induces the molecule formation by photoassociating the atomic pair in a high or intermediate vibrational level of an excited electronic molecular state. This step is followed by a dump pulse in an intermediate vibrational level of the ground state. The last step corresponds to the vibrational cooling or vibrational stabilization process. Taking advantage of the permanent dipole moment, an infrared chirped pulse induces downward transitions among the vibrational levels of the ground electronic state, reaching the ground vibrational level. We perform the strategy with with fixed-shaped pulses and also with an optimized chirped pulse for the stabilization step. To perform the optimization, we introduce an optimal control technique in which the optimization of the chirping is carried out in the time domain. This methodology has the benefit of limiting the pulse amplitude while focusing only on the frequency of the field. The proposed scheme is an alternative to the use of two pairs of pump-dump pulses or to the direct photoassociation and vibrational stabilization in the ground state.
We propose an improved photoassociation scheme to produce ultracold molecules in their vibronic ground state for the generic case in which nonadiabatic effects facilitating transfer to deeply bound levels are absent. Formation of molecules is achieved by short laser pulses in a Raman-like pump-dump process where an additional near-infrared laser field couples the excited state to an auxiliary state. The coupling due to the additional field effectively changes the shape of the excited-state potential and allows for efficient population transfer to low-lying vibrational levels of the electronic ground state. Repetition of many pump-dump sequences together with collisional relaxation allows for accumulation of molecules in v=0v=0v=0.
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.
We discuss the production of ultracold molecules in their electronic ground state by photoassociation employing electronically excited states with ion-pair character and strong spin-orbit interaction. A short photoassociation laser pulse drives a nonresonant three-photon transition for alkali-metal atoms colliding in their lowest triplet state. The excited-state wave packet is transferred to the ground electronic state by a second laser pulse, driving a resonant two-photon transition. After analyzing the transition matrix elements governing the stabilization step, we discuss the efficiency of population transfer using transform-limited and linearly chirped laser pulses. Finally, we employ optimal control theory to determine the most efficient stabilization pathways. We find that the stabilization efficiency can be increased by one and two orders of magnitude when using linearly chirped and optimally shaped laser pulses, respectively.