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Physical Review A

Formation of 85 Rb 2 ultracold molecules via photoassociation by two-color laser fields modulating the Gaussian amplitude

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

Published Oct 16, 2012• 12 citations
Publisher

Abstract

The formations of ${}^{85}{\text{Rb}}_{2}$ 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 $>$1.0 cm${}^{\ensuremath{-}1}$ with respect to the $5S+5{P}_{1/2}$ 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.

DOI
10.1103/physreva.86.043420

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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 >>>1.0 cm\ensuremath−1{}^{\ensuremath{-}1}\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.
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.
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.
Abstract Photoassociation (PA) of 85Rb atoms from the ground X 1 Σ g + state to the excited A 1 Σ g + and b 3 Π u states by two-color laser pulses at 100 μ K × k B is investigated by using quantum wavepacket method. Two pulses with detunings δ 1 and δ 2 varying from −1.0 to 1. cm−1 are taken into account. The specific case δ 1 = − δ 2 is generalized to the condition of arbitrary combination of δ 1 and δ 2 for both the Gaussian-pulse field and the slowly-turned-on and rapidly-turned-off (STRT) field. It is found that the introduce of the detunings in the two pluses can enhance the asymmetry of the time profile and broaden the linewidth of the laser field. The two factors can further enhance the PA probability for both resonant and nonresonant regions. Compared to the Gaussian field, the STRT field which is even more asymmetric in time profile and more broaden in linewidth can significantly enhance the PA probability, with the nonresonant transition dominating the PA process. It can be expected that once the two detunings are both positive, which is a relatively loose restriction for coherent control, a considerable PA probability can be obtained in a two-color STRT field.
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.