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Physical Review A

Photoassociation driven by a short laser pulse at millikelvin temperature

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

Published Oct 20, 2017• 8 citations
Publisher

Abstract

We investigate theoretically the photoassociation process of $^{85}\mathrm{Rb}$ atoms driven by a short laser pulse at several millikelvins. At this temperature, the actions of the rotational barrier, weights of initial scattering states, and shape resonance emerge and have an influence on the thermally averaged photoassociation probability. The calculated thermal weighted population distribution of rotational states agrees well with photoassociation spectrum experiment. The thermally averaged photoassociation probability decreases with an increase in temperature.

DOI
10.1103/physreva.96.043417

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A nonperturbative treatment is presented for laser-pulse-driven formation of heteronuclear diatomic molecules in a thermal gas of atoms. Based on the assumption of full controllability, the maximum possible photoassociation yield is obtained. A one-dimensional model is used for calculating the photoassociation probability as a function of the laser parameters as well as for different temperatures. The dependence of the photoassociation yield on the laser frequency and amplitude reveals complex patterns of one- and multiphoton transitions. The photoassociation yield induced by subpicosecond pulses of a priori fixed shape is very low compared to the maximum possible yield.

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We investigate theoretically the photoassociation process of 85Rb^{85}\mathrm{Rb}85Rb atoms driven by a short laser pulse at several millikelvins. At this temperature, the actions of the rotational barrier, weights of initial scattering states, and shape resonance emerge and have an influence on the thermally averaged photoassociation probability. The calculated thermal weighted population distribution of rotational states agrees well with photoassociation spectrum experiment. The thermally averaged photoassociation probability decreases with an increase in temperature.
A quantum dynamical description of an atomic collision pair interacting with the electric field of a short infrared laser pulse is developed. Inelastic processes in the electronic ground state are due to stimulated emission resulting in photoassociation, or absorption leading to photoacceleration. A perturbative approach based on a state space representation is compared with a numerical treatment using a grid representation in coordinate space. Special emphasis is on the role of rotations and, in particular, of shape resonances. It is shown that these quasibound states which are supported by the centrifugal barrier (for J ≠ 0) can be used as initial states to effectively populate a selected bound state with specific vibrational and rotational quantum number (photoassociation), or a partial wave of a scattering state with defined energy and rotational quantum number (photoacceleration). Simulations are carried out for the prototype H + Cl collision pair. Also the effect of averaging over initial conditions (velocity, angular momenta) is investigated for a supersonic beam experiment. For a narrow velocity distribution, we predict the presence of a resonance structure of the association and acceleration probability as a function of the mean collision energy.
Photoassociation is a possible route for the formation of chemical bonds. In this process, the binding of colliding atoms can be induced by means of a laser field. Photoassociation has been studied in the ultracold regime and also with temperatures well above millikelvins in the thermal energy domain, which is a situation commonly encountered in the laboratory. A photoassociation mechanism can be envisioned based on the use of infrared pulses to drive a transition from free colliding atoms on the electronic ground state to form a molecule directly on that state. This work takes a step in this direction, investigating the laser-pulse-driven formation of heteronuclear diatomic molecules in a thermal gas of atoms including rotational effects. Based on the assumption of full system controllability, the maximum possible photoassociation yield is deduced. The photoassociation probability is calculated as a function of the laser parameters for different temperatures. Additionally, the photoassociation yield induced by subpicosecond pulses of a priori fixed shape is compared to the maximum possible yield.
We investigate theoretically the rovibrational cooling of the 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ molecule resulting from the photoassociation of 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ atoms at millikelvin temperature. At several millikelvin temperature, the populations of the initial state and the photoassociated 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ molecule are distributed on hundreds of rovibrational levels. In the laser rovibrational cooling process, the population of the photoassociated molecule is first transferred to the deep vibrational state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=39}\ensuremath{\rangle}$ and then further to the rovibrational ground state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=0,l=0}\ensuremath{\rangle}$ via the intermediate state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}$. After the cooling process is over, the population transferred from the intermediate state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}$ is fully distributed in the vibrational ground state $|{v}^{\ensuremath{''}}=0\ensuremath{\rangle}$. Of the population in the vibrational ground state, 51.5951.59%51.59 is concentrated in the rotational ground state $|l=0\ensuremath{\rangle}$, and the rest of population is distributed in the low rotational states $|l=1\ensuremath{-}3\ensuremath{\rangle}$.
We investigate theoretically the photoassociation (PA) of two Cs\mathrm{Cs}Cs atoms using a slowly-turned-on and rapidly-turned-off (STRT) laser pulse at the temperature of $54\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ by taking the thermal average of the initial continuum states into account. For comparison, the PA probabilities under the action of the STRT and typical Gauss-type pulses are calculated, respectively. The rising and falling times of the STRT pulse are set to be ${\ensuremath{\tau}}_{r}=10$ ps and ${\ensuremath{\tau}}_{f}=0.2$ ps, and the two Gauss-type pulses are set to be ${\ensuremath{\tau}}_{r}={\ensuremath{\tau}}_{f}=10$ ps and ${\ensuremath{\tau}}_{r}={\ensuremath{\tau}}_{f}=5.1$ ps, respectively. Compared to the calculation considering a single initial continuum state (non-thermal-average calculations), the PA probabilities with the consideration of the thermal average are reduced to different extents according to different laser pulses. The PA process induced by the STRT pulse is more robust than that by the two Gauss-type pulses. For the STRT pulse, the PA probability is reduced by roughly 30%, while for the two Gauss-type pulses, it is reduced by roughly 97% and 64%, respectively. Because of the larger bandwidth and the asymmetric time profile of the STRT pulse, the PA probability induced by this pulse is related to both the off-resonant and the near-resonant transitions in a much broader phase space formed by the initial continuum states and the final vibrational states. Consequently, the thermal average of the initial continuum states has relatively smaller influence on the PA probability induced by the STRT pulse. By changing the pulse shape of the standard Gaussian to the sin2{\mathrm{sin}}^{2}sin2 and the Lorentz ones, the STRT pulse still results in the highest PA probability and is the most robust to the thermal average.
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.
A nonperturbative treatment is presented for laser-pulse-driven formation of heteronuclear diatomic molecules in a thermal gas of atoms. Based on the assumption of full controllability, the maximum possible photoassociation yield is obtained. A one-dimensional model is used for calculating the photoassociation probability as a function of the laser parameters as well as for different temperatures. The dependence of the photoassociation yield on the laser frequency and amplitude reveals complex patterns of one- and multiphoton transitions. The photoassociation yield induced by subpicosecond pulses of a priori fixed shape is very low compared to the maximum possible yield.