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Physical Review A

Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field

Jiří Vala, Olivier Dulieu, Françoise Masnou-Seeuws, P. Pillet, Ronnie Kosloff

Published Dec 12, 2000• 107 citations
Publisher

Abstract

Enhancement of the production of cold molecules via photoassociation is considered for the ${\mathrm{Cs}}_{2}$ 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 ${\mathrm{Cs}}_{2}$ 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.

DOI
10.1103/physreva.63.013412

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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\ensuremathΣu+{}^{3}{\ensuremath{\Sigma}}_{u}^{+}3\ensuremathΣu+​ to the excited 0g\ensuremath−{0}_{g}^{\ensuremath{-}}0g\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 0g\ensuremath−{0}_{g}^{\ensuremath{-}}0g\ensuremath−​ surface leaves a void in the nuclear density of the ground 3\ensuremathΣu+{}^{3}{\ensuremath{\Sigma}}_{u}^{+}3\ensuremathΣu+​ 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 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=98v=98v=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.
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.
This paper investigates the formation of cold molecules in the photoassociation of two cold atoms by a strong laser pulse applied at short interatomic distances, which lead to molecular dynamics taking place in the light-induced (adiabatic) potentials. A two-electronic-state model in the caesium dimer is used to analyse the effects of this strong coupling regime and to show specific results: (i) acceleration of the ground-state population to the inner zone due to a non-impulsive regime of coupling at short and intermediate interatomic distances, (ii) formation of cold molecules in strongly bound levels of the ground state, where the population at the end of the pulse is much bigger than the population photoassociated in bound levels of the excited state, and (iii) the final momentum distribution of the ground-state wavepacket keeping the signatures of the maxima in the initial wavefunction continuum. It is shown that the topology of the light-induced potentials plays an important role in dynamics.
The paper investigates cold molecules formation in the photoassociation of two cold atoms by a strong laser pulse applied at short interatomic distances, which lead to a molecular dynamics taking place in the light-induced (adiabatic) potentials. A two electronic states model in the cesium dimer is used to analyse the effects of this strong coupling regime and to show specific results: i) acceleration of the ground state population to the inner zone due to a non-impulsive regime of coupling at short and intermediate interatomic distances; ii) formation of cold molecules in strongly bound levels of the ground state, where the population at the end of the pulse is much bigger than the population photoassociated in bound levels of the excited state; iii) the final momentum distribution of the ground state wavepacket keeping the signatures of the maxima in the initial wavefunction continuum. It is shown that the topology of the light-induced potentials plays an important role in dynamics.
In this work, the coherence properties of the matter is studied in the frame of photoassociation of ultracold alkali atoms by using short and ultrashort laser pulses. Ultracold can be described with temperatures below 100 microK. When energy approaches the ultracold regime, quantum properties of matter becomes visible. In this regime matter such as atoms and molecules show wave properties. Coherent control employs the wave properties of matter to steer a physical process toward a desired target. It can be implemented with coherent radiation such as laser light. In particular, femtosecond laser pulses can be shaped. They thus have become a standard tool for coherent control. Since matter shows its wave properties most clearly at ultralow temperatures, ultracold matter represents the perfect object for coherent control. In the other hand using incoherent fields on ultracold matter does not give us good opportunities to drive quantum properties of it. In this work, it is aimed to bring together ultracold and ultrafast regimes in the frame of photoassociation. Photoassociation, excitation of two colliding atoms by laser light creates very weakly bound molecules. In the first part of this study, femtosecond photoassociation experiments are simulated. In these experiments and simulations, the broad spectrum of the femtosecond pulses addressing both atomic and molecular transitions is manipulated in a way to prevent the atomic transitions and to promote the molecular transitions. Then the effect of chirp and the effect of additional phase to the pulse are examined. Excited and ground state population are monitored by carrying out quantum dynamical simulations. The driving ultrafast dipole dynamics are presented. The photoassociation rate is limited by the low initial atomic pair density at inter-nuclear separations where photoassociation is feasible. In the second part of this study, a new scheme is proposed in order to manage this low pair density by manipulating the shape resonances of the initial atom pair. A shape resonance which is a metastable state occurs when some part of the wavefunction of partial waves with J > 0 trapped by a rotational barrier shows a bound structure in the closer internuclear distances where the rest of it shows a scattering wavefunction behavior. Most of the shape resonances in alkaline and alkaline earth metals occur typically at temperatures of a few milli-Kelvin. Therefore, the thermal weight of a shape resonance at photoassociation temperatures is quite small. By applying a non-resonant laser to the system the energy of the resonant state is brought close to the energies those corresponding to the photoassociation temperatures. Thus, the thermal weight of a shape resonance is amplified and initial pair density is enhanced. This effect is studied in both adiabatic and non-adiabatic time scales with respect to the rotational period of the system, intensity effects on the resonance energy and lifetime are presented.
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.