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The Journal of Chemical Physics

Local control theory applied to molecular photoassociation

Philipp Marquetand, Volker Engel

Published Aug 28, 2007• 44 citations
Publisher

Abstract

Local control theory (LCT) is employed to achieve molecular photoassociation with shaped laser pulses. Within LCT, the control fields are constructed from the response of the system to the perturbation which makes them accessible to a straightforward interpretation. This is shown regarding the ground-state collision of H+F and H+I atoms. Different objectives are defined, which aim at the formation of vibrational cold or hot associated molecules, respectively. Results are presented for s-wave scattering, where the rotational degree of freedom is ignored and also for full scale calculations including rotations, in order to describe more realistic conditions.

DOI
10.1063/1.2762222

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Local control theory (LCT) is employed to achieve molecular photoassociation with shaped laser pulses. Within LCT, the control fields are constructed from the response of the system to the perturbation which makes them accessible to a straightforward interpretation. This is shown regarding the ground-state collision of H+F and H+I atoms. Different objectives are defined, which aim at the formation of vibrational cold or hot associated molecules, respectively. Results are presented for s-wave scattering, where the rotational degree of freedom is ignored and also for full scale calculations including rotations, in order to describe more realistic conditions.
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.
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.
The development of the field of the science of ultra-cold matter has opened some exciting possibilities in exploring the quantum-mechanical processes which dominate matter interactions at the sub-microscopic scale. Although methods of cooling atoms are well established, molecular cooling is made difficult by molecules’ additional vibrational and rotational degrees of freedom. It was the goal of the research in this work to approach molecular cooling indirectly, by using broadband shaped-pulse photoassociation for the generation of tightly bound ultracold Rb2 molecules. The experiments towards this goal conducted by our group included a pumpdecay experiment to observe the generation of ground state singlet or triplet molecules. However, attempts to observe an increase in ground state population have been unsuccessful. A pump-probe study of wavepacket dynamics in the 5s+5p electronic state was conducted in order to determine the appropriate timing for the application of an additional pulse to dump population into the ground state. Although the attempt to observe wavepacket oscillations has been unsuccessful, pump-probe studies have yielded the observation of loosely bound excited state molecules as a result of the photoassociation pulse. These results are promising as a first stage in a fully coherent pump-dump approach to stabilisation into the lowest vibrational ground state. This thesis will provide an introduction and overview to the concerns involved in addressing the problem of molecular cooling and generation. Experimental techniques will be discussed including pulsed laser systems, optical parametric amplifi- cation, and the presentation of an original design for pulse shaping with an acoustooptic modulator. The emphasis of these discussions will be on the principles and operating procedures required for the use of these devices as home-built systems. The thesis will conclude with the results of pump-probe experiments utilising the pulse shaper as a spectral cutting device.
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.
Wave-mechanical phenomena such as resonance and interference, in both light and matter, are central to the principles of quantum coherent control over molecular processes. Focusing on the dynamical aspects, this dissertation is a compilation of studies on the interaction physics involving wave packets in molecules, the driving light field, and the underlying coherence and control. In each work, we will demonstrate interesting correlations between the properties of a carefully designed excitation light field and desirable outcomes of the molecules quantum dynamics. We will analyze the dynamical effect of a Feshbach resonance in the adiabatic Raman photoassociation for ultracold diatomic molecule formation from ultracold atoms. A narrow resonance is shown to be able to increase the effective number of collisions, in an ultracold atomic gas, that are available for photoassociation. This results in an optimal resonance width much smaller than the atomic collision energy bandwidth, due to the balance between the effective collision rate and single-collision transfer probability. Next, we demonstrate the linear molecular response to high-intensity, broadband, shaped optical fields. We show that this originates from interferences based on intra-pulse Raman excitations, and thus response linearity is not unique to the first-order perturbative limit and can not be used to infer the strength of the field. In the last study, we simulate the stochastic vibrational wave packet and dissociation-flux dynamics in a molecule excited by light with temporal and spectral incoherent properties. Between this case and that using a coherent pulse with the same spectral profile, we compare the vibrational wave functions and the loss of electronic and vibrational coherence, and demonstrate the qualitative difference between coherently and incoherently driven dynamics in molecules.