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Physical Review A

Decoherence of molecular vibrational wave packets: Observable manifestations and control criteria

Constantin Brif, HERSCHEL A. RABITZ, Sascha Wallentowitz, Ian A. Walmsley

Published May 7, 2001• 48 citations
Publisher

Abstract

Decoherence of molecular vibrational wave packets in hot alkaline dimers due to the vibration-rotation coupling is considered. The focus is on the study of observable manifestations of the decoherence process in molecular emission tomography. Criteria are presented for control over decoherence by means of driving molecular transitions with suitably shaped ultrafast laser pulses.

DOI
10.1103/physreva.63.063404

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Decoherence of molecular vibrational wave packets in hot alkaline dimers due to the vibration-rotation coupling is considered. The focus is on the study of observable manifestations of the decoherence process in molecular emission tomography. Criteria are presented for control over decoherence by means of driving molecular transitions with suitably shaped ultrafast laser pulses.
Any real system, no matter how well isolated, unavoidably interacts with the environment. This interaction makes the evolution of a quantum system nonunitary and destroys the coherence of quantum superpositions. This process, known as decoherence, is widely regarded as the most important and fundamental obstacle to the practical realization of quantum information processing. On the other hand, the objectives of quantum control are predicated on the ability to manipulate the system coherently over a period of time. Quantum control has been applied successfully to several experimental systems and coupling such a controlled system to an environment makes the study of coherence loss possible. The standard model of decoherence is formulated in terms of a system, defined by the observables that can be measured, and a reservoir, de¯ned by those degrees of freedom that are not accessed by observation. The vibrational and rotational degree of freedom of diatomic molecules form an experimental model of such a system and bath 1. The nature of the ro-vibrational coupling does not allow a Decoherence Free Subspace, instead we try to identify a Decoherence Resistant Subspace using closed loop control. We set up a learning control loop experiment to monitor the coherence in a vibrational wavepacket, consisting of about 6 vibrational states of the A(1Σ+g ) electronic state, excited by a shaped, ultrashort optical pulse, and then to determine the pulse shape that yielded the longest coherence lifetime. The coherence of the vibrational wavepacket was monitored by measuring the fluorescence quantum beats from the outer turning point of the wave packet's trajectory. The closed loop controller altered the shape of the driving optical pulse to maximize the the depth of modulation of the quantum beats at a prescribed time after excitation, within the constraints of the laser system. The outcome of this closed loop control experiment shows an improvement of the beat decay constant of about 60%, as shown in Fig. (1), a result which occurs for several di®erent pulse shapes. Our experiments show that a number of interesting decoherence-resistant excitations exist. The nature of the dephasing was examined theoretically. Using measured optical pulse shapes, we simulated numerically the molecular wavepacket in the limit of perturbation theory. The experiment and simulations show that there are di®erent mechanisms contributing to the decoherence resistant excitation. The shaped pulse reduces the °uctuations in the wave packet spatial extent, which in turn changes the system reservoir coupling. Other components of the optimal pulse are a sequence of pulses that creates constructive interference of the vibrational wavepacket at the desired time, and chirp which compensates for the anharmonicity of the adiabatic potential. The experimental results show general agreement with numerical simulations. We conclude that wavepackets resistant to dephasing do exist,and that learning algorithms provide an effcient means for finding them.
In this thesis, we discuss the possibilities for suppression of decoherence, the loss of purity in an open quantum system, and the related process of dephasing. In the first chapter, we review the literature on the subject of open system dynamics, decoherence and methods of decoherence suppression. In the second chapter, we focus on the specific case of a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wavepackets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wavepacket phases. It appears that over long timescales, phase-only control is not possible, but for earlier timescales the possibility of phase-only control of dephasing remains. In addition, we point out that the time-dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states. In the final chapter, we discuss the same system, but apply a qualitatively different method of dephasing suppression based on the nonlinear resonance effect in a driving field. We extend previous work on the topic (Shapiro et al. [1]) by considering the effect of using a train of laser pulses as the driving field, in place of a two-colour continuous-wave laser field. We demonstrate that the pulse train method can be more effective at suppressing dephasing than the two-colour CW case.
We consider a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wave packets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wave packet phases. It appears that over long time scales, phase-only control is not possible, but for earlier time scales the possibility of phase-only control of dephasing remains. In addition, we point out that the time dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states.
We present an analytical calculation that predicts the collapse of vibrational wavepackets in molecules due to the coupling of the rotational and vibrational degrees of freedom. At longer times a new class of revivals is predicted in the vibrational degree of freedom, due to the finite size and discrete nature of the rotational reservoir. The interplay of these competing behaviours is studied in the context of current experiments, and conditions for observing the revivals are described. Furthermore, the conditions for which the molecular vibration and rotation can be regarded as a system and its reservoir-like environment are described, in which case the ro-vibrational coupling can be considered effectively as a mechanism for decoherence of the vibrational motion. Comparison of the dephasing time predicted by this model with that observed in recent experiments is made.
It is well known that the application of a pulse to a molecular electronic transition leaves the molecules vibrational modes in different electronic states in well-localized states, or wave packets[1]. One method of detecting the wave packets is via the time-dependent spectra of spontaneous emission from the excited molecule[2]. The emission consists in general of two parts, an incoherent part that depends only on the wave packet in the excited state, and a coherent part, that depends on the wave packets in both excited and ground electronic states (of a two-state molecule). This can be seen from the following simple calculation.