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Physical Review A

Target states and control of molecular alignment in a dissipative medium

Dominique Sugny, Cyrill Kontz, Hans Rudolf Jauslin

Published Nov 14, 2006• 20 citations
Publisher

Abstract

We investigate how and to what extent molecular alignment can be controlled in a dissipative medium by a suitable train of laser pulses. We focus primarily on the extension of a scheme of control originally constructed for unitary evolution. The procedure is applied to control the alignment of CO molecules in an Ar gas. The parameters of the train of kicks---i.e., the intensity of each kick and the delay between them---are either obtained by a systematic procedure (maximum strategy) or by optimization by evolutionary algorithms.

DOI
10.1103/physreva.74.053411

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We investigate how and to what extent molecular alignment can be controlled in a dissipative medium by a suitable train of laser pulses. We focus primarily on the extension of a scheme of control originally constructed for unitary evolution. The procedure is applied to control the alignment of CO molecules in an Ar gas. The parameters of the train of kicks---i.e., the intensity of each kick and the delay between them---are either obtained by a systematic procedure (maximum strategy) or by optimization by evolutionary algorithms.
Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, postpulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.
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We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.
Efficient and long-lived field-free molecular orientation is achieved using only two kicks appropriately delayed in time. The understanding of the mechanism rests upon a molecular target state providing the best efficiency versus persistence compromise. An optimal control scheme is referred to for fixing the free parameters (amplitudes and the time delay between them). The limited number of kicks, the robustness and the transposability to different molecular systems advocate in favor of the process, when considering its experimental feasibility.
A density matrix approach is developed for the control of a mixed-state quantum system using a time-dependent external field such as a train of pulses. This leads to the definition of a target density matrix constructed in a reduced Hilbert space as a specific combination of the eigenvectors of a given observable through weighting factors related to the initial statistics of the system. A train of pulses is considered as a possible strategy to reach this target. An illustration is given by considering the laser control of molecular alignment and orientation in thermal equilibrium.
Suppressing molecular alignment dephasing is of significant practical value for applications involving nonrigid rotors. In this work, we propose a strategy that employs a train of time-delayed, phase-modulated laser pulses to achieve the elimination of alignment dephasing over an extended temporal window. Our findings demonstrate that for molecules with short rotational periods, such as CO or N 2 used in this study, dephasing can be completely eliminated for at least a dozen revival periods, thereby restoring alignment approaching the rigid-rotor limit. For molecules exhibiting longer revival periods, however, the effectiveness of this approach is somewhat diminished. While complete dephasing elimination is not achieved in such cases, the method remains sufficiently effective for most practical applications. We also qualitatively analyze the underlying reasons for the reduced performance in molecules with longer rotational periods.