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arXiv:physics/0306173 · Journal of Physics B Atomic Molecular and Optical Physics

Coherent optimal control of multiphoton molecular excitation

Bijoy K Dey

Published May 24, 2001• 3 citations
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Abstract

We give a framework for molecular multiphoton excitation processes induced by an optimally designed electric field. The molecule is initially prepared in a coherent superposition state of two of its eigenfunctions. The relative phase of the two superposed eigenfunctions has been shown to control the optimally designed electric field which triggers multiphoton excitation in the molecule. This brings forth flexibility in designing the optimal field in the laboratory by suitably tuning the molecular phase and hence by choosing the most favourable interfering routes that the system follows to reach the target. We follow the quantum fluid dynamical formulation for designing the electric field for the HBr molecule.

DOI
10.1088/0953-4075/34/11/311

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We give a framework for molecular multiphoton excitation processes induced by an optimally designed electric field. The molecule is initially prepared in a coherent superposition state of two of its eigenfunctions. The relative phase of the two superposed eigenfunctions has been shown to control the optimally designed electric field which triggers multiphoton excitation in the molecule. This brings forth flexibility in designing the optimal field in the laboratory by suitably tuning the molecular phase and hence by choosing the most favourable interfering routes that the system follows to reach the target. We follow the quantum fluid dynamical formulation for designing the electric field for the HBr molecule.
We give a framework for molecular multiphoton excitation processes induced by an optimally designed electric field. The molecule is initially prepared in a coherent superposition state of two of its eigenfunctions. The relative phase of the two superposed eigenfunctions has been shown to control the optimally designed electric field which triggers multiphoton excitation in the molecule. This brings forth flexibility in designing the optimal field in the laboratory by suitably tuning the molecular phase and hence by choosing the most favourable interfering routes that the system follows to reach the target. We follow the quantum fluid dynamical formulation for designing the electric field for the HBr molecule. 1.
Coherent femtosecond optical pulses provide a unique means to manipulate the collision process between a pair of ultracold atoms. The capability to arbitrarily shape strong electric fields gives the possibility of dynamically sculpting the system Hamiltonian on the collisional timescale. In this paper we explore theoretically physically intuitive excitation schemes by which a control field can manipulate the vibronic state populations in an ultracold molecular system, with the goal of bringing atom pairs to short ( R < 10 Å) separations where they may form a tightly bound molecule. The microscopic dynamics of individual pairs of colliding atoms under the influence of an external optical field are explored through explicitly time-dependent numerical simulations. The results provide physical justification for the employment of optimal control techniques for the achievement of state-selective formation of ultracold molecules.
A quantum fluid-dynamic (QFD) control formulation is presented for optimally manipulating atomic and molecular systems. In QFD the control quantum system is expressed in terms of the probability density \ensuremath{\rho} and the quantum current j. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid-dynamical variables. The QFD approach is illustrated for manipulation of the ground electronic state dynamics of HCl induced by an external electric field.
By combining the theories of optimal control and coherent control, we derive an analytical formulation to evaluate the optimal 1-photon and n -photon fields together with their relative phase and intensity in the optimal “1 + n ”-coherent control scheme. The optimal coherent control exploits tailored light pulses to produce the best overlap with a predefined nuclear target in an electronically degenerate region. It also exploits explicitly the quantum interference between two optimal excitation pathways to achieve the product electronic selectivity. Numerical demonstrations are carried out to selectively control a minimum-uncertainty outgoing wave packet target in a molecular system. The electronically degenerate byproduct is shown to be completely discriminated against via the destructive interference between two optimal excitation pathways. The target considered in this paper would neither be achievable via the conventional continuous-wave coherent control nor via a single optimal control pathway in the weak response regime. Proposed is also a time-dependent excitation frequency degeneracy condition that incorporates the evolution of carrier frequencies in the optimal coherent control with tailored light fields.
Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.
We present a non-perturbative framework for the quantum treatment of vibrational excitation in molecular systems driven by electric fields with arbitrary time dependence. For harmonic potentials with linear dipole coupling, the field-induced dynamics is exactly described by a displaced coherent state, whose evolution is completely determined by a complex phase-space coordinate. Closed-form expressions for this coordinate reveal a clear distinction between resonant and non-resonant regimes. The resulting vibrational populations follow a Poisson distribution determined by a dimensionless time-dependent phase-space displacement, for both resonant and non-resonant driving. Resonant driving results in an enhanced phase-space displacement, whereas finite detuning between the driving and vibrational frequencies leads to an exponential suppression of the phase-space displacement and vibrational excitation. While the approach reduces to the standard time-dependent perturbation theory in the weak-field limit, it remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and enable non-perturbative state preparation in ultrafast spectroscopy.