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arXiv:quant-ph/0510114 · Physical Review A

Control of mixed-state quantum systems by a train of short pulses

Dominique Sugny, Arne Keller, Osman Atabek, D. Daems, Claude M. Dion, S. Guérin, Hans Rudolf Jauslin

Published Sep 9, 2005• 47 citations
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Abstract

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.

DOI
10.1103/physreva.72.032704

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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.
This paper considers the optimal control of quantum systems. The controlled quantum systems are described by the probability-density-matrix-based Liouville–von Neumann equation. Using projection operators, the states of the quantum system are decomposed into two sub-spaces, namely the 'main state' space and the 'remaining state' space. Since the control energy is limited, a solution for optimizing the external control force is proposed in which the main state is brought to the desired main state at a certain target time, while the population of the remaining state is simultaneously suppressed in order to diminish its effects on the final population of the main state. The optimization problem is formulated by maximizing a general cost functional of states and control force. An efficient algorithm is developed to solve the optimization problem. Finally, using the hydrogen fluoride (HF) molecular population transfer problem as an illustrative example, the effectiveness of the proposed scheme for a quantum system initially in a mixed state or in a pure state is investigated through numerical simulations.
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.
Controlled manipulation by atomic- and molecular-scale quantum systems has attracted a lot of research attention in recent years. A fundamental problem is to provide deterministic methods for controlled engineering of arbitrary quantum states. This work proposes a deterministic method for engineering arbitrary pure and mixed states of a wide class of quantum systems. The method exploits a special combination of incoherent and coherent controls (incoherent and coherent radiation) and has two properties which are specifically important for manipulating by quantum systems: it realizes the strongest possible degree of their state control, complete density matrix controllability, meaning the ability to steer arbitrary pure and mixed initial states into any desired pure or mixed final state, and it is all-to-one, such that each particular control transfers all initial system states into one target state.
In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined functional is maximized. This leads to a monotonically convergent algorithm which is computationally not more expensive than the standard optimal-control techniques to push a system, without specifying the path, from a given initial to a given final state. The method is successfully applied to drive the time-dependent density along a given trajectory in real space and to control the time-dependent occupation numbers of a two-level system and of a one-dimensional model for the hydrogen atom.
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.
Dynamical model of open quantum systems in a matrix form is transformed into the model in a vector form using Liouville super-operator.Given a dynamical model of a dissipative quantum system in the presence of a time-dependent external control field,we achieve an improved optimal control law with the squared error between density matrices of system state and target state as the performance index.The states transfer experiment on a spin 1/2 particle system is carried out.Under the proposed optimal control,eigenstates,pure states,and mixed states are taken as initial and target states of the system,respectively.Detailed comparative analyses are given.