Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

Abstract

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

A Probabilistic Framework for Controlling Quantum Systems

“…In this section we provide the matrices à and Ñ appearing in equation ( 9) for a tow-dimensional system. The vectorisation (8)…”

“…The idea of controlling quantum physical systems dates back to the end of last century when laser technology was invented [1][2][3][4][5][6][7]. Since it lies at the heart of all quantum information theory and quantum technology [8][9][10][11][12], this field has been rapidly growing in recent years both theoretically and experimentally. Theoretically, several approaches to control quantum physical systems were developed including optimal control theory [13,14],…”

A Probabilistic Framework for Controlling Quantum Systems

“…As discussed in earlier sections, the quantum system state is described by the vector xt which is the vectorisation of the density matrix recalled in equation (8). At the initial time, we assume that the system is prepared in the ground state.…”

Optimal Probabilistic Quantum Control Theory

“…For quantum systems governed by the Liouville-von Neumann equation (1), that are also driven by external control field, u t , the state vector of the vectorised density matrix is shown in Appendix (B) to be given by the following bilinear equation [55],…”

“…In recent years, quantum control theory has been acknowledged as an enabling tool for the development of new quantum technology and quantum information theory applications [1][2][3][4][5]. One of the main objectives in quantum control theory is to develop methods that can manipulate and control quantum systems.…”