Laser control for the optimal evolution of pure quantum states

Abstract

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, post-pulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.

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

“…This has roughly an overall similitude with the scheme followed for a pure quantum state [11,12], but the two approaches have to be contrasted at the level of the target state. In the pure-state case, it is a specific linear combination of rotational states, constituting a wavepacket evolving through the Schrödinger equation.…”

“…The specific properties of the target density matrix cannot be inferred from a Boltzmann superposition of wavefunctions, separately time-propagated, i.e. it cannot be obtained from the analysis of Refs [11,12].…”

“…The difference of treatment between pure and mixed-state quantum systems at this first step is that, while the initial state of a pure quantum system is usually a single eigenstate of H 0 [12], that of a mixed-state system is a density operator involving a thermal average of all eigenstates of H 0 .…”

“…We have recently proposed a laser control strategy [11,12], for a molecular system initially in a pure quantum state, aiming at the maximalization (or minimalization) of the expectation value of a given observable, which does not commute with the field-free Hamiltonian. This control scheme consists in applying sudden pulses each time a given quantity (such as the expectation value of the observable under consideration) reaches its maximum.…”

Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

“…Problems of simultaneous control of a finite collection of systems have been addressed recently in applications related to quantum control [20][21][22][23][24][25][26][27][28][29][30][31]. In such circumstances, the system is a collection of molecules or atoms or spin systems and the control is a magnetic field (in NMR) or a laser.…”