Towards Laser Control of Open Quantum Systems: Memory Effects

Laser control of Open Quantum Systems (OQS) is a challenging issue as compared to its counterpart in isolated small size molecules, basically due to very large numbers of degrees of freedom to be accounted for. Such a control aims at appropriately optimizing decoherence processes of a central two-level system (a given vibrational mode, for instance) towards its environmental bath (including, for instance, all other normal modes). A variety of applications could potentially be envisioned, either to preserve the central system from decaying (long duration molecular alignment or orientation, qubit decoherence protection) or, to speed up the information flow towards the bath (efficient charge or proton transfers in long chain organic compounds). Achieving such controls require some quantitative measures of decoherence in relation with memory effects in the bath response, actually given by the degree of non-Markovianity. Characteristic decoherence rates of a Spin-Boson model are calculated using a Nakajima-Zwanzig type master equation with converged HEOM expansion for the memory kernel. It is shown that, by adequately tuning the two-level transition frequency through a controlled Stark shift produced by an external laser field, non-Markovianity can be enhanced in a continuous way leading to a first attempt towards the control of OQS

Time-dependent unitary perturbation theory for intense laser driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.Comment: 16 pages, 6 figure

Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation

The constraint of time-integrated zero-area on the laser field is a fundamental, both theoretical and experimental requirement in the control of molecular dynamics. By using techniques of local and optimal control theory, we show how to enforce this constraint on two benchmark control problems, namely molecular orientation and photofragmentation. The origin and the physical implications on the dynamics of this zero-area control field are discussed.Comment: 19 pages, 7 figure

Reaching optimally oriented molecular states by laser kicks

We present a strategy for post-pulse orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.Comment: 4 pages, 3 figure

Laser control for the optimal evolution of pure quantum states

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.Comment: 16 pages, 9 figure

Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics

We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime

Optimized time-dependent perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems

We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.Comment: 4 pages, 2 figure

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

Pulse-driven quantum dynamics beyond the impulsive regime

We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure