Towards laser control of open quantum systems: memory effects

Abstract

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 twolevel 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.

Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

“…different initial and target states). The field-free energy gap is 0.33 eV and the optimal fields induce different Stark shifts in a range of about 0.25-0.65 eV, so that the instantaneous resonance frequency ω 0 (t) moves with respect to the spectral density peaks, with its expected consequences on non-Markovianity [29,30]. Obviously, different initial states, with different field-free energy gaps (characterizing heterojunction models with different inner-fragment distances [38]) will result into different control parameters, but still with transposable strategies and generic enough results.…”

“…Other non-Markovianity signatures refer to a re-amplification of the volume of accessible states during the decay process [11], the detection of a negative canonical decay rate [12,13], or a non-monotonous time evolution of the system von Neumann entropy [14]. Even more importantly, the role of transitory information back flow in externally controlled dynamics remains an open issue and an active research area [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

“…Our main purpose is to take advantage of the back flow of information from the surrounding bath, characterizing non-Markovianity, to enforce the control of the central system physical observables, protecting them against decoherence. At that respect, the present paper is a second one of a series of three [29,30] where an optimal control scheme is worked out, still acting on the central system alone, aiming at some protection against decoherence (population revivals, or robust and efficient transfers) and subsequently examine its consequences in terms of the bath non-Markovian response. More precisely, we analyze non-Markovianity during an ultrashort field pulse optimized by quantum control [32][33][34] in a spin-boson (SB) model [1,2,35] where the active sub-system strongly interacts with the bath.…”

Non-Markovian dynamics of the electronic subsystem in a laser-driven molecule: Characterization and connections with electronic-vibrational entanglement and electronic coherence

“…with γ 1,2 being the decoherence rates given in Eq. (39) and D 11 , D 12 , D 22 being the elements of the decoherence matrix shown in Eqs. (33 -36).…”

“…Let us analyze the signs of the decoherence rates γ i (t) given by Eqs. (39,40). Since P g P e ≥ | < ψ g |ψ e > | 2 , and with Eq.…”