The scaling of weak field phase-only control in Markovian dynamics

Abstract

We consider population transfer in open quantum systems, which are described by quantum dynamical semigroups (QDS). Using second order perturbation theory of the Lindblad equation, we show that it depends on a weak external field only through the field's autocorrelation function, which is phase independent. Therefore, for leading order in perturbation, QDS cannot support dependence of the population transfer on the phase properties of weak fields. We examine an example of weak-field phase-dependent population transfer, and show that the phase-dependence comes from the next order in the perturbation.

Training Schrödinger’s cat: quantum optimal control

“…For example, can population transfer from a ground to the excited surface be phase-controlled for a dye molecule in solution? While this has theoretically been shown to be impossible if the time evolution is Markovian [213], most solvents lead to non-Markovian system dynamics.…”

Considerations regarding one-photon phase control

“…5 Properties of interference have been used to devise strict conditions on the possibility of coherent control in a variety of scenarios. [6][7][8][9][10][11][12] These conditions have an important role in informing the interpretation of coherent control experiments.…”

“…Recently, Kukura et al failed to reproduce earlier results using a methodology which, in principle, should eliminate any non-phase effects. 32 Steady-state onephoton phase control has been shown to be impossible for certain classes of open quantum systems, 9 as it is for closed systems. 7 In addition, it has been demonstrated that multiphoton effects can create large contribution even in the linear absorption regime, 14,[33][34][35] which might lead to multiphoton phase control in seemingly one-photon experiments.…”

“…This is a significant extension to previous work on the impossibility of one-photon phase control in the steady state. [6][7][8][9] Indeed, the bound on control provided herein quantifies the "steady state" of past results, in a fully general manner based on physical parameters.…”

On Weak-Field (One-Photon) Coherent Control of Photoisomerization

“…32 Note also that previous work suggests that the possibility of weak-field control is destroyed by the Markov approximation. 30,34 In this exploratory study, we want to investigate whether pure energy dissipation can lead to phase control in the weak-field limit. To that end, we start from the Time-Dependent Hartree (TDH) approximation for the system-bath coupling which is also often referred to as the Time-Dependent-Self-Consistent-Field (TDSCF) approximation.…”