Liouvillian of the Open STIRAP Problem

Thomas Mathisen,Jonas Larson

doi:10.3390/e20010020

Abstract

With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system’s (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.

Highlights

Coherent control has become an essential part of many branches in quantum physics, ranging from atomic and molecular thermal gases to solid state devises and ultracold atomic condensates [1,2,3,4]
The evolution behaviour can be divided into two regimes; for small decay rates, one should chose a such that there is a balance between non-adiabatic excitations and environment induced excitations, while, for large γs, a Zeno-type effect sets in which implies that it might be favorable to prolong the process in order to achieve a more complete Zeno-freezing of the population transfer
The desired adiabatic state is the instantaneous steady state for the case of dissipation, and the slower the process becomes, the more efficient population transfer to the target state. This is in agreement with the definition of adiabaticity for open quantum systems in terms of steady states [35], which states that, if the system is initially in a steady state, and the process is infinitely slow, the system remains in the same instantaneous steady state for all times

Summary

Introduction

Coherent control has become an essential part of many branches in quantum physics, ranging from atomic and molecular thermal gases to solid state devises and ultracold atomic condensates [1,2,3,4]. Dephasing among the lower states will effectively couple the different adiabatic states, and result in deterioration of the population transfer success rate. Instead of directly integrating the Lindblad master Equation (1), which has been the standard route in the past, we start from the properties of the Liouvillian Lin order to analyse the general open STIRAP problem. A too fast STIRAP will imply non-adiabatic excitations taking you out from the desired instantaneous eigenstate This expected behaviour is found for weak couplings to the environment, and the optimal time for the process should be such that the inherent unitary and the external irreversible time scales agree. It might be preferable to consider a slow process despite the coupling to the environment It is explained from a Zeno freezing effect of the population transfer between the different diabatic states. In the Appendices, we especially point out some remarks about the Liouvillian matrix

The Open STIRAP Model

Results and Discussion

The Liouvillian Matrix for the Λ System

Dynamics—Numerical Results

Conclusions