Controllability on relaxation-free subspaces: On the relationship between adiabatic population transfer and optimal control

TL;DR

This paper investigates the limits of quantum state transfer via intermediate decaying states, identifying optimal control strategies and their limitations, especially in the context of adiabatic processes like STIRAP.

Contribution

It provides analytic solutions for multi-step decay pathways and characterizes the topologies achievable under finite power constraints in quantum control.

Findings

STIRAP is the global optimum for single intermediate state transfer at infinite time.

Optimal control with two intermediate states cannot achieve perfect transfer at finite power, even with infinite time.

The topology of achievable paths under finite power is characterized and limited.

Abstract

We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer. For a single intermediate decaying state, we recover the Stimulated Raman Adiabatic Passage (STIRAP) process which we identify as the global optimum in the limit of infinite control time. We also present analytic solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that in this case, for finite power the optimal control does not approach perfect state transfer even in the infinite time limit. We generalize our findings to characterize the topologies of paths that can be achieved by coherent control under the assumption of finite power.