Weak stochastic ratchets and dynamic localization in measurement-induced quantum trajectories

TL;DR

This paper explores how weak, state- and time-dependent measurements on a qubit can induce control-free control, stochastic ratchets, and localization effects, revealing new dynamics in measurement-induced quantum trajectories.

Contribution

It introduces a novel approach to control quantum trajectories through weak measurements without direct intervention, including stochastic ratchets and dynamical localization phenomena.

Findings

Weak measurements can induce control-like effects without direct action.

A stochastic ratchet mechanism can be realized in quantum trajectories.

Dynamical localization occurs near specific states when measurement strength is reduced.

Abstract

We consider a qubit governed by a sequence of weak measurements, with the measurement strength modified in a time- and state-dependent manner. The resulting trajectory of the qubit in the phase space can be weakly controlled without any direct action on the qubit (control-free control), even only one fixed observable is measured. Here we show a possibility of a weak form of a stochastic ratchet, allowing to create an additional "force" without changing the corresponding effective average potential. Furthermore, if the weak measurement strength is significantly reduced in a way conditioned to some particular state, a dynamical localization near this state takes place. If the measurement strength is reduced to zero, a singularity appears, which behaves like an artificial basis state.