Abstract
We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. The quantum Zeno effect (QZE), namely evolution slowdown of unstable quantum systems by frequent quantum measurements, has long been held to be a basic universal consequence of quantum mechanics for either isolated ('closed') or 'open' quantum systems, i.e. systems coupled to their environment (a 'bath'). Although for less frequent measurements there can be a reversal of the QZE, known as the anti-Zeno effect (AZE), the universal onset of QZE under sufficiently frequent measurement is still unchallenged.
Main results. This paper shows that a basic aspect of the dynamics of frequently measured (monitored) open quantum systems has been overlooked, namely their inevitable convergence to a steady state (equilibrium) that is determined by the measurement rate. Our treatment draws on the richness of non-Markovian dynamics to achieve diverse steady states by manipulations that are affected by the detector, which couples to the system alone and does not directly act on the system–bath coupling. An important corollary of the analysis is the possible 'freezing' of states by choosing monitoring rates that set the equilibrium state as the desired one.
Wider implications. Our findings can be tested in a variety of quantum systems coupled to baths whose memory effects are experimentally accessible. They shed new light on a fundamental issue at the interface of quantum measurement theory and the quantum dynamics of open systems: the interplay between measurement-induced and bath-induced non-Markovian dynamics. In particular, they essentially revise the notion of evolution freezing that has long been associated with the quantum Zeno effect.