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arXiv:2107.06046 · Physical Review A

Quantum Zeno effect in self-sustaining systems: Suppressing phase diffusion via repeated measurements

Wenlin Li, Najmeh Eshaqi-Sani, Wen-Zhao Zhang, David Vitali

Published Apr 19, 2021• 12 citations
arXivHTMLPDF

Abstract

We study the effect of frequent projective measurements on the dynamics of quantum self-sustaining systems by considering the prototypical example of the quantum van der Pol oscillator. Quantum fluctuations are responsible for phase diffusion which progressively blurs the semiclassical limit-cycle dynamics and synchronization, either to an external driving or between two coupled self-sustained oscillators. We show that by subjecting the system to repeated measurements of heterodyne type at an appropriate repetition frequency one can significantly suppress phase diffusion without spoiling the semiclassical dynamics. This quantum Zeno-like effect may be effective in the case of either one or two coupled van der Pol oscillators, and we discuss its possible implementation in the case of trapped ions.

DOI
10.1103/physreva.103.043715

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We study the effect of frequent projective measurements on the dynamics of quantum self-sustaining systems by considering the prototypical example of the quantum van der Pol oscillator. Quantum fluctuations are responsible for phase diffusion which progressively blurs the semiclassical limit-cycle dynamics and synchronization, either to an external driving or between two coupled self-sustained oscillators. We show that by subjecting the system to repeated measurements of heterodyne type at an appropriate repetition frequency one can significantly suppress phase diffusion without spoiling the semiclassical dynamics. This quantum Zeno-like effect may be effective in the case of either one or two coupled van der Pol oscillators, and we discuss its possible implementation in the case of trapped ions.
Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of multilevel systems that exhibit the quantum localization of classical chaos. The analysis is based on the wave function and Schr\"odinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the effect of measurement on the dynamics by randomizing the phases of the measured states. This analysis is extended to investigate the dynamics of multilevel systems driven by an intense external force and affected by frequent measurements. We show that frequent measurements of such quantum systems results in delocalization of the quantum suppression of classical chaos. This result is the opposite of the quantum Zeno effect. The phenomenon of delocalization of the quantum suppression and restoration of quasi-classical time evolution of these systems, owing to repetitive frequent measurements, can therefore be called the quantum anti-Zeno effect. From this analysis we furthermore conclude that frequently or continuously observable quasiclassical systems evolve basically in a classical manner.
Classical self-sustained oscillators, which generate periodic motion without periodic external forcing, are ubiquitous in science and technology. The realization of nonclassical self-oscillators is an important goal of quantum physics. We here present the experimental implementation of a quantum van der Pol oscillator, a paradigmatic autonomous quantum driven-dissipative system with nonlinear damping, using a single trapped atom. We demonstrate the existence of a quantum limit cycle in phase space in the absence of a drive and the occurrence of quantum synchronization when the nonlinear oscillator is externally driven. We additionally show that synchronization can be enhanced with the help of squeezing perpendicular to the direction of the drive and, counterintuitively, linear dissipation. We also observe the bifurcation to a bistable phase-space distribution for large squeezing. Our results pave the way for the exploration of self-sustained quantum oscillators and their application to quantum technology.
Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne measurement. The resulting quantum trajectories, i.e., time evolutions of the quantum state conditioned on the measurement outcome, make the quantum limit cycles apparent. We focus on the paradigmatic model of the quantum van der Pol oscillator and on two-level systems. Our work provides insights into limit cycles in quantum systems, emphasizing their similarity to classical limit cycles subject to noise. Additionally, we connect theoretical measures of quantum synchronization to quantities experimentally accessible via heterodyne detection.
Van der Pol oscillators are prototypical self-sustaining oscillators which have been used to model nonlinear processes in biological and other classical processes. In this work, we investigate how quantum fluctuations affect phase-locking in one or many van der Pol oscillators. We find that phase-locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for 171Yb+{}^{171}\text{Yb}^+171Yb+ achievable with current technology.
Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.
The fact that repeated projective measurements can slow down (the Zeno effect) or speed up (the anti-Zeno effect) quantum evolution is well-known. However, to date, studies of these effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.