Dynamics of Quantum Zeno and Anti-Zeno Effects in Open System

TL;DR

This paper develops a general dynamical framework to analyze quantum Zeno and anti-Zeno effects in open systems under repeated non-demolition measurements, extending understanding beyond wave function collapse models and including effects of measurement imperfections.

Contribution

It introduces a measurement-based dynamical model for quantum Zeno effects, applicable to arbitrary measurement periods, temperatures, and noise spectra, unifying various quantum control schemes.

Findings

Reproduces known decay rates under ideal measurements at zero temperature.

Shows non-ideal measurements can enhance Zeno and anti-Zeno effects.

Derives rate equations for long-time evolution with arbitrary measurement intervals and environmental conditions.

Abstract

We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.