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arXiv:quant-ph/0011077 · Physical Review A

Zeno and anti-Zeno effects for photon polarization dephasing

Abraham G. Kofman, Gershon Kurizki, Tomáš Opatrný

Published Mar 19, 2001• 43 citations

Abstract

We discuss a simple, experimentally feasible scheme, which elucidates the principles of controlling the reservoir spectrum and the spectral broadening incurred by repeated measurements. This control can yield either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of the quasiexponential decay of the observed state by means of frequent measurements. In the discussed scheme, a photon is bouncing back and forth between two perfect mirrors, each time passing a polarization rotator. The horizontal and vertical polarizations can be viewed as analogs of an excited and a ground state of a two level system (TLS). A polarization beam splitter and an absorber for the vertically polarized photon are inserted between the mirrors, and effect measurements of the polarization. The polarization angle acquired in the electrooptic polarization rotator can fluctuate randomly, e.g., via noisy modulation. In the absence of an absorber the polarization randomization corresponds to TLS decay into an infinite-temperature reservoir. The non-Markovian nature of the decay stems from the many round trips required for the randomization. We consider the influence of the polarization measurements by the absorber on this non-Markovian decay, and develop a theory of the Zeno and anti-Zeno effects in this system.

DOI: 10.1103/physreva.63.042108

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We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements, establishing the ability of a single photon subjected to random polarization noise to diagnose non-Markovian temporal correlations of such a noise process. Both the noise spectrum and temporal correlations are diagnosed by probing the photon with frequent (partially) selective polarization measurements. We show that noise with positive temporal correlations corresponds to our single photon undergoing a dynamical regime enabled by the quantum Zeno effect (QZE), whereas noise characterized by negative (anti) correlations corresponds to regimes associated with the anti-Zeno effect (AZE). This is the first step toward a novel noise spectroscopy based on QZE and AZE in single-photon state probing able to extract information on the noise while protecting the probe state, a conceptual paradigm shift with respect to traditional interferometric measurements.

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In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such non-selective measurements. Importantly, we show that there is a difference between using non-selective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems, and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective measurements can differ very significantly as compared to the repeated selective measurement scenario.

Simply speaking quantum Zeno effect for an unstable quantum system represents total decay probability decrease by frequent decay detections.Analogously simply speaking quantum anti-Zeno effect for an unstable quantum system represents total no-decay probability decrease by frequent decay detections.Also, some authors considered optical, i.e. polarization detection analogy of quantum Zeno and anti-Zeno effects.In this work we consider basic standard quantum mechanical concepts in quantum Zeno and anti-Zeno effect.We use simplest (Malus law) form of mentioned ideas on the photon polarization detection analogy of quantum Zeno and anti-Zeno effects and we suggest some new situations (non-equivalent time durations of the quantum dynamical evolutions between different frequent detections).Correspondingly we define new quantum effects, quantum Hamlet effect (when, by frequent detections, final total polarization angle and state converge but total probability for appearance of this state diverges) and quantum anti-Hamlet effect (when, by frequent detections, final total polarization angle and state diverge but total probability for appearance of this state converges).Also, we consider a rough classical mechanical analogy of Zeno effect.Finally we consider frequent interference of single photon at beam splitters and obtain for different values of reflection and transmission coefficients analogies of quantum Zeno and anti-Zeno effect as well as analogy of usual exponentially decreasing decay law.