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arXiv:1302.2477

Quantum Zeno dynamics of qubits in a squeezed reservoir: effect of measurement selectivity

Md. Manirul Ali, Po‐Wen Chen, Alec Maassen van den Brink, Hsi‐Sheng Goan

Published Feb 11, 2013• 0 citations
arXivHTMLPDF

Abstract

A complete suppression of the exponential decay in a qubit (interacting with a squeezed vacuum reservoir) can be achieved by frequent measurements of adequately chosen observables. The observables and initial states (Zeno subspace) for which the effect occurs depend on the squeezing parameters of the bath. We show these_quantum Zeno dynamics_ to be substantially different for selective and non-selective measurements. In either case, the approach to the Zeno limit for a finite number of measurements is also studied numerically. The calculation is extended from one to two qubits, where we see both Zeno and anti-Zeno effects depending on the initial state. The reason for the striking differences with the situation in closed systems is discussed.

DOI
10.48550/arxiv.1302.2477

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A complete suppression of the exponential decay in a qubit (interacting with a squeezed vacuum reservoir) can be achieved by frequent measurements of adequately chosen observables. The observables and initial states (Zeno subspace) for which the effect occurs depend on the squeezing parameters of the bath. We show these_quantum Zeno dynamics_ to be substantially different for selective and non-selective measurements. In either case, the approach to the Zeno limit for a finite number of measurements is also studied numerically. The calculation is extended from one to two qubits, where we see both Zeno and anti-Zeno effects depending on the initial state. The reason for the striking differences with the situation in closed systems is discussed.
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.
The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample different portions of the bath. We compare the Zeno effects arising from dispersive energy measurements and purely dephasing "quasimeasurements," showing energy measurements are not necessary to accelerate or suppress the decay process.
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 projective 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 nonselective measurements. Importantly, we show that there is a difference between using non-selective projective 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 projective measurements can differ very significantly as compared to the repeated selective measurement scenario.
We discuss the appearance of Zeno or anti-Zeno effects in an exponentially decaying system. We consider the quantum dynamics of a continuously monitored two level system interacting with a squeezed bath. We find that the behavior of the system depends critically on the way in which the squeezed bath is prepared. For specific choices of the squeezing phase the system shows Zeno or anti-Zeno effects in conditions for which it would decay exponentially if no measurements were done. This result allows for a clear interpretation in terms of the equivalent spin system interacting with a fictitious magnetic field.
We examine the critical system parameters which affect the quantum Zeno–anti-Zeno transition in a spin–boson system by applying the notion of correlated Zeno subspaces beyond the qubit system to its decayed part represented by a collective reservoir of oscillators. We also examine the effect of coherent control via a periodic sequence of dynamical decoupling pulses prior to projective measurement. Our results show that depending on the system bias and measurement time interval of the spin–boson model, coherent control via periodic dynamical decoupling pulses eliminates the Zeno–anti-Zeno transition behavior. We extend the calculations to examine the entanglement dynamics of two initially entangled qubits coupled to independent reservoirs with varying configuration and subjected to frequent measurements. In a multipartite system, in which one or more qubit–reservoir system can undergo the Zeno–anti-Zeno transition, we show that the effects of measurements made in a one qubit–reservoir subsystem can reverberate noticeably throughout a whole array of N pairs of qubit–reservoir subsystems.