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Physical Review B

Quantum Zeno and anti-Zeno effect of a nanomechanical resonator measured by a point contact

Po‐Wen Chen, Dong-Bang Tsai, Philip Bennett

Published Mar 8, 2010• 33 citations
Publisher

Abstract

The occurrence of either the quantum Zeno effect (QZE) or anti-Zeno effect (AZE) resulting from the short-time behavior of the environment-induced decoherence for quantum Brownian motion (QBM) model has been discussed [S. Maniscalco, J. Piilo, and K. A. Suominen, Phys. Rev. Lett. 97, 130402 (2006)]. We discuss here while the shuttering time period (length) of the frequent observations is changed, the system of interest, i.e., a nanomechanical oscillator, will undergo a QZE to AZE crossover. Instead of interacting with an equilibrium bosonic bath in a QBM model, we investigate the occurrence of either QZE or AZE of a nanomechanical oscillator coupled to a nonequilibrium fermionic reservoir [quantum point contact (QPC) detector as a measuring device]. We find that Zeno and anti-Zeno behaviors depend on the values of the system and reservoir parameters such as the oscillator frequency, energy cutoff, bias voltage, and reservoir temperature.

DOI
10.1103/physrevb.81.115307

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The occurrence of either the quantum Zeno effect (QZE) or anti-Zeno effect (AZE) resulting from the short-time behavior of the environment-induced decoherence for quantum Brownian motion (QBM) model has been discussed [S. Maniscalco, J. Piilo, and K. A. Suominen, Phys. Rev. Lett. 97, 130402 (2006)]. We discuss here while the shuttering time period (length) of the frequent observations is changed, the system of interest, i.e., a nanomechanical oscillator, will undergo a QZE to AZE crossover. Instead of interacting with an equilibrium bosonic bath in a QBM model, we investigate the occurrence of either QZE or AZE of a nanomechanical oscillator coupled to a nonequilibrium fermionic reservoir [quantum point contact (QPC) detector as a measuring device]. We find that Zeno and anti-Zeno behaviors depend on the values of the system and reservoir parameters such as the oscillator frequency, energy cutoff, bias voltage, and reservoir temperature.
In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.
In this paper we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behaviour of environment induced decoherence is the ultimate responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context .
The effect of the anti-rotating terms on the short-time evolution and the quantum Zeno (QZE) and anti-Zeno (AQZE) effects is studied for a two-level system coupled to a bosonic environment. A unitary transformation and perturbation theory are used to obtain the electron self-energy, energy shift and the enhanced QZE or the AQZE, simultaneously. The calculated Zeno time depends on the atomic transition frequency sensitively. When the atomic transition frequency is smaller than the central frequency of the spectrum of boson environment, the Zeno time is prolonged and the anti-rotating terms enhance the QZE; when it is larger than that the Zeno time is reduced and the anti-rotating terms enhance the AQZE. PACS numbers: 03.65.Xp; 42.50.Ct; 03.65.Yz 1 The quantum Zeno effect (QZE) and anti-Zeno effects (AQZE) have been widely discussed for decades theoretically [** * early papers and recent papers] and recently experimentally [***the paper of Ref. B and others]. In an unstable quantum twolevel (multi-level) system, frequently measurement can reduce or accelerate the decay
We examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists.
We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) by modulating the central frequency of the cavity mode. Our results are obtained without using the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. When the central frequency of the cavity mode is resonant with the qubit energy level spacing, the normalized decay rate of the qubit is lower than 1, which manifests the QZE. However, when the cavity frequency is detuned from resonance, the normalized decay rate becomes larger than 1, which corresponds to the AZE. The change from the QZE to the AZE, by just varying the central frequency of the cavity mode, should allow to distinguish these two different effects. Moreover, we find that in the presence of both qubit's intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the qubit energy level spacing and the central frequency of the cavity mode, but also on the coupling strength between the qubit and the cavity mode.
The quantum Zeno effect predicts that the decay of an unstable system can be slowed down by measuring the system frequently enough. In some systems, however, an enhancement of the decay due to frequent measurements, namely the anti-Zeno effect, may occur. In this paper we study the Zeno-anti-Zeno crossover for quantum Brownian motion. Moreover, we propose a way to manipulate the decay of the system and to observe a controlled continuous passage from decay suppression to decay acceleration by using reservoir engineering techniques.