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arXiv:0710.0275 · Physical Review A

Quantum Zeno effect in cavity quantum electrodynamics: Experimental proposal with nonideal cavities and detectors

R. Rossi, A.R. Bosco de Magalhães, Maria Carolina Nemes

Published Jan 18, 2008• 6 citations
arXivHTMLPDF

Abstract

We propose an experiment for the observation of the quantum Zeno effect (QZE) in a bipartite system. The setup involves two microwave cavities and a ``tunneling'' photon, which is observed by the passage of Rydberg atoms. Our proposal allows for the consideration of two types of measurements, namely, sequential observations of the atomic state and its inclusive measurement. In the present system the two processes are shown to lead to the same result in the ideal case. We consider realistic atom-field interaction times, cavity dissipation, and limited detection efficiency. Analytical expressions for the ``tunneling'' probability are obtained exhibiting a competition between the environment induced exponential decay and the characteristic ${t}^{2}$ (for short times) dependence of the QZE. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.

DOI
10.1103/physreva.77.012107

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We propose an experiment for the observation of the quantum Zeno effect (QZE) in a bipartite system. The setup involves two microwave cavities and a tunneling'' photon, which is observed by the passage of Rydberg atoms. Our proposal allows for the consideration of two types of measurements, namely, sequential observations of the atomic state and its inclusive measurement. In the present system the two processes are shown to lead to the same result in the ideal case. We consider realistic atom-field interaction times, cavity dissipation, and limited detection efficiency. Analytical expressions for the tunneling'' probability are obtained exhibiting a competition between the environment induced exponential decay and the characteristic t2{t}^{2}t2 (for short times) dependence of the QZE. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.
We investigate some effects related to quantum measurement process. We study a theoretical model for atomic detections in microwave cavity experiments. The model allows for the introduction of empirical imperfections in the analysis of experiments in this system. Two investigations on foundations of Quantum Zeno Effect are presented. Thefirst one consists in experimental proposals for the effect observation in a bipartite system. Empirical limitations are made explicit. In the second investigation, we show that the Quantum Zeno Effect prevails even if the measurements are not complete. Finally we present a protocol which allows for the quantum evolution control through a single auxiliary system.
We present a scheme for experimentally observing the quantum Zeno effect using the quantum-nondemolition measurement recently proposed by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. The Zeno effect refers to the freezing of the (unitary) free dynamics of a system by rapid measurements. We generalize the Zeno effect to be any change in the survival probability of an initial state induced by very rapid measurements, when such measurements are the dominant source of fluctuations in the system. We derive a master equation for the evolution of a cavity mode when the photon number is monitored by this method. This equation describes a phase-diffusion process. We propose that this measurement scheme be used to monitor the exchange of a single photon between the cavity and a single Rydberg atom. We show that for very rapid monitoring the free oscillation of the atomic inversion is disrupted and the atom can be trapped close to the initial excited state. This is the quantum Zeno effect.
The traditional approach to the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in open quantum systems (implicitly) assumes that the bath (environment) state returns to its original state after each instantaneous projective measurement on the system and thus ignores the cross-correlations of the bath operators between different Zeno intervals. However, this assumption is not generally true, especially for a bath with a considerably nonnegligible memory effect and for a system repeatedly projected into an initial general superposition state. We find that, in stark contrast to the result of a constant value found in the traditional approach, the scaled average decay rate in unit Zeno interval of the survival probability is generally time dependent or shows an oscillatory behavior. In the case of a strong bath correlation, the transition between the QZE and the QAZE depends sensitively on the number of measurements NNN. For a fixed NNN, a QZE region predicted by the traditional approach may in fact already be in the QAZE region. We illustrate our findings using an exactly solvable open qubit system model with a Lorentzian bath spectral density, which is directly related to realistic circuit cavity quantum electrodynamics systems. Thus the results and dynamics presented here can be verified with current superconducting circuit technology.
We present a dispersive-coupling-based interpretation for the quantum Zeno effect (QZE) where measurements are dynamically treated as dispersive couplings of the measured system to the apparatus rather than the von Neumann's projections. It is found that the explicit dependence of the survival probability on the decoherence time quantitatively distinguishes this dynamic QZE from the usual one based on projection measurements. By revisiting the cavity-QED experiment of the QZE [J. Bernu et al., Phys. Rev. Lett. 101, 180402 (2008)], we suggest an alternative scheme to verify our theoretical consideration that frequent measurements slow down the increase of photon number inside a microcavity due to the nondemolition couplings with the atoms in large detuning.
We analyze the detection of itinerant photons using a quantum nondemolition measurement. An important example is the dispersive detection of microwave photons in circuit quantum electrodynamics, which can be realized via the nonlinear interaction between photons inside a superconducting transmission line resonator. We show that the back action due to the continuous measurement imposes a limit on the detector efficiency in such a scheme. We illustrate this using a setup where signal photons have to enter a cavity in order to be detected dispersively. In this approach, the measurement signal is the phase shift imparted to an intense beam passing through a second cavity mode. The restrictions on the fidelity are a consequence of the quantum Zeno effect, and we discuss both analytical results and quantum trajectory simulations of the measurement process.