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arXiv:1904.03872

Quantum Zeno effect in the multimode quantum Rabi model

Shu He, Chen Wang, Xuezao Ren, Liwei Duan, Qing‐Hu Chen

Published Apr 8, 2019• 0 citations
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Abstract

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of the multimode quantum Rabi model(MQRM). We derive an analytic expression for the decay rate of the survival probability where cavity modes are initially prepared as thermal equilibrium states. A crossover from QZE to QAZE is observed due to the energy backflow induced by high frequency cavity modes. In addition, we apply a numerically exact method based on the thermofield dynamics(TFD) theory and the matrix product states(MPS) to study the effect of squeezing of the cavity modes on the QZE of the MQRM. The influence of the squeezing angle, squeezing strength and temperature on the decay rate of the survival probability are discussed.

DOI
10.48550/arxiv.1904.03872

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We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of the multimode quantum Rabi model(MQRM). We derive an analytic expression for the decay rate of the survival probability where cavity modes are initially prepared as thermal equilibrium states. A crossover from QZE to QAZE is observed due to the energy backflow induced by high frequency cavity modes. In addition, we apply a numerically exact method based on the thermofield dynamics(TFD) theory and the matrix product states(MPS) to study the effect of squeezing of the cavity modes on the QZE of the MQRM. The influence of the squeezing angle, squeezing strength and temperature on the decay rate of the survival probability are discussed.
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 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.
We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of a two-level system interacting with an environment of harmonic oscillators, the spin-boson model. By applying a numerically exact method based on matrix product states, the previously obtained picture on the influence of counter-rotating terms has to be modified: For physical bath initial states, the transition from QZE to QAZE with increasing measurement interval is only absent at weak coupling, while present at strong coupling. Furthermore, we find that the transition occurs always for the widely used bare bath initial state. Within a more realistic measurement scheme where only the qubit is projectively measured, the above scenario for the bare bath initial state remains qualitatively unchanged, apart from accelerated decay for intermediate measurement intervals.
Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. \textbf{18}, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.
Modeling an arbitrarily accelerating qubit as an open quantum system, we derive an exact solution for the pure-dephasing model (σzσ_zσz​ coupling) under arbitrary qubit space-time trajectories, as well as general expressions for the survival probabilities of finite-length qubits interacting with a massless scalar field under σxσ_xσx​ coupling (an Unruh-DeWitt detector) to second order. We follow the regularization scheme presented in a previous paper by S. Schlicht, to allow a finite length quantum detector to couple to the massless scalar field. We compute the decay rate of the qubit in different coupling regimes, (pure dephasing, Unruh-DeWitt) and explore the Quantum Zeno (QZE) and Quantum Anti Zeno Effect (QAZE) as the qubit decoheres under it's interaction with the environment. We compute results for four example trajectories: stationary, uniform acceleration, oscillation and circular orbits.