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arXiv:1710.02110 · Physical Review A

Zeno effect of an open quantum system in the presence of 1/f noise

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

Published Feb 20, 2018• 7 citations
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Abstract

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has $1/f$ noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.

DOI
10.1103/physreva.97.022108

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We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has 1/f1/f1/f noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.
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.
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 study the quantum Zeno effect (QZE) induced by continuous partial measurement in the presence of short-correlated noise in the system Hamiltonian.We study the survival probability and the onset of the QZE as a function of the measurement strength and find that, depending on the noise parameters, the quantum Zeno effect can be enhanced or suppressed by the noise in different regions of parameter space.Notably, the conditions for the enhancement of the QZE are different when determined by the short-time or long-time behavior of the survival probability, or by the measurement strength marking the onset of the quantum Zeno regime.
We study the quantum Zeno effect (QZE) induced by continuous partial measurement in the presence of short-correlated noise in the system Hamiltonian. We study the survival probability and the onset of the QZE as a function of the measurement strength and find that, depending on the noise parameters, the quantum Zeno effect can be enhanced or suppressed by the noise in different regions of parameter space. Notably, the conditions for the enhancement of the QZE are different when determined by the short-time or long-time behavior of the survival probability, or by the measurement strength marking the onset of the quantum Zeno regime.
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
In this article, we systematically study the spontaneous decay phenomenon of a two-level system under the influences of both its environment and repetitive measurements. In order to clarify some well-established conclusions about the quantum Zeno effect (QZE) and the quantum anti-Zeno effect (QAZE), we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. We examine various spectral distributions by making use of our present approach in comparison with other approaches. It is found that with respect to a bare excited state even without the RWA, the QAZE can still happen for some cases, for example, the interacting spectra of hydrogen. However, for a physical excited state, which is a renormalized dressed state of the atomic state, the QAZE disappears and only the QZE remains. These discoveries inevitably show a transition from the QZE to the QAZE as the measurement interval changes.