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arXiv:1011.3862

The transition from Quantum Zeno to anti-Zeno effects for a qubit in a cavity by modulating the cavity frequency

Xiufeng Cao, Qing Ai, C. P. Sun, Franco Nori

Published Nov 17, 2010• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1011.3862

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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.
Abstract We investigate the long time evolution of a qubit coupled to an intrinsic bath and a single mode field which is coupled with a cavity bath, with and without repetitive measurements. We also analyze the measurement-modified decay rate, which shows that the free decay rate does not necessarily exist in some systems. The free decay rate is widely used to distinguish the quantum Zeno effect and anti-Zeno effect (AZE). It indicates that one cannot always make that clear if a decay of a system is accelerated. Our model confirms this conclusion; it shows that the AZE is not a universal concept.
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
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.
We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This is done for two separate cases: either with measurements or without them. This approach is based on a unitary transformation and does not require the rotating-wave approximation. In the case without measurement, we show that, for low-frequency noise, the bath shifts the qubit energy toward higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy toward lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the dynamics of the qubit subject to measurements (quantum Zeno regime) in two cases: low- and high-frequency baths. For very frequent projective measurements, the low-frequency bath gives rise to the quantum anti-Zeno effect on the qubit. The quantum Zeno effect only occurs in the high-frequency-cutoff Ohmic bath, after counterrotating terms are considered. In the condition that the decay rate due to the two kinds of baths are equal under the Wigner-Weisskopf approximation, we find that without the approximation, for a high-frequency environment, the decay rate should be faster (without measurements) or slower (with frequent measurements, in the Zeno regime), compared to the low-frequency bath case. The experimental implementation of our results here could distinguish the type of bath (either a low- or high-frequency one) and protect the coherence of the qubit by modulating the dominant frequency of its environment.
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) 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.