We study the quantum Zeno effect of the circuit-QED system at finite temperature for both selective measurement and nonselective measurement proposals. For the selective measurement proposal, we explicitly show that the counter-rotating terms (CRTs) become as significant as rotating wave terms (RWTs) with increase of temperature. We also derive an analytic expression for the survival probability which correctly captures the leading contribution for both RWTs and CRTs in the frequent measurement limit. Beyond this limit, we observe a nonexponential decay of the survival probability by further considering the effect of the variation of initial states during repeated measurements. For the nonselective measurement proposal, we find that the survival probability demonstrates the same behavior as in the selective measurement case in the short-time regime while it deviates from an exponential form and approaches a nonvanishing value in the long-time scale due to the repopulation effect.
We study the quantum Zeno effect of the circuit-QED system at finite temperature for both selective measurement and nonselective measurement proposals. For the selective measurement proposal, we explicitly show that the counter-rotating terms (CRTs) become as significant as rotating wave terms (RWTs) with increase of temperature. We also derive an analytic expression for the survival probability which correctly captures the leading contribution for both RWTs and CRTs in the frequent measurement limit. Beyond this limit, we observe a nonexponential decay of the survival probability by further considering the effect of the variation of initial states during repeated measurements. For the nonselective measurement proposal, we find that the survival probability demonstrates the same behavior as in the selective measurement case in the short-time regime while it deviates from an exponential form and approaches a nonvanishing value in the long-time scale due to the repopulation effect.
If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α≥1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.
We present a theoretical study of the quantum Zeno effect in a driven superconducting charge qubit strongly and ultrastrongly coupled to a transmission line resonator. Using the dressed-state approach, we predict the different dynamics behaviors of the dressed qubit subjected to two opposite projection measurements. We show that, for very frequent measurements, the survival probability of the initial state is of exponential form and the Zeno time of the dressed qubit can be several orders of magnitude longer than that of the bare qubit. For slowly repeated measurements, the detuning of the driving field has significant impact on the measurement dynamics, and by choosing appropriate parameters for the dressed qubit, the Zeno effect can occur in the nonresonant coupling case. Such a Zeno effect is excluded from a usual two-level system.
Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.
In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective projective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such nonselective measurements. Importantly, we show that there is a difference between using non-selective projective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective projective measurements can differ very significantly as compared to the repeated selective measurement scenario.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the
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.