Real measurements and Quantum Zeno effect

In 1977, Mishra and Sudarshan showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.Comment: 3 figure

Projection Postulate and Atomic Quantum Zeno Effect

The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show analytically that for a wide range of parameters such a short laser pulse acts as an effective level measurement to which the usual projection postulate applies with high accuracy. The corrections to the ideal reductions and their accumulation over n pulses are calculated. Our conclusion is that the projection postulate is an excellent pragmatic tool for a quick and simple understanding of the slow-down of time evolution in experiments of this type. However, corrections have to be included, and an actual freezing does not seem possible because of the finite duration of measurements.Comment: 25 pages, LaTeX, no figures; to appear in Phys. Rev.

Influence of the detector's temperature on the quantum Zeno effect

In this paper we study the quantum Zeno effect using the irreversible model of the measurement. The detector is modeled as a harmonic oscillator interacting with the environment. The oscillator is subjected to the force, proportional to the energy of the measured system. We use the Lindblad-type master equation to model the interaction with the environment. The influence of the detector's temperature on the quantum Zeno effect is obtained. It is shown that the quantum Zeno effect becomes stronger (the jump probability decreases) when the detector's temperature increases

Weak measurement of arrival time

The arrival time probability distribution is defined by analogy with the classical mechanics. The difficulty of requirement to have the values of non-commuting operators is circumvented using the concept of weak measurements. The proposed procedure is suitable to the free particles and to the particles subjected to an external potential, as well. It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time determination.Comment: 3 figure

Output spectrum of a detector measuring quantum oscillations

We consider a two-level quantum system (qubit) which is continuously measured by a detector and calculate the spectral density of the detector output. In the weakly coupled case the spectrum exhibits a moderate peak at the frequency of quantum oscillations and a Lorentzian-shape increase of the detector noise at low frequency. With increasing coupling the spectrum transforms into a single Lorentzian corresponding to random jumps between two states. We prove that the Bayesian formalism for the selective evolution of the density matrix gives the same spectrum as the conventional master equation approach, despite the significant difference in interpretation. The effects of the detector nonideality and the finite-temperature environment are also discussed.Comment: 8 pages, 6 figure

Effect of dissipation and measurement on a tunneling system

We consider a parametrically driven Kerr medium in which the pumping may be sinusoidally varied. It has been previously found that this system exhibits coherent tunneling between two fixed points which can be either enhanced or suppressed by altering the driving frequency and strength. We numerically investigate the dynamics when damping is included. This is done both by solving a master equation and using the quantum-trajectory method. In the latter case it is also possible to model the result of a continuous heterodyne measurement of the cavity output. The dissipation destroys the coherences which give rise to the tunneling, causing the sinusoidal oscillation of the mean to give way to a stochastic jumping between the fixed points, manifested as a random telegraph signal. In the quantum-trajectory picture we show that the coherences responsible for tunneling are an exponentially decreasing function of the signal-to-noise ratio for heterodyne measurements. However, evidence of both the bare tunneling rate and the driving modified tunneling rate are still apparent in the random telegraph signal

Interpretation of quantum jump and diffusion-processes illustrated on the Bloch sphere

It is shown that the evolution of an open quantum system whose density operator obeys a Markovian master equation can in some cases be meaningfully described in terms of stochastic Schrödinger equations (SSE’s) for its state vector. A necessary condition for this is that the information carried away from the system by the bath (source of the irreversibility) be recoverable. The primary field of application is quantum optics, where the bath consists of the continuum of electromagnetic modes. The information lost from the system can be recovered using a perfect photodetector. The state of the system conditioned on the photodetections undergoes stochastic quantum jumps. Alternative measurement schemes on the outgoing light (homodyne and heterodyne detection) are shown to give rise to SSE’s with diffusive terms. These three detection schemes are illustrated on a simple quantum system, the two-level atom, giving new perspectives on the interpretation of measurement results. The reality of these and other stochastic processes for state vectors is discussed

Selective quantum evolution of a qubit state due to continuous measurement

We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We discuss the Bayesian formalism for such ``selective'' evolution of an individual qubit and apply it to several solid-state setups. In particular, we show how to suppress the qubit decoherence using continuous measurement and the feedback loop.Comment: 15 pages (including 9 figures