anti-Zeno Effect Research Articles

Unstable system dynamics: Do we understand it fully?

We review some recent results in the theory of decaying quantum systems related to the Zeno and anti-Zeno effects. We also give an example showing that contrary to common belief the decay law can be a rather irregular function.

Quantum Zeno and anti-Zeno effects in an unstable system with two bound states

We analyze the experimental observations reported by Fischer et al. [M.C. Fischer, B. Gutiérrez-Medina, M.G. Raizen, Phys. Rev. Lett. 87 (2001) 040402] by considering a system of coupled unstable bound quantum states | A 〉 and | B 〉 . The state | B 〉 is coupled to a set of continuum states | C Θ ( ω ) 〉 . We investigate the time evolution of | A 〉 when it decays into | C Θ ( ω ) 〉 via | B 〉 , and find that frequent measurements on | A 〉 leads to both the quantum Zeno effect and the anti-Zeno effects depending on the frequency of measurements. We show that it is the presence of | B 〉 which allows for the anti-Zeno effect.

Observation-assisted optimal control of quantum dynamics

This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics.

Quantum control by von Neumann measurements

A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.

Zeno and Anti-Zeno Effects for Quantum Brownian Motion

In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.

Electromagnetic manipulation for the anti-Zeno effect in an engineered quantum tunneling process

We investigate the quantum Zeno and anti-Zeno effects for the irreversible quantum tunneling from a quantum dot to a ring array of quantum dots. By modeling the total system with the Anderson-Fano-Lee model, it is found that the transition from the quantum Zeno effect to quantum anti-Zeno effect can happen as the magnetic flux and the gate voltage were adjusted.

Quantum trajectory method for the quantum Zeno and anti-Zeno effects

We perform stochastic simulations of the quantum Zeno and anti-Zeno effects for a two-level system and for a decaying one. Instead of a simple projection postulate approach, a more realistic model of a detector interacting with the environment is used. The influence of the environment is taken into account using the quantum trajectory method. Simulation of the measurement for a single system exhibits probabilistic behavior showing the collapse of the wave packet. When a large ensemble is analyzed using the quantum trajectory method, the results are the same as those produced using the density matrix method. The results of numerical calculations are compared with the analytical expressions for the decay rate of the measured system, and good agreement is found. Since the analytical expressions depend on the duration of the measurement only, the agreement with the numerical calculations shows that other parameters of the model are not important.

Zeno and anti-Zeno effect for a two-level system in a squeezed bath

We discuss the appearance of Zeno or anti-Zeno effects in an exponentially decaying system. We consider the quantum dynamics of a continuously monitored two level system interacting with a squeezed bath. We find that the behavior of the system depends critically on the way in which the squeezed bath is prepared. For specific choices of the squeezing phase the system shows Zeno or anti-Zeno effects in conditions for which it would decay exponentially if no measurements were done. This result allows for a clear interpretation in terms of the equivalent spin system interacting with a fictitious magnetic field.

Sufficient conditions for the anti-Zeno effect

The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno effects is in fact very narrow.

The quantum Zeno effect: a solvable model for indirect pre-measurements

A simple model of indirect pre-measurements on an unstable quantum state is presented in this paper. The model is completely solvable and the solutions are used to compare the time evolution of the unstable state with and without the influence of the pre-measurement. We find that by choosing the details of the process of pre-measurement appropriately, it is possible to observe both suppression and enhancement of the rate of decay of the unstable state. When the pre-measurements are assumed to lead on to actual measurements, we see that the quantum Zeno effect, and in some instances the 'anti-Zeno' effect, can be produced by repeating the measurement many times in succession. The Zeno effect can appear in our model either as a real consequence of repeated measurements or sometimes merely as an artefact of the manner in which the observations on the system are performed. The anti-Zeno effect appears almost exclusively as an artefact of the details of the measurement. Numerical investigations are included to delineate the regimes in which the quantum Zeno effect and possibly the anti-Zeno effect can occur.

Quantum anti-Zeno effect by false measurements.

We have investigated how the decay dynamics of an unstable quantum system is affected by a false measurement, where the decay is monitored by detecting a decay product but the active energy band of the detector does not match the energy of the decay product. It is shown that, although such a measurement is ineffective and has almost no effect if the detector response is slow, the detectability of decay is increased and the decay is accelerated considerably if the response is fast. This is due to the new decay channel, which is generated as a counteraction of measurement.

Dynamical control of macroscopic quantum tunneling.

We show that the quantum Zeno and anti-Zeno effects are realizable for macroscopic quantum tunneling by current-bias modulation in Josephson junctions (and their analogs in atomic condensates).

General expression for the quantum Zeno and anti-Zeno effects

In this paper we investigate the quantum Zeno and anti-Zeno effects without using any particular model of the measurement. Making a few assumptions about the measurement process we derive an expression for the jump probability during the measurement. From this expression the equation, obtained by Kofman and Kurizki [Nature (London) 405, 546 (2000)] can be derived as a special case.

Adiabatic population transfer in a liquid: taking advantage of a decaying target state.

The feasibility of efficient population transfer between an initial state and a decaying target state of the same parity without populating an intermediate state, in the presence of large-amplitude stochastic energy level fluctuations that mimic the dephasing in a solute molecule due to the influence of a solvent, is demonstrated theoretically. In particular, it is shown that a decaying target state, whose decay rate constant is large compared with the band width of picosecond laser pulses but small compared with the associated peak Rabi frequencies, can dramatically suppress the dephasing-induced nonadiabaticity associated with the dynamics of population transfer, resulting in, irrespective of the correlation time of stochastic energy level fluctuations, negligible population in the intermediate state and complete population transfer to the decaying target state. These results should further motivate experimental studies of optical control of molecular dynamics in a liquid. An interesting connection between our results and the quantum Zeno and anti-Zeno effects is also discussed.

Fluorescence resonance energy transfer and quantum Zeno effect

It is shown that the transition from coherent to incoherent fluorescence resonance energy transfer can be considered as a demonstration of quantum Zeno or anti-Zeno effect.

Necessary and sufficient conditions for the quantum Zeno and anti-Zeno effect

A necessary and sufficient condition for the occurrence of the quantum Zeno effect is given, refining a recent conjecture of Luo, Wang and Zhang. An analogous condition is derived for the quantum anti-Zeno effect. Both results rely on a formal connection between the quantum (anti-)Zeno effect and the weak law of large numbers.

Zeno and anti-Zeno effects in two-level systems

We examine the appearance of Zeno and anti-Zeno effects when the unitary evolution of a two-level system is observed. We demonstrate that, contrary to previous claims, the anti-Zeno effect can occur in two-level systems so that the observation can enhance the transition probability. Moreover, for nonresonant couplings we show that the Zeno and anti-Zeno effects always appear sequentially in the evolution of the same system: there is Zeno effect in the short-time regime and anti-Zeno effect in the long-time regime.

Quantum Zeno and anti-Zeno effects by indirect measurement with finite errors

We study the quantum Zeno effect and the anti-Zeno effect in the case of `indirect' measurements, where a measuring apparatus does not act directly on an unstable system, for a realistic model with finite errors in the measurement. A general and simple formula for the decay rate of the unstable system under measurement is derived. In the case of a Lorentzian form factor, we calculate the full time evolutions of the decay rate, the response of the measuring apparatus, and the probability of errors in the measurement. It is shown that not only the response time but also the detection efficiency plays a crucial role. We present the prescription for observing the quantum Zeno and anti-Zeno effects, as well as the prescriptions for avoiding or calibrating these effects in general experiments.

Decay of an Excited Atom under Imperfect Photon Counting Measurement

We investigate the decay of an excited two-level atom under a situation where the emitted photon is detected by the conventional photon counting measurement. We discuss an imperfect measurement with finite probability of failing in counting the emitted photon. By analyzing the extended quantum system including the measurement apparatus, we have calculated the survival probability of the excited atom, as well as the response of the apparatus and the errors in the measurement. The decay rate under the measurement is obtained in a simple form. It is shown that not only the response time of the detector but also the measurement error play crucial roles in modification of the decay rate. The conditions to observe the quantum Zeno effect and the anti-Zeno effect are also clarified for the case of Lorentzian form factor.

Quantum Description of Classical Apparatus: Zeno Effect and Decoherence

We study the measurement process by treating classical detectors entirely quantum mechanically. As a generic model we use a point-contact detector coupled to an electron in a quantum dot and tunneling into the continuum. Transition to the classical description and the mechanism of decoherence are investigated. We con-centrate on the influence of the measurement on the electron decay rate to the continuum. We demonstrate that the Zeno (or the anti-Zeno) effect requires a nonuniform density of states in the continuum. In this case we show that the anti-Zeno effect relates only to the average decay rate, whereas for sufficiently small time the Zeno effect always takes place. We discuss the experimental consequences of our results and the role of the projection postulate in a measurement process. PACS: 73.21.La; 74.78.Na; 03.65.Ta; 03.65.Xp; 03.65.Yz