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.
A numerical model of spontaneous decay continuously monitored by a distant detector of emitted particles is constructed. It is shown that there is no quantum Zeno effect in such quantum measurement if the interaction between emitted particle and detector is short-range and the mass of emitted particle is not zero.
We study the quantum Zeno effect in the case of indirect measurement, where the detector does not interact directly with the unstable system. Expanding on the model of Koshino and Shimizu [Phys. Rev. Lett., 92, 030401, (2004)] we consider a realistic Hamiltonian for the detector with a finite bandwidth. We also take explicitly into account the position, the dimensions and the uncertainty in the measurement of the detector. Our results show that the quantum Zeno effect is not expected to occur, except for the unphysical case where the detector and the unstable system overlap.
We analyze the influence of the finite duration of the measurement on the quantum Zeno effect, using a simple model of the measurement. It is shown that the influence of the finite duration of the measurement is uninportant when this duration is small compared to the duration of the free evolution between the measurements.
We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the d…
The quantum Zeno paradox is fully resolved for purely indirect and incomplete measurements performed by the detectors outside the system. If the outside detectors are prepared to observe propagating signals of a decay event of an excited state in the core region, the survival probability of the state is not changed at all by the outside measurements, as long as the wavefunction of the signals does not have reflectional-wave contributions going back to the core by the outside detectors. The proof is independendent of the decay law of the survival probabilities. Just watching frequently from out…
We critically study the possibility of quantum Zeno effect for indirect measurements. If the detector is prepared to detect the emitted signal from the core system, and the detector does not reflect the signal back to the core system, then we can prove the decay probability of the system is not changed by the continuous measurement of the signal and the quantum Zeno effect never takes place. This argument also applies to the quantum Zeno effect for accelerated two-level systems, unstable particle decay, etc.
We propose an experiment with two coupled microwave cavities and a "tunneling" photon observed by the passage of Rydberg atoms. We model the coupled cavities as in Ref. \cite{art1} and include dissipative effects as well as limited detection efficiency. We also consider realistic finite atom-field interaction times and provide for a simple analytical expression for the photon "tunneling" probability including all these effects. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.
Modeling an arbitrarily accelerating qubit as an open quantum system, we derive an exact solution for the pure-dephasing model ($σ_z$ coupling) under arbitrary qubit space-time trajectories, as well as general expressions for the survival probabilities of finite-length qubits interacting with a massless scalar field under $σ_x$ coupling (an Unruh-DeWitt detector) to second order. We follow the regularization scheme presented in a previous paper by S. Schlicht, to allow a finite length quantum detector to couple to the massless scalar field. We compute the decay rate of the qubit in different c…
The quantum Zeno effect -- suppression of decay by frequent measurements -- was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected so far.
The linear optics approach to quantum computing has several potential advantages but the logic operations are probabilistic. Here we review the use of the quantum Zeno effect to suppress the intrinsic failure events in these kinds of devices, which would produce deterministic logic operations without the need for ancilla photons or high-efficiency detectors. The potential advantages of implementing Zeno gates using micro-cavities and electromagnetically-induced transparency are discussed.
We show that the quantum Zeno effect can be used to suppress the failure events that would otherwise occur in a linear optics approach to quantum computing. From a practical viewpoint, that would allow the implementation of deterministic logic gates without the need for ancilla photons or high-efficiency detectors. We also show that the photons can behave as if they were fermions instead of bosons in the presence of a strong Zeno effect, which leads to a new paradigm for quantum computation.
In this work, we study the decay behavior of a two-level system under the competing influence of a dissipative environment and repetitive measurements. The sign of the second derivative of the environmental spectral density function with respect to the system transition frequency is found to be a sufficient condition to distinguish between the quantum Zeno (negative) and the anti-Zeno (positive) effects raised by the measurements. We check our criterion for practical measurement intervals, which are larger than the conceptual Zeno time, in various environments. In particular, with the Lorentzi…
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 ini…
It was shown that different mechanisms of perturbation of spontaneous decay constant: inelastic interaction of emitted particles with particle detector, decay onto an unstable level, Rabi transition from the final state of decay (electromagnetic field domination) and some others are really the special kinds of one general effect - perturbation of decay constant by dissipation of the final state of decay. Such phenomena are considered to be Zeno-like effects and general formula for perturbed decay constant is deduced.
In this paper, we first demonstrate how to realize quantum state transferring (QST) from one atom to another based on quantum Zeno dynamics. Then, the QST protocol is generalized to realize the quantum state swapping (QSS) between two arbitrary atoms with the help of a third one. Furthermore, we also consider the QSS within a quantum network. The influence of decoherence is analyzed by numerical calculation. The results demonstrate that the protocols are robust against cavity decay.
We perform stochastic simulations of the quantum Zeno and anti-Zeno effects for two level system and for the decaying one. Instead of 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. The simulation of the measurement for a single system exhibits the probabilistic behavior showing the collapse of the wave-packet. When a large ensemble is analysed using the quantum trajectory method, the results are the same as those produced using the de…
We analyze a simple and feasible practical scheme displaying Zeno, anti-Zeno, and inverse-Zeno effects in the observation of wave-packet spreading caused by free evolution. The scheme is valid both in spatial diffraction of classical optical waves and in time diffraction of a quantum wave packet. In the optical realization, diffraction spreading is observed by placing slits between a light source and a light-power detector. We show that the occurrence of Zeno or anti-Zeno effects depends just on the frequency of observations between the source and detector. These effects are seen to be related…
When the interaction of a quantum system with a detector is changing from weak to strong coupling limits, the system experiences a transition from the regime with quantum mechanical coherent oscillations to the regime with a frozen dynamics. In addition to this quantum Zeno transition, we show that the full counting statistics of detector signal events experiences a topological phase transition at the boundary between two phases at intermediate coupling of a quantum system to the detector. We demonstrate that this transition belongs to the class of topological phase transitions that can be cla…
Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration which can undergo a rapid decay. The object - realized by a laser beam - prevents this decay due to the indirect quantum Zeno effect and thus, i…
We investigate the evolution of a quantum system under the influence of sequential measurements. The measurement scheme distinguishes whether or not the system is in a specified state $| {f_n}>$ at the $n^{\rm th}$ step, where $| {f_n}>$ varies with $n$. Dark evolution corresponds to the situation when all measurements give negative results. We show that dark evolution is unitary in the continuous measurement limit. We derive the effective Hamiltonian, and indicate how $| {f_n}>$ controls quantum state transport.
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 concentrate 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 deca…
We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherenc…
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
We study one-step implementation of the Fredkin gate in a bi-modal cavity under both resonant and large detuning conditions based on quantum Zeno dynamics, which reduces the complexity of experiment operations. The influence of cavity decay and atomic spontaneous emission is discussed by numerical calculation. The results demonstrate that the fidelity and the success probability are robust against cavity decay in both models and they are also insensitive to atomic spontaneous emission in the large detuning model. In addition, the interaction time is rather short in the resonant model compared …
We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of the multimode quantum Rabi model(MQRM). We derive an analytic expression for the decay rate of the survival probability where cavity modes are initially prepared as thermal equilibrium states. A crossover from QZE to QAZE is observed due to the energy backflow induced by high frequency cavity modes. In addition, we apply a numerically exact method based on the thermofield dynamics(TFD) theory and the matrix product states(MPS) to study the effect of squeezing of the cavity modes on the QZE of the MQRM. The influence …
We discuss a simple, experimentally feasible scheme, which elucidates the principles of controlling ("engineering") the reservoir spectrum and the spectral broadening incurred by repeated measurements. This control can yield either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of the quasi-exponential decay of the observed state by means of frequent measurements. In the discussed scheme, a photon is bouncing back and forth between two perfect mirrors, each time passing a polarization rotator. The horizontal and vertical polarizations can be viewed as analogs of an excited…
The driven evolution of the spin of an individual atomic ion on the ground-state hyperfine resonance is impeded by the observation of the ion in one of the pertaining eigenstates. Detection of resonantly scattered light identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state is free of relaxation and correlated with the detector by a null signal. Null events represent the straightforward demonstration of the quantum Zeno paradox. Also, high probability of survival was demonstrated when the ion, driven by a fractionated $π$ pulse, was probed {\em and monitored} during the…
We investigate the discrete-time quantum walk evolution under the influence of the periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace, $P(0, t)$ is compared with the survival probability after frequent ($n$) measurements at interval $τ= t/n$, $P(0, τ)^n$. We show that $P(0, τ)^n > P(0, t)$ leading to the quantum Zeno effect in the position subspace when a parameter $θ$ in the quantum coin operations and frequency of measurements is greater than the critical value, $θ> θ_{c}$ and $n>n_{c}$. This Zeno effect in the subspace p…
The dynamics of any quantum system is unavoidably influenced by the external environment. Thus, the observation of a quantum system (probe) can allow the measure of the environmental features. Here, to spectrally resolve a noise field coupled to the quantum probe, we employ dissipative manipulations of the probe, leading to so-called Stochastic Quantum Zeno (SQZ) phenomena. A quantum system coupled to a stochastic noise field and subject to a sequence of protective Zeno measurements slowly decays from its initial state with a survival probability that depends both on the measurement frequency …
In this paper, we systematically study the spontaneous decay phenomenon of a two-level system under the influences of both its environment and continuous 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 stil…
Detailed schemes are investigated for experimental verification of Quantum Zeno effect with a superconducting qubit. A superconducting qubit is affected by a dephasing noise whose spectrum is 1/f, and so the decay process of a superconducting qubit shows a naturally non-exponential behavior due to an infinite correlation time of 1/f noise. Since projective measurements can easily influence the decay dynamics having such non-exponential feature, a superconducting qubit is a promising system to observe Quantum Zeno effect. We have studied how a sequence of projective measurements can change the …
We study the dynamics of a charge qubit, consisting of a single electron in a double well potential, coupled to a point-contact (PC) electrometer using the quantum trajectories formalism. In contrast with previous work, our analysis is valid for arbitrary source-drain bias across the PC, but is restricted to the sub-Zeno limit. We find that the dynamics is strongly affected by inelastic tunnelling processes in the PC. These processes reduce the efficiency of the PC as a qubit readout device, and induce relaxation even when the source-drain bias is zero. We show that the sub-Zeno dynamics are d…
We analyze the detection of itinerant photons using a quantum non-demolition (QND) measurement. We show that the backaction due to the continuous measurement imposes a limit on the detector efficiency in such a scheme. We illustrate this using a setup where signal photons have to enter a cavity in order to be detected dispersively. In this approach, the measurement signal is the phase shift imparted to an intense beam passing through a second cavity mode. The restrictions on the fidelity are a consequence of the Quantum Zeno effect, and we discuss both analytical results and quantum trajectory…
A model for quantum Zeno effect based upon an effective Schrödinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that inhibition of stimulated transitions between the two levels appears as a consequence of the influence of the meter whenever measurements of energy, either continuous or pulsed, are performed at quantum level of sensitivity. The generality of this approach allows to qualitatively understand the inhibition of spontaneous transitions as the decay of unstable partic…
The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied in dependence of the time lag $τ$ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.
We study the dynamics of a charge qubit, consisting of a single electron in a double well potential coupled to a point-contact (PC) electrometer, using the quantum trajectories formalism. Contrary to previous predictions, we show formally that, in the sub-Zeno limit, coherent oscillations in the detector output are suppressed, and the dynamics is dominated by inelastic processes in the PC. Furthermore, these reduce the detector efficiency and induce relaxation even when the source-drain bias is zero. This is of practical significance since it means the detector will act as a source of decohere…
It was predicted that frequently repeated measurements on an unstable quantum state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recentl…
We demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by an imaging process. A {\em in situ} imaging technique is used to acquire repeated images of an ultracold gas confined in a shallow optical lattice. The backaction induced by these position measurements modifies the coherent quantum tunneling of atoms within the lattice. By smoothly varying the rate at which spatial information is extracted from the atomic ensemble, we observe the continuous crossover from the 'weak measurement regime' where position measurements have little infl…
We investigate how relativity influences the spin correlation of entangled fermions measured by moving detectors. In particular, we show that the Clauser-Horne-Shimony-Holt Bell inequality is not violated by quantum mechanics when the left and right spin detectors move fast enough.
We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.
We investigate how the polarization correlations of entangled photons described by wave packets are modified when measured by moving detectors. For this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a function of the apparatus velocity. Our analysis is motivated by future experiments with entangled photons designed to use satellites. This is a first step towards the implementation of quantum information protocols in a global scale.
We investigate the discrimination between photon polarizations when measured by moving detectors. Both unambiguous and minimum-error discriminations are considered, and we analyze the the optimal successful (correct) probability as a function of the apparatus' velocity. The Holevo bound for polarization discrimination is also discussed and explicit calculation shows that the Holevo bound and the optimal successful (correct) probability for unambiguous (minimum-error) discrimination simultaneously increase or decrease.
We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density-matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the st…
We consider the continuous measurement of a double quantum dot by a weakly coupled detector (tunnel point contact nearby). While the conventional approach describes the gradual system decoherence due to the measurement, we study the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the double-dot density matrix. Nonlinear Langevin equation is derived for the random evolution of the density matrix which is reflected and caused by the stochastic detector output. Gradual collapse, gradual purification, and quantum Zeno effect are …
We consider the problem of photon creation from vacuum inside an ideal cavity with vibrating walls in the resonance case, taking into account the interaction between the resonant field mode and a detector modeled by a quantum harmonic oscillator. The frequency of wall vibrations is taken to be twice the cavity normal frequency, modified due to the coupling with the detector. The dynamical equations are solved with the aid of the multiple scales method. Analytical expressions are obtained for the photon mean numbers and their variances for the field and detector modes, which are supposed to be …
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturall…
The dynamical properties of a quantum system can be profoundly influenced by its environment. Usually, the environment provokes decoherence and its action on the system can often be schematized by adding a noise term in the Hamiltonian. However, other scenarios are possible: we show that by increasing the strength of the noise, the Hilbert space of the system gradually splits into invariant subspaces, among which transitions become increasingly difficult. The phenomenon is equivalent to the formation of the quantum Zeno subspaces. We explore the possibility that noise can {\em prevent}, rather…
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the `bare' survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturall…
A continuous projective measurement of a quantum system often leads to a suppression of the dynamics, known as the Zeno effect. Alternatively, generalized nonprojective, so-called "weak" measurements can be carried out. Such a measurement is parameterized by its strength parameter that can interpolate continuously between the ideal strong measurement with no dynamics-the strict Zeno effect, and a weak measurement characterized by almost free dynamics but blurry observations. Here we analyze the stochastic properties of this uncertainty component in the resulting observation trajectory. The obs…
The recently demonstrated robustness of fluctuation theorems against measurements [M. Campisi \emph{et al.}, Phys. Rev. Lett. \textbf{105} 140601 (2010)] does not imply that the probability distributions of nonequilibrium quantities, such as heat and work, remain unaffected. We determine the impact of measurements that are performed during a running force protocol on the characteristic function of work. The results are illustrated by means of the Landau-Zener(-Stückelberg-Majorana) model. In the limit of continuous measurements the quantum Zeno effect suppresses any unitary dynamics. It is dem…
Superconducting detectors for quantum key distribution require expensive cooling but have advantageous detection properties. A linear programming algorithm and heuristic for network cooling placement are proposed and validated. Co-locating cooled detectors provides cost-effective solutions even when cooling costs exceed the equipment cost of multiple links.
We study the influence of a detector on the decay law of a quantum state whose "undisturbed" survival probability is purely exponential. In particular, we consider a detector with a finite energy band of detection, i.e. it interacts only with decay products having an energy within a certain range of values. In one case, we assume that the detector performs many repeated measurements at short time intervals in all of which a collapse of the wave function occurs (bang-bang or pulsed-type measurements). In the second case, we assume a continuous measurement which preserves unitarity. We confirm t…
In every experimental test of a Bell inequality, we are faced with the problem of inefficient detectors. How we treat the events when no particle was detected has a big influence on the properties of the inequality. In this work, we study this influence. We show that the choice of post-processing can change the critical detection efficiency, the equivalence between different inequalities or the applicability of the non-signaling principle. We also consider the problem of choosing the optimal post-processing strategy. We show that this is a non-trivial problem and that different strategies are …
We investigated the electron tunneling out of a quantum dot in the presence of a continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time-development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, $\exp (-Γt)$, contrary to expectations based on the Quantum Zeno effect . However, the width of the energy distribution of the tunneling electron is no more $Γ$, but …
We consider evolution of a double quantum dot (DQD) two-electron spin qubit which is continuously weakly measured with a linear charge detector (quantum point contact). Since the interaction between the spins of two electrons depends on their charge state, the charge measurement affects the state of two spins, and induces non-trivial spin dynamics. We consider the regimes of strong and weak coupling to the detector, and investigate the measurement-induced spin dynamics both analytically and numerically. We observe emergence of the negative-result evolution and the system stabilization due to a…
