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.
The suppression of spin-exchange relaxation in dense alkali-metal vapors discovered in 1973 and governing modern atomic magnetometers is here reformulated in terms of quantum measurement theory and the quantum Zeno effect. This provides a new perspective of understanding decoherence in spin-polarized atomic vapors.
We investigate the quantum Zeno and anti-Zeno effects in quantum dissipative systems by employing a hierarchical equations of motion approach which is beyond the usual Markovian approximation, the rotating wave approximation, and the perturbative approximation. The quantum Zeno and anti-Zeno dynamics of a biased qubit-boson model and a biased qutrit-boson model are provided as illustrative examples. It is found that (i) there exists multiple Zeno-anti-Zeno crossover phenomena, (ii) the non-Markovian characteristic of the bath may be favorable for the accessibility of the Zeno dynamics, and (ii…
Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is already different from the previously studied population decay problem, even without taking into account any back action from the environment. For many two-level systems interacting with a common environment, multiple transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the system-environment coupling strength is not weak, we show that the n…
Repeated measurements in quantum mechanics can freeze (the quantum Zeno effect) or enhance (the quantum anti-Zeno effect) the time-evolution of a quantum system. In this paper, we present a general treatment of the quantum Zeno and anti-Zeno effects for arbitrary driven open quantum systems, assuming only that the system-environment coupling is weak. In particular, we obtain a general expression for the effective decay rate of a two-level system subjected to arbitrary driving fields as well as periodic measurements. We demonstrate that the driving fields change the decay rate, and hence the qu…
The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.
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.
One can reduce the involved derivation of Balachandran and Roy of their `anti-Zeno' effect [Phys.Rev.Lett. 84, 4019 (2000)] to the derivation of standard Zeno effect. The mechanism of what the authors call `anti-Zeno' effect is a dynamic version of Zeno effect.
In this paper 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 behaviour of environment induced decoherence is the ultimate 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 u…
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 analyze the short-time behavior of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that this probability is not necessary analytic at the time origin. The time when the quantum Zeno effect could be observed is found to be much smaller than usually estimated. We have also studied the anti-Zeno era and have estimated its duration.
Recent studies suggest that both the quantum Zeno (increase of the natural lifetime of an unstable quantum state by repeated measurements) and anti-Zeno (decrease of the natural lifetime) effects can be made manifest in the same system by simply changing the dissipative decay rate associated with the environment. We present an {\underline{exact}} calculation confirming this expectation.
Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear ($χ^{\left(2\right)}$) waveguides that are interacting with each other via the evanescent waves. Both the waveguides operate under second harmonic generation. However, to study quantum Zeno and anti-Zeno effects one of them is considered as the system and the other one is considered as the probe. Considering all the fields involved as weak, a completely quantum mechanical description is provided, and the analytic solutions of Heisenberg's equations of motion for all the f…
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 enha…
The dynamic behavior of the entanglement for two two-level atoms coupled to a common lossy cavity is studied. We find that the speed of disentanglement is a decreasing (increasing) function of the damping rate of the cavity for on/near (far-off) resonant couplings. The quantitative explanations for these phenomena are given, and further, it is shown that they are related to the quantum Zeno and anti-Zeno effect induced by the non-Markovian environment.
We discuss the appearance of Zeno (QZE) or anti-Zeno (QAE) effect 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 effect 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 fi…
We point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable only in spectrally finite reservoirs, i.e., in cavities and waveguides, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, such measurements can only accelerate decay in free space.
We analyze the experimental observations reported by Fischer et. al. [in Phys. Rev. Lett. 87, 040402 (2001)] 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. We investigate the time evolution of A when it decays into C 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.
In this paper we study the possibility of modifying the dynamics of both quantum correlations, such as entanglement and discord, and classical correlations of an open bi-partite system by means of the quantum Zeno effect. We consider two qubits coupled to a common boson reservoir at zero temperature. This model describes, for example, two atoms interacting with a quantized mode of a lossy cavity. We show that, when the frequencies of the two atoms are symmetrically detuned from that of the cavity mode, oscillations between Zeno and anti-Zeno regimes occur. We also calculate analytically the ti…
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.
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 …
We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal $\mathrm{^{13}C}$ nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a $^{13}$C nuclear spin in the vicinity of an NV center.
By repeatedly measuring a quantum system, the evolution of the system can be slowed down (the quantum Zeno effect) or sped up (quantum anti-Zeno effect). We study these effects for a single two-level system coupled to a collection of harmonic oscillators. Previously, such systems have been studied in both the weak and the strong system-environment coupling regimes. In this paper, we apply a polaron transformation in a manner that allows us to study the quantum Zeno and anti-Zeno effects for a large variety of system-environment parameters. Using this approach, we reproduce previous results for…
In this work we show that is possible to obtain Total Quantum Zeno Effect in an unstable systems for times larger than the correlation time of the bath. The effect is observed for some particular systems in which one can chose appropriate observables which frequent measurements freeze the system into the initial state. For a two level system in a squeezed bath one can show that there are two bath dependent observables displaying Total Zeno Effect when the system is initialized in some particular states. We show also that these states are intelligent states of two conjugate observables associat…
A general treatment of the quantum Zeno and anti-Zeno effects is presented which is valid for an arbitrary system-environment model in the weak system-environment coupling regime. It is shown that the effective lifetime of a quantum state that is subjected to repeated projective measurements depends on the overlap of the spectral density of the environment and a generalized `filter function' which in turn depends on the system state that is repeatedly being prepared, the measurement interval, the system parameters, the system-environment coupling, and the environment correlation function. This…
In this work a simple classical analog of the quantum Zeno effect is suggested. As it is well known, in the quantum mechanics, in the limit of the infinite series of alternative short dynamical evolution and measurement, an unstable quantum system will never decay, that is called quantum Zeno effect. Here an ideal (without resistance), classical LC oscillating circuit with quick switch ON-OFF alternation is considered. In the limit of the infinite series of alternative short electrical current regime (switch in the ON state) and no-current regime (current breaking by quick switch ON-OFF state …
Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler are studied. The asymmetric nonlinear optical coupler is composed of a linear waveguide ($χ^{\left(1\right)}$) and a nonlinear waveguide ($χ^{\left(2\right)}$) interacting with each other through the evanescent waves. The nonlinear waveguide has quadratic nonlinearity and it operates under second harmonic generation. A completely quantum mechanical description is used to describe the system. The closed form analytic solutions of Heisenberg's equations of motion for the different field modes are obtained using Sen-Man…
A "continuous measurement" Quantum Zeno Effect (QZE) in the context of trapped ions is predicted. We describe the physical system and study its exact time evolution showing the appearance of Zeno Phenomena. New indicators for the occurrence of QZE in oscillatory systems are proposed and carefully discussed.
We investigate the quantum Zeno and anti-Zeno effects on pairwise entanglement dynamics of a collective of non-interacting qubits which have been initially prepared in a Werner state and are off-resonantly coupled to a common and non-Markovian environment. We obtain the analytical expression of the concurrence in the absence and presence of the non-selective measurements. In particular, we express our results in the strong and weak coupling regimes and examine the role of the system size, and the effect of the detuning from the cavity field frequency on the temporal behaviour of the pairwise e…
Generalizing a recent analysis, we model the quantum Zeno and anti-Zeno effects with a quickly switched, ideal LC/LR circuit, in the limiting case of it alternating very many times between its short LC and even shorter LR regime. If the initial current is arranged to be negligible, the capacitor turns out never to discharge. If the initial current is made dominant, this capacitor discharges, and faster than the exponential decay to which it limits. The existence and simplicity of these phases in such a rudimentary model indicates that the corresponding effects are ubiquitous throughout physics…
We report the first observation of the Quantum Zeno and Anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong non-exponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of non-exponential decay. Depending on the frequency of measurements we …
It is shown that inverse quantum Zeno effect (IZE) may exist in a three-level system with Rabi oscillations between discrete atomic states. The experiment to observe IZE in such a system is proposed.
As of October 2006, there were approximately 535 citations to the seminal 1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox (more often called the quantum Zeno effect). In simple terms, the quantum Zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. There has been much disagreement as to how the quantum Zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of "ordinary" quantum mechanics. The experiment of Itano, Heinzen, Bollinge…
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum …
The quantum Zeno effect is deeply related to the quantum measurement process and thus studies of it may help shed light on the hitherto mysterious measurement process in quantum mechanics. Recently, the spatial quantum Zeno effect is observed in a Bose-Einstein condensate depleted by an electron beam. We theoretically investigate how different intrinsic tendencies of filling affect the quantum Zeno effect in this system by changing the impinging point of the electron beam along the inhomogeneous condensate. Surprisingly, we find no visible effect on the critical dissipation intensity at which …
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 c…
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 d…
The giant atom system is a new paradigm in quantum optics, in which the traditional dipole approximation is not available. In this paper, we construct an artificial giant atom model by coupling a superconducting circuits to a transmission line by two coupling points. In the ultrastrong coupling regime, we show that the Lamb shift of the giant atom, which is induced by the non-negligible counter-rotating atom-waveguide coupling term, will modify its dissipation process. Furthermore, we investigate quantum Zeno and anti-Zeno effect where the size of the giant atom serves as a sensitive controlle…
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…
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.
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.
Quantum Zeno effect is conventionally interpreted by the assumption of the wave-packet collapse, in which does not involve the duration of measurement. However, we predict duration $τ_m$ of each measurement will appear in quantum Zeno effect by a dynamical approach. Moreover, there exists a model-free critical measurement time, which quantum Zeno effect does not occur when $τ_m$ takes some special values. In order to give these predictions, we first present a description of quantum Zeno effect in the Heisenberg picture, which is based on the expectation value of an observable and its fluctuati…
In this paper, we look into what happens to a quantum system under repeated measurements if it interacts with two independent reservoirs. In particular, we look at the behavior of a two-level system interacting with reservoirs consisting of harmonic oscillators. The interaction with one reservoir is weak with a dissipative-type coupling, while the interaction with the other reservoir is strong with a dephasing-type coupling. Using a polaron transformation, we show that the presence of the strongly coupled reservoir can actually reduce the decay rate of the quantum system due to the effect of t…
The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and sever…
The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical observables is slowed down through measurements even though the quantum state changes randomly with time. Based on the operator quantum Zeno effect, we show how we can protect quantum information from decoherence with two-qubit measurements, realizable with noisy two-qubit interactions.
The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time $t_{S}$, (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes and leading to an inverse power law decay. At this last cross-over time $t_{R}$ a survival collapse becomes possible…
The dynamics of a quantum system undergoing measurements is investigated. Depending on the features of the interaction Hamiltonian, the decay can be slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by changing the time interval between successive (pulsed) measurements or, alternatively, by varying the "strength" of the (continuous) measurement.
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…
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…
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 measurements - only the …
The effect of entangling evolution induced by frequently repeated quantum measurement is presented. The interesting possibility of conditional freezing the system in maximally entangled state out of Zeno effect regime is also revealed. The illustration of the phenomena in terms of dynamical version of ``interaction free'' measurement is presented. Some general conclusions are provided.
Three different manifestations of the quantum Zeno effect are discussed, compared and shown to be physically equivalent. We look at frequent projective measurements, frequent unitary "kicks" and strong continuous coupling. In all these cases, the Hilbert space of the system splits into invariant "Zeno" subspaces, among which any transition is hindered.
We develop a protocol based on 2M pairwise interacting qubits, which through Quantum Zeno Effect controls the entanglement distribution of the system. We also show that if the coupling constants are different the QZE may be used to achieve perfect entanglement swap.
Measurements in quantum mechanics can not only effectively freeze the state of the quantum system (the quantum Zeno effect) but also accelerate the time evolution of the system (the quantum anti-Zeno effect). In studies of the quantum Zeno and anti-Zeno effects, a quantum state, usually an excited state of the system, is prepared repeatedly by projecting the quantum state onto the initial state again and again. In this paper, we repeatedly prepare the initial quantum state in a different manner. Instead of only performing projective measurements, we allow unitary operations to be performed, on…
We analyse non-quadratic in time Zeno effect which arises when a few-atom state initially trapped between two high laser-induced barriers is briefly released to free evolution. We identify the Zeno time, analyse the energy distributions of those atoms which have escaped an remained inside the trap, and obtain a simple relation between the survival and non-escape probabilities. The relevant time scales are such that the effect would be observable for the atomic species used in current laser experiments.
In this paper, we show that the quantum Zeno effect occurs for any frequent quantum measurements or operations. As a result of the Zeno effect, for non-selective measurements (or trace preserving completely positive maps), the evolution of a measurement invariant state is governed by an effective Hamiltonian defined by the measurements and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, while some physical quantities (operators) still evolve as the effective dynamics.
Quantum Zeno effect is a significant tool in quantum manipulating and computing. We propose its observation in superconducting phase qubit with two experimentally feasible measurement schemes. The conventional measurement method is used to achieve the proposed pulse and continuous readout of the qubit state, which are analyzed by projection assumption and Monte Carlo wave-function simulation, respectively. Our scheme gives a direct implementation of quantum Zeno effect in a superconducting phase qubit.
It is well known that repeated projective measurements can either speed up (the Zeno effect) or slow down (the anti-Zeno effect) quantum evolution. Until now, however, studies of these effects for a two-level system interacting strongly with its environment have focused on repeatedly preparing the excited state of the two-level system via the projective measurements. In this paper, we consider the repeated preparation of an arbitrary state of a two-level system that is interacting strongly with an environment of harmonic oscillators. To handle the strong interaction, we perform a polaron trans…
