Under certain assumptions it is shown that the decay of level 2 of a three-level system onto level 1 is slowed down because of the further decay of level 1 onto level 0. It is argued that this phenomenon may be interpreted as a consequence of the quantum Zeno effect. The reason why this may be possible is that the second decay (or accompanying photon radiation) may be considered as a sign of the transition 2 -> 1 so that during the first transition the system is under continuous observation.
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.
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 …
We analyze the Zeno phenomenon in quantum field theory. The decay of an unstable system can be modified by changing the time interval between successive measurements (or by varying the coupling to an external system that plays the role of measuring apparatus). We speak of quantum Zeno effect if the decay is slowed and of inverse quantum Zeno (or Heraclitus) effect if it is accelerated. The analysis of the transition between these two regimes requires close scrutiny of the features of the interaction Hamiltonian. We look in detail at quantum field theoretical models of the Lee type.
We consider a driven 2-level system with one level showing spontaneous decay to an otherwise uncoupled third level. Rabi transitions to the unstable level are strongly damped. This simple configuration can be used to demonstrate and to explore the quantum Zeno effect leading to a freezing of the system to the initial level. A comparison with repeated projection measurements is given. A treatment within a phenomenological theory of continuous measurements is sketched. The system visualizes the important role of null measurements (negative result measurements) and may serve as a good example for…
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 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 theoretically propose a scheme for verification of quantum Zeno effect (QZE) to suppress a decay process with Nuclear Magnetic Resonance (NMR). Nuclear spins are affected by low frequency noise, and so one can naturally observe non-exponential decay behavior, which is prerequisite in observing QZE. We also describe that a key component for QZE, namely measurements on the nuclear spin, can be realized with NMR in the current technology
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.
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.
The time evolution of an unstable quantum mechanical system coupled with an external measuring agent is investigated. According to the features of the interaction Hamiltonian, a quantum Zeno effect (hindered decay) or an inverse quantum Zeno effect (accelerated decay) can take place, depending on the response time of the apparatus. The transition between the two regimes is analyzed for both pulsed and continuous measurements.
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 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…
We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a Field injected in the cavity by a classical source. This manifestation of the Quantum Zeno effect illustrates the back action of the photon number determination onto the Field phase. The residual growth of the Field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the meas…
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…
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…
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 …
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…
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.
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the the statistical indistinguishability of neighboring quantum states. The accessibility of quantum Zeno dynamics under unitary time evolution can be quantitatively estimated by quantum Zeno time in terms of Fisher information. In this work, we investigate the accessibility of quantum Zeno dynamics in quantum open systems by calculating noisy Fisher information, in which a trace preserving and co…
The quantum Zeno effect is the prediction, going back to Alan Turing, that the decay of an unstable system can be slowed down by measuring it frequently enough. It was also noticed later that the opposite effect, i.e., enhancement of the decay due to frequent measurements, is rather common. An important question arising in this regards is how to choose the optimal measurement strategy to achieve the highest possible decay rate. Here we rigorously prove the universal optimality of the stroboscopic measurement protocol in the sense that it always provides the shortest expected decay time among a…
Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the experimental setup for the observation, one could obtain the so called (direct) quantum Zeno and inverse quantum Zeno effects corresponding to a slowing down or a speeding up of the decay, respectively. We argue that the inverse quantum Zeno effect is in principle detectable at a percent level for the neutron decay in experiments with trapped ultracold neutrons. Conver…
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.
We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never escapes from the region -- this is the Zeno effect. The aim of this paper is to show how the Zeno effect disappears in the classical limit in this and similar examples. We give a general argument showing that the Zeno effect is suppressed in the presence of a decoherence mechanism which kills interference between histories. We show how this works explicitly by cou…
Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article, Nature 405, 546 (2000), Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of a…
A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli. The central idea is to treat the perception process in terms of the evolution of an unstable two-state quantum system, yielding a quantum Zeno type of effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.
We experimentally demonstrate all-optical interaction-free switching using the quantum Zeno effect, achieving a high contrast of 35:1. The experimental data matches a zero-parameter theoretical model for several different regimes of operation, indicating a good understanding of the switch's characteristics. We also discuss extensions of this work that will allow for significantly improved performance, and the integration of this technology onto chip-scale devices.
The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these…
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…
S. Longhi [1] studied the survival probability P(t) of an unstable state coupled to a tight-binding lattice finding an exact analytical solution that describes the nonexponential decay. When the first coupling is smaller than the others, he shows that P(t) has a natural decomposition into two terms; one is the exponential decay, consistent with the Gamow's approach, and the other is the correction to this decay. The first purpose of this Comment is to show that the condition imposed on the system; the site energy of the first site is set in the center of the band, limits the generality of the …
We study the temporal behavior of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. We analyze the dependence of the lifetime of the initial state on the intensity of the laser field. The phenomenon we discuss is related to both electromagnetic induced transparency and quantum Zeno effect.
A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to ob…
We use a caricature model of a system consisting of a quantum wire and a finite number of quantum dots, to discuss relation between the Zeno dynamics and the stable one which governs time evolution of the dot states in the absence of the wire. We analyze the weak coupling case and argue that the two time evolutions can differ significantly only at times comparable with the lifetime of the unstable system undisturbed by perpetual measurement.
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the meas…
Frequent Measurements on an unstable particle located at observable initial state freeze the particle on this state, known as quantum Zeno effect [1-14]. Measurements on an observable subspace further open the prelude of quantum Zeno dynamics [15-17]. These phenomena affect the results of quantum measurement that has been widely used in quantum information and quantum computation [18-21]. However, this common argument is insufficient when the initial state is coupled with a continuum reservoir. In such an irreversible system, intrinsic decay property destroys the frozen behavior. Although it h…
In a renormalizable theory the survival probability of an unstable quantum state features divergences as a consequence of the rapid growth of the density of states with energy. Introducing a high energy cutoff $Λ$, the transient dynamics during a time scale $\simeq 1/Λ$ describes the renormalization of the bare into a `quasiparticle' state which decays on longer time scales. During this early transient the decay law features Zeno behavior $e^{-(t/t_Z)^2}$ with the Zeno time-scale $t_Z \propto 1/Λ^{3/2}$. We introduce a dynamical renormalization framework that allows to separate consistently th…
We modify the theory of the Quantum Zeno Effect to make it consistent with the postulates of quantum mechanics. This modification allows one, throughout a sequence of observations of an excited system, to address the nature of the observable and thereby to distinguish survival from non-decay, which is necessary whenever excited states are degenerate. As a consequence, one can determine which types of measurements can possibly inhibit the exponential decay of the system. We find that continuous monitoring taken as the limit of a sequence of ideal measurements will only inhibit decay in special …
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 discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is $Γ(ω)=g^{2}ω^α,$ then -- under quite general assumptions -- t…
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.
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse--power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probabilit…
We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time-development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the…
Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($τ_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the term "quantum jump." The problem studied here is whether the "jump" can be assigned a duration, in theory and in experiment. Two characteristic times are defined, jump time ($τ_J$) and passage time ($τ_P$). Both use Zeno time, $τ_Z$, defined in terms of $H$ and its initial state as $τ_Z \equiv \hbar/\sqrt{<ψ| (H-E_ψ)^2 |ψ>}$, with $E_ψ\equiv <ψ|H|ψ>$. $τ_J$ is de…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to d…
We describe -- in a didactical and detailed way -- the so-called Lee model (which shares similarities with the Jaynes-Cummings and Friedrichs models) as a tool to study unstable quantum states/particles. This Lee model is based on Quantum Mechanics (QM) but possesses some of the features of Quantum Field Theory (QFT). The decay process can be studied in great detail and typical QFT quantities such as propagator, one-loop resummation, and Feynman rules can be introduced. Deviations from the exponential decay law as well as the Quantum Zeno effects can be studied within this framework. The survi…
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 …
