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 using engineered reservoirs in the trapped ion context .
We study the quantum Brownian motion of a harmonic oscillator undergoing a sequence of generalized position measurements. Our exact analytical results capture the interplay of the measurement backaction and dissipation. Here we demonstrate that no freeze-in Zeno effect occurs upon increasing the monitoring frequency. A similar behavior is also found in the presence of generalized momentum measurements.
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.
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…
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…
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.
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…
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…
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…
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 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 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 have studied a hybrid system of a one-dimensional coupled-cavity waveguide with a two-level system inside, which subject to a external periodical field. Using the extended Hilbert space formalism, the time-dependent Hamiltonian is reduced into an equivalent time-independent one. Via computing the Floquet-Green's function, the Zeno-anti-Zeno crossover is controlled by the driven intensity and frequency, and the detuning between the cavity and the two-level system.
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.
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 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 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 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 …
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…
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…
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 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…
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…
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 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…
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…
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…
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 demonstrate that near threshold decay processes may be accelerated by repeated measurements. Examples include near threshold photodetachment of an electron from a negative ion, and spontaneous emission in a cavity close to the cutoff frequency, or in a photon band gap material.
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…
We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements. Specifically, we establish the ability of a single photon, subjected to random polarisation noise, to diagnose non-Markovian temporal correlations of such a noise process. In the frequency domain, these noise correlations correspond to colored noise spectra, as opposed to the ones related to Markovian, white noise. Both the noise spectrum and its corresponding temporal correlations are diagnosed by probing the photon by means of frequent, (partially-)selective polarisation measurements. Our m…
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 …
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 show theoretically how the periodic coupling between an engineered reservoir and a quantum Brownian particle leads to the formation of a dynamical steady state which is characterized by an effective temperature above the temperature of the environment. The average steady state energy of the system has a higher value than expected from the environmental properties. The system experiences repeatedly a non-Markovian behavior -- as a consequence the corresponding effective decay for long evolution times is always on average stronger than the Markovian one. We also highlight the consequences of …
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…
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…
Quantum Zeno and Anti-Zeno Responses: Universal Spectral Criterion for Measurement-Induced Decay
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；Center of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences（中国科学院大学物质科学与光电技术研究中心）
A novel scheme is proposed for dissipative generation of maximally entanglement between two Rydberg atoms in the context of cavity QED. The spontaneous emission of atoms combined with quantum Zeno dynamics and Rydberg antiblockade guarantees a unique steady solution of the master equation of system, which just corresponds to the antisymmetric Bell state $|S\rangle$. The convergence rate is accelerated by the ground-state blockade mechanism of Rydberg atoms. Meanwhile the effect of cavity decay is suppressed by the Zeno requirement, leading to a steady-state fidelity about $90\%$ as the single-…
We propose a new methodology, namely "quantum Zeno blockade," for managing light scattering at a few-photon level in general nonlinear-optical media, such as crystals, fibers, silicon microrings, and atomic vapors. Using this tool, antibunched emission of photon pairs can be achieved, leading to potent quantum-optics applications such as deterministic entanglement generation without the need for heralding. In a practical implementation using an on-chip toroidal microcavity immersed in rubidium vapor, we estimate that high-fidelity entangled photons can be produced on-demand at MHz rates or hig…
We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) by modulating the central frequency of the cavity mode. Our results are obtained without using the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. When the central frequency of the cavity mode is resonant with the qubit energy level spacing, the normalized decay rate of the qubit is lower than 1, which manifests the QZE. However, when the cavity frequency is detuned from resonance, the normalized decay rate becomes larger than 1, wh…
Anti-Zeno boost in an autonomous quantized-piston thermal machine
Faculty of Basic Sciences, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology（吉尔·伊沙克汗工程科学与技术学院基础科学学院）；National Center for Quantum Computing, University of Engineering and Technology Narowal（纳罗瓦尔工程技术大学国家量子计算中心）
We combine the collisional picture for open system dynamics and the control of the rate of decoherence provided by the quantum (anti-)Zeno effect to illustrate the temporal unfolding of the redundant encoding of information into a multipartite environment that is at the basis of Quantum Darwinism, and to control it. The rate at which such encoding occurs can be enhanced or suppressed by tuning the dynamical conditions of system-environment interaction in a suitable and remarkably simple manner. This would help the design of a new generation of quantum experiments addressing the elusive phenome…
The fact that repeated projective measurements can slow down (the Zeno effect) or speed up (the anti-Zeno effect) quantum evolution is well-known. However, to date, studies of these effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then…
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…
In this paper, we look into what happens to a quantum system under repeated measurements if system evolution is removed before each measurement is performed. Beginning with investigating a single two-level system coupled to two independent baths of harmonic oscillators, we move to replacing it with a large collection of such systems, thereby invoking the large spin-boson model. Whereas each of our two-level systems interacts strongly with one of the aforementioned baths, it interacts weakly with the other. A polaron transformation is used to make it possible for the problem in the strong coupl…
Consequences of the deviation from the linear on time quantum transition probabilities leading to the nonexponential decay law and to the so-called Zeno effect are analysed. Main features of the quantum Zeno and quantum anti-Zeno effects for induced transitions are revealed on simple model systems.
Protecting Quantum States via the Super-Zeno Effect and Anticoherence
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；School of Physics and Optoelectronic Engineering, Hainan University（海南大学物理与电子工程学院）；Tikhonov Moscow Institute of Electronics and Mathematics, HSE University（高等经济大学季霍诺夫莫斯科电子与数学研究所）
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…
Quantum Zeno and anti-Zeno effects are studied in an asymmetric nonlinear optical coupler composed of a probe waveguide and a system waveguide. The system is a nonlinear waveguide operating under non-degenerate hyper-Raman process, while both the pump modes in the system are constantly interacting with the probe waveguide. The effect of the presence of probe on the temporal evolution of the system in terms of the number of photons in Stokes and anti-Stokes modes as well as phonon number is quantified as Zeno parameter. The negative (positive) values of the Zeno parameter in the specific mode a…
We demonstrate through exact solutions that a spin bath leads to stronger (faster) dephasing of a qubit than a bosonic bath with identical bath-coupling spectrum. This difference is due to the spin-bath "dressing" by the coupling. Consequently, the quantum statistics of the bath strongly affects the pulse sequences required to dynamically decouple the qubit from its bath.
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…
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…
