Zeno dynamics for open quantum systems

In this paper, we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems, we present a condition for stability of the asymptotic Zeno dynamics.     

Quantum Zeno Dynamics Through Stochastic Protocols

Quantum measurements play a crucial role in quantum mechanics since they perturb, unavoidably and irreversibly, the state of the measured quantum system. More extremely, the constant observation of a quantum system can even freeze its dynamics to a subspace, effectively truncating the Hilbert space of the system. It represents the quantum version of the famous flying arrow Zeno paradox, and is called quantum Zeno dynamics. In general, it can be obtained by applying frequent consecutive quantum measurements that are equally spaced in time. Here, we introduce time disorder in the measurement sequence, and analytically investigate how this temporal stochasticity may affect the confinement probability of the system in the subspace. As main result, we then exploit how different dissipative and coherent Zeno protocols can be generalized to this stochastic scenario. Finally, our analytical predictions are numerically tested on a paradigmatic spin chain where we find a trade‐off between a probabilistic scheme with high fidelity (compared to perfect subspace dynamics) and a deterministic one with a slightly lower fidelity, moving further steps towards new schemes of Zeno‐based control for future quantum technologies.     

Nonlocality of interaction and quantum Zeno paradox

The short-time behavior of the evolution operator has been investigated in the context of the quantum Zeno paradox. It is shown that the nonlocality during interaction in a quantum system radically changes the short-time behavior of the dynamics, and, as result, the Zeno effect may not occur in such interactions.     

Quantum Zeno effect: Quantum shuffling and Markovianity

The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.     

Zeno and anti-Zeno effects for quantum Brownian motion

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

Quantum computing using dissipation to remain in a decoherence-free subspace

We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.     

Tunneling measurement of a single quantum spin

Measurement of the tunneling current of spin-polarized electrons via a molecule with a localized spin provides information on the orientation of that spin. We show that a strong tunneling current due to the shot noise suppresses the spin dynamics, such as the spin precession in an external magnetic field, and the relaxation due to the environment (quantum Zeno effect). A weak tunneling current preserves the spin precession with the oscillatory component of the current of the same order as the noise. We propose an experiment to observe the Zeno effect in a tunneling system and describe how the tunneling current may be used to read a qubit represented by a single spin 1/2.     

Thermal modulation in Zeno and anti-Zeno effects on quantum measurement

We have proposed the mathematical formulations of quantum Zeno and anti-Zeno effects at non-zero temperature on vibrational population transfer and dissociation of a diatomic system. The proposed formulation has been tested for diatomic systems HBr⁺ and HI using time-dependent Fourier grid Hamiltonian method. The effect of temperature on the dynamics is incorporated through the population distribution at different vibrational states following Boltzmann distribution formula. It has been found that with increase in temperature Zeno effect increases and anti-Zeno effect decreases in case of survival probability on ground vibrational state. In case of dissociation, with increase in temperature Zeno effect increases while anti-Zeno effect remains almost same.     

A structural model of market dynamics,and why it matters

In this paper, we explore an approach to understanding price fluctuations within a market via considerations of functional dependencies between asset prices. Interestingly, this approach suggests a class of models of a type used earlier to describe the dynamics of real and artificial neural networks. Statistical physics approaches turn out to be suitable for an analysis of their collective properties. In this paper, we first motivate the basic phenomenology and modelling arguments before moving on to discussing some major issues with inference and empirical verification. In particular, we focus on the natural creation of market states through the inclusion of interactions and how these then interfere with inference. This is primarily addressed in a synthetic setting. Finally we investigate real data to test the ability of our approach to capture some key features of the behaviour of financial markets.     

Quantum Zeno and Anti-Zeno Effects in the Dynamics of Non-Degenerate Hyper-Raman Processes Coupled to Two Linear Waveguides

The effect of the presence of two probe waveguides on the dynamics of hyper-Raman processes is studied in terms of quantum Zeno and anti-Zeno effects. Specifically, the enhancement (diminution) of the evolution of the hyper-Raman processes due to interaction with the probe waveguides via evanescent waves is viewed as quantum Zeno (anti-Zeno) effect. This study considers the two probe waveguides interacting with only one of the optical modes at a time. For instance, as a specific scenario, it is considered that the two non-degenerate pump modes interact with each probe waveguide linearly, while Stokes and anti-Stokes modes do not interact with the probes. Similarly, in another scenario, it is assumed both the probe waveguides interact with Stokes (anti-Stokes) mode simultaneously. The present results show that quantum Zeno (anti-Zeno) effect is associated with phase-matching (mismatching). However, it do not find any relation between the presence of the quantum Zeno effect and antibunching in the bosonic modes present in the hyper-Raman processes.     

The chemical zeno effect in exchange-coupled radical Pairs: 1. Triplet radical pairs

It was shown that spin-selective intracage recombination could influence the limiting triplet-singlet conversion stage and, therefore, the whole chemical dynamics. An increase in the rate constant for intracage recombination w decreases the S-T evolution frequency and changes its character by transforming the oscillating spin conversion mode into “kinetic.” As a result, an increase in w can decrease the yield of intracage recombination products and increase the yields of products formed in competing extracellular radical reaction channels. The chemical Zeno effect and its consequences are an analogue of the quantum Zeno effect (quantum evolution “deceleration” caused by successive measurements), and spin-selective recombination is similar to quantum state measurements.     

Preparing Greenberger-Horne-Zeilinger States by Lypunov Control

International Journal of Theoretical Physics - A scheme is proposed for preparing Greenberger-Horne-Zeilinger (GHZ) states by Lyapunov control based on quantum Zeno dynamics. The advantage of our...     

Protecting entanglement via the quantum Zeno effect

We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect.     

Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics

We discuss an implementation of quantum Zeno dynamics in a cavity quantum electrodynamics experiment. By performing repeated unitary operations on atoms coupled to the field, we restrict the field evolution in chosen subspaces of the total Hilbert space. This procedure leads to promising methods for tailoring nonclassical states. We propose to realize "tweezers" picking a coherent field at a point in phase space and moving it towards an arbitrary final position without affecting other nonoverlapping coherent components. These effects could be observed with a state-of-the-art apparatus.     

One-step implementation of the Toffoli gate via quantum Zeno dynamics

Based on the quantum Zeno dynamics, we present a scheme for one-step implementation of a Toffoli gate via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity. The effects of decoherence such as spontaneous emission and the loss of cavity are also considered.     

Single-photon-level light storage with distributed Rydberg excitations in cold atoms

We present an improved version of the superatom (SA) model to examine the slow-light dynamics of a few-photons signal field in cold Rydberg atoms with van der Waals (vdW) interactions. A main feature of this version is that it promises consistent estimations on total Rydberg excitations based on dynamic equations of SAs or atoms. We consider two specific cases in which the incident signal field contains more photons with a smaller detuning or less photons with a larger detuning so as to realize the single-photon-level light storage. It is found that vdW interactions play a significant role even for the slow-light dynamics of a single-photon signal field as distributed Rydberg excitations are inevitable in the picture of dark-state polariton. Moreover, the stored (retrieved) signal field exhibits a clearly asymmetric (more symmetric) profile because its leading and trailing edges undergo different (identical) traveling journeys, and higher storage/retrieval efficiencies with well preserved profiles apply only to weaker and well detuned signal fields. These findings are crucial to understand the nontrivial interplay of single-photon-level light storage and distributed Rydberg excitations.     

Zeno effect in quantum Newton's cradle

We describe a chain of quantum oscillators which behaves analogously to Newton's cradle. The energy swings between the ends of the chain with very low population in its interior. Moreover, the oscillators at the ends can entangle with each other with negligible entanglement with the intermediate oscillators that mediate the process. Up to a certain number of oscillators, the system evolves in a manner similar to two coupled oscillators. The conditions for such behavior and the characteristic periods are analyzed. When that number exceeds a threshold, the dynamical regime changes to virtually freezing. In the oscillatory regime, Zeno effect can be observed. The parallelism between the Zeno dynamics in quantum Newton's cradle and in two coupled oscillators is highlighted. Promising platforms to observe such phenomena in the laboratory are cavities in photonic-band-gap material and trapped ions.     

Tripartite entanglement of atoms trapped in coupled cavities via quantum Zeno dynamics

A scheme is proposed for the generation of a W state for three atoms trapped in spatially separated cavities connected by optical fibers via quantum Zeno dynamics. Our scheme is based on the resulting effective dynamics induced by continuous coupling between the atoms and cavities. The effects of decoherence such as atomic spontaneous emission and the fiber and cavity losses are considered. Numerical results show that the scheme is very robust against the cavity decay due to a tiny excitation probability of the cavity fields during the operation.     

Distributed qutrit-qutrit entanglement via quantum Zeno dynamics

A scheme is proposed to generate a three-dimensional entangled state for two atoms trapped in two distant cavities via quantum Zeno dynamics. We study such system in the regime of resonant atom-field interactions, which makes the scheme work very fast. We also investigate the influence of dissipation, due to atomic spontaneous emission and photon leakage, on the qutrit-qutrit entanglement.     

Space Zeno Effect

The Zeno effect has been defined and discussed theoretically, and even proved experimentally, only in connection with time-displaced wave functions. This time displacement corresponds to the measurement time of the relevant experiment. If this experiment is repeated successively a very large number of times in a finite time where, in the limit of dense measurement, we take an infinitesimal measurement time, then the initial state is preserved. This is the usual definition of the Zeno effect. In this work the Zeno effect is discussed explicitly in connection with space-displaced wave functions. Here the repetition of the same experiment over the time axis is replaced by simultaneous performances of the same experiment in a number of identical independent nonoverlapping regions of space. We show that when these regions of space shrink infinitesimally (corresponding to the infinitesimal shrinkage of the measurement times in the time Zeno effect), then we obtain a space Zeno effect, that is, the simultaneous performance of such closely spaced experiments has a null effect.