Zeno Effect Research Articles

External-level assisted cooling by measurement

A quantum resonator in a thermal-equilibrium state with a high temperature has a large average population and is featured with significant occupation over Fock states with a high excitation number. The resonator could be cooled down via continuous measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we introduce strong driving between the excited state of the qubit and an external level. It can remarkably broaden the cooling range in regard to the non-vanishing populated Fock states of the resonator. Without any precooling procedure, our strategy allows a significant reduction of the populations over Fock states with a high excitation number, giving rise to nondeterministic ground-state cooling after a sequence of measurements. The driving-induced fast transition constrains the resonator and the ancillary qubit at their ground state upon measurement and then simulates the quantum Zeno effect. Our protocol is applied to cool down a high-temperature magnetic resonator. Additionally, it is generalized to a hybrid cooling protocol by interpolating the methods with and without strong driving, which can accelerate the cooling process and increase the overlap between the final state of the resonator and its ground state.

Revisiting quantum Zeno effect and anti-Zeno effect: Universality vs non-universality

Universality vs non-universality on the quantum Zeno effect and the anti-Zeno effect is discussed. It is well-known that the Zeno effect is a result of the branch point effect based on the constraint that the energy spectrum is bounded from below. On the other hand, we show that the anti-Zeno effect arises from the interference of multiple complex poles in the lower half energy plane on a larger time scale compared with the Zeno time. Since the production of extra complex poles depends on the characteristics of the interaction Hamiltonian, we emphasize that the anti-Zeno effect is model-dependent and non-universal, while the Zeno effect is a universal phenomenon independent of the form of the interaction.

Discrete optical Zeno effect for polarization of light

Quantum Zeno effect concerns deterministic dynamics of a quantum system induced by a series of projective quantum measurements. Applying this effect in optics, one can achieve an arbitrary lossless transformation of linear polarization of light with help of linear polarizers. However, to demonstrate this effect in practice, we have to take into account unavoidable losses in each polarizer that limits probability of successful transformations. In this work, we theoretically study a realistic quantum Zeno effect with an optimal discrete set of polarizers and find the maximum success probability

The tunable 0−π qubit: Dynamics and relaxation

In this paper, we present a systematic treatment of a [Formula: see text] qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian are obtained. The effect of the flux noise on the qubit relaxation is obtained using the perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

Shape effects of localized losses in quantum wires: Dissipative resonances and nonequilibrium universality

We study the effects of the spacial structure of localized losses in weakly-interacting fermionic quantum wires. We show that multiple dissipative impurities give rise to resonant effects visible in the transport properties and the particles' momentum distribution. These resonances can enhance or suppress the effective particle losses in the wire. Moreover, we investigate the interplay between interactions and the impurity shape and find that, differently from the coherent scatterer case, the impurity shape modifies the scaling of the scattering probabilities close to the Fermi momentum. We show that, while the fluctuation-induced quantum Zeno effect is robust against the shape of the impurities, the fluctuation-induced transparency is lifted continuously. This is reflected in the emergence of a continuous line of fixed points in the renormalization group flow of the scattering probabilities.

Rényi entropy dynamics and Lindblad spectrum for open quantum systems

In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second R\'enyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second R\'enyi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.

Abrupt energy flipping in a continuously observed Rabi driven quantum bit

In the presence of a periodic external drive, the mean value of the energy of a two-level quantum system (or qubit) displays the well-known Rabi oscillatory dynamics that is usually described within the rotating wave approximation. In order to calculate its standard deviation, we get rid of this latter and obtain a huge ratio (of order unity) of standard deviation over mean value. This is due to the large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. In presence of continuous measurement of, say, the ground state energy that yields the quantum Zeno effect, the system remains frozen in its ground state as long as the dynamics of the driven system allows its energy to stay within its Rabi standard deviation. When reaching the boundary, the energy suddenly flips over to the excited level in order to stay further within its standard deviation. We model this energy flip by use of parametrized quantum transitions and show that it can be defined as the result of action quantization. We check our theory by recovering the so-called “quantum jumps” published by Minev et al. (2019).

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

Quantum Zeno Jumps in a Resonantly Driven Qubit under Frequent Measurements

In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.

Relativity: photon

For the case of interaction of polarized light with an analyzer (a polarizing device), an experimental scheme based on the Feynman idea of path integrals is proposed. Real and virtual photons are considered in the context of the Lenz rule (in terms of constructive and destructive induction). The Planck formula for the photon energy in the format of a verbal description is considered. The complexity of identifying the wave description of the photon with the ideas of the Ancient Greeks about elementary particles is shown. From the point of view of chronogeometry, it is shown that the stationary observer does not exist at the point of intersection of the cone of the past and the future, but in the time interval separating these regions. It is proposed to consider the fluctuations of the physical vacuum as a relic of the process of permanent inflation according to Linde. Based on the assumption of the self-measurement of the Universe, the quantum Zeno effect, and Hawking’s idea of the Universe being a quantum object with the Nth sum of Feynman stories, it is assumed that the history of the Universe is deterministic. From the perspective of the orthogonality of the electromagnetic field vectors E and B, the Heisenberg equation of the form Δp × Δx = ħ/2 is considered. A thought experiment is considered showing the complexity in describing the interaction of a photon with an electron of an atom from the point of view of the classical interaction of an electromagnetic wave with an antenna device. It is proposed to consider the absorption of a photon by an electron as its inertial collapse on an atom.

Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit

Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.

Strong correlations in lossy one-dimensional quantum gases: From the quantum Zeno effect to the generalized Gibbs ensemble

We consider strong two-body losses in bosonic gases trapped in one-dimensional optical lattices. We exploit the separation of time scales typical of a system in the many-body quantum Zeno regime to establish a connection with the theory of the time-dependent generalized Gibbs ensemble. Our main result is a simple set of rate equations that capture the simultaneous action of coherent evolution and two-body losses. This treatment gives an accurate description of the dynamics of a gas prepared in a Mott insulating state and shows that its long-time behaviour deviates significantly from mean-field analyses. The possibility of observing our predictions in an experiment with $^{174}$Yb in a metastable state is also discussed.

Quantum Zeno Effect in Open Quantum Systems

We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for open quantum systems in the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.

Quantum Zeno control of spin mixing and squeezing in a spinor Bose–Einstein condensate

We study the effect of dephasing on the spin-mixing dynamics of a spinor Bose–Einstein condensate. We focus on a short-time dynamics and derive an analytical dynamics equations for the system by using mean-field approximation. We show the spin-mixing is suppressed via a quantum Zeno effect (QZE) in which the phase-noise intensity is much stronger than the inverse correlation time of the stimulated process. We also investigate the spin-nematic squeezing in the process of spin-mixing dynamics and show the squeezing is restrained by the QZE.

F-cluster: Reaction-induced spin correlation in multi-radical systems.

We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space

We experimentally study quantum Zeno effects in a parity-time (PT) symmetric cold atom gas periodically coupled to a reservoir. Based on the state-of-the-art control of inter-site couplings of atoms in a momentum lattice, we implement a synthetic two-level system with passive PT symmetry over two lattice sites, where an effective dissipation is introduced through repeated couplings to the rest of the lattice. Quantum Zeno (anti-Zeno) effects manifest in our experiment as the overall dissipation of the two-level system becoming suppressed (enhanced) with increasing coupling intensity or frequency. We demonstrate that quantum Zeno regimes exist in the broken PT symmetry phase, and are bounded by exceptional points separating the PT symmetric and PT broken phases, as well as by a discrete set of critical coupling frequencies. Our experiment establishes the connection between PT-symmetry-breaking transitions and quantum Zeno effects, and is extendable to higher dimensions or to interacting regimes, thanks to the flexible control with atoms in a momentum lattice.

Dynamic Quantum Games

Quantum games represent the really twenty-first century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated games. In this paper, we aim at initiating the truly dynamic theory with strategies chosen by players in real time. Since direct continuous observations are known to destroy quantum evolutions (so-called quantum Zeno paradox), the necessary new ingredient for quantum dynamic games must be the theory of non-direct observations and the corresponding quantum filtering. Apart from the technical problems in organizing feedback quantum control in real time, the difficulty in applying this theory for obtaining mathematically amenable control systems is due partially to the fact that it leads usually to rather non-trivial jump-type Markov processes and/or degenerate diffusions on manifolds, for which the corresponding control is very difficult to handle. The starting point for the present research is the remarkable discovery (quite unexpected, at least to the author) that there exists a very natural class of homodyne detections such that the diffusion processes on projective spaces resulting by filtering under such arrangements coincide exactly with the standard Brownian motions (BM) on these spaces. In some cases, one can even reduce the process to the plain BM on Euclidean spaces or tori. The theory of such motions is well studied making it possible to develop a tractable theory of related control and games, which can be at the same time practically implemented on quantum optical devices.

Quantum Zeno effect in self-sustaining systems: Suppressing phase diffusion via repeated measurements

We study the effect of frequent projective measurements on the dynamics of quantum self-sustaining systems by considering the prototypical example of the quantum van der Pol oscillator. Quantum fluctuations are responsible for phase diffusion which progressively blurs the semiclassical limit-cycle dynamics and synchronization, either to an external driving or between two coupled self-sustained oscillators. We show that by subjecting the system to repeated measurements of heterodyne type at an appropriate repetition frequency one can significantly suppress phase diffusion without spoiling the semiclassical dynamics. This quantum Zeno-like effect may be effective in the case of either one or two coupled van der Pol oscillators, and we discuss its possible implementation in the case of trapped ions.

Taking the measure of quantum dynamics

1. Quantum Zeno effect and the many-body entanglement transition Authors: Y. Li, X. Chen, and M.P. A. Fisher Phys. Rev. B 98, 205136 (2018); DOI: 10.1103/PhysRevB.98.205136 2. Measurement-Induced Phase Transitions in the Dynamics of Entanglement Authors: B. Skinner, J. Ruhman, and A. Nahum Phys. Rev. X 9, 031009 (2019); DOI: 10.1103/PhysRevX.9.031009 3. Unitary-projective entanglement dynamics […]

Quantum dynamics under continuous projective measurements: Non-Hermitian description and the continuum-space limit

The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian. As a specific example we consider the evolution of a quantum particle on a one-dimensional lattice that is subjected to position measurements at a specific site. By solving the corresponding non-Hermitian wave function evolution equation, we present analytic closed-form results on the survival probability and the first arrival time distribution. Finally we discuss the limit of vanishing lattice spacing and show that this leads to a continuum description where the particle evolves via the free Schrodinger equation with complex Robin boundary conditions at the detector site. Several interesting physical results for this dynamics are presented.