Linear and nonlinear quantum Zeno and anti-Zeno effects in a nonlinear optical coupler

Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear ($\chi^{\left(2\right)}$) 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 field modes are obtained using a perturbative technique. Photon number statistics of the second harmonic mode of the system is shown to depend on the presence of the probe, and this dependence is considered as quantum Zeno and anti-Zeno effects. Further, it is established that as a special case of the momentum operator for $\chi^{\left(2\right)}-\chi^{\left(2\right)}$ symmetric coupler we can obtain momentum operator of $\chi^{\left(2\right)}-\chi^{\left(1\right)}$ asymmetric coupler with linear ($\chi^{\left(1\right)}$) waveguide as the probe, and in such a particular case, the expressions obtained for Zeno and anti-Zeno effects with nonlinear probe (which we referred to as nonlinear quantum Zeno and anti-Zeno effects) may be reduced to the corresponding expressions with linear probe (which we referred to as the linear quantum Zeno and anti-Zeno effects). Linear and nonlinear quantum Zeno and anti-Zeno effects are rigorously investigated, and it is established that in the stimulated case, we may switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the system or probe.Comment: 13 pages 9 figure

Stability of Zeno Equilibria in Lagrangian Hybrid Systems

This paper presents both necessary and sufficient conditions for the stability of Zeno equilibria in Lagrangian hybrid systems, i.e., hybrid systems modeling mechanical systems undergoing impacts. These conditions for stability are motivated by the sufficient conditions for Zeno behavior in Lagrangian hybrid systems obtained in [11]—we show that the same conditions that imply the existence of Zeno behavior near Zeno equilibria imply the stability of the Zeno equilibria. This paper, therefore, not only presents conditions for the stability of Zeno equilibria, but directly relates the stability of Zeno equilibria to the existence of Zeno behavior

Electromagnetic manipulation for anti-Zeno effect in an engineered quantum tunneling process

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.Comment: 6 pages, 5 figure

Zeno dynamics in quantum open systems

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 completely positive map is assumed. We firstly study the consequences of non-Markovian noise on quantum Zeno effect and give the exact forms of the dissipative Fisher information and the quantum Zeno time. Then, for the operator-sum representation, an achievable upper bound of the quantum Zeno time is given with the help of the results in noisy quantum metrology. It is of significance that the noise affecting the accuracy in the entanglement-enhanced parameter estimation can conversely be favorable for the accessibility of quantum Zeno dynamics of entangled states.Comment: 6 pages, 2 figure

Quantum Populations in Zeno Regions inside Black Holes

Schwarzschild black-hole interiors border on space-like singularities representing classical information leaks. We show that local quantum physics is decoupled from these leaks due to dynamically generated boundaries, called Zeno borders. Beyond Zeno borders black-hole interiors become asymptotically silent, and quantum fields evolve freely towards the geodesic singularity with vanishing probability measure for populating the geodesic boundary. Thus Zeno borders represent a probabilistic completion of Schwarzschild black holes within the semiclassical framework.Comment: 5 pages, 2 figures, more pedagogical presentation of our unchanged results including an introduction to Zeno region

How to stop time stopping

Zeno-timelocks constitute a challenge for the formal verification of timed automata: they are difficult to detect, and the verification of most properties (e.g., safety) is only correct for timelock-free models. Some time ago, Tripakis proposed a syntactic check on the structure of timed automata: If a certain condition (called strong non-zenoness) is met by all the loops in a given automaton, then zeno-timelocks are guaranteed not to occur. Checking for strong non-zenoness is efficient, and compositional (if all components in a network of automata are strongly non-zeno, then the network is free from zeno-timelocks). Strong non-zenoness, however, is sufficient-only: There exist non-zeno specifications which are not strongly non-zeno. A TCTL formula is known that represents a sufficient-and-necessary condition for non-zenoness; unfortunately, this formula requires a demanding model-checking algorithm, and not all model-checkers are able to express it. In addition, this algorithm provides only limited diagnostic information. Here we propose a number of alternative solutions. First, we show that the compositional application of strong non-zenoness can be weakened: Some networks can be guaranteed to be free from Zeno-timelocks, even if not every component is strongly non-zeno. Secondly, we present new syntactic, sufficient-only conditions that complement strong non-zenoness. Finally, we describe a sufficient-and-necessary condition that only requires a simple form of reachability analysis. Furthermore, our conditions identify the cause of zeno-timelocks directly on the model, in the form of unsafe loops. We also comment on a tool that we have developed, which implements the syntactic checks on Uppaal models. The tool is also able to derive, from those unsafe loops in a given automaton (in general, an Uppaal model representing a product automaton of a given network), the reachability formulas that characterise the occurrence of zeno-timelocks. A modified version of the CSMA/CD protocol is used as a case-study