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arXiv:1103.2445 · Physical Review A

Linear and nonlinear Zeno effects in an optical coupler

F. Kh. Abdullaev, V. V. Konotop, V. S. Shchesnovich

Published Apr 12, 2011• 18 citations
arXivHTMLPDF

Abstract

It is shown that, in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe an optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a counterintuitive enhancement of transparency of the coupler with an increase of the dissipation and represents an optical analog of the quantum Zeno effect. Experimental realization of the phenomenon based on the use of chalcogenide glasses is proposed. The system allows for observation of the crossover between the linear and nonlinear Zeno effects, as well as the effective manipulation of light transmission through the coupler.

DOI
10.1103/physreva.83.043811

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We theoretically demonstrate the possibility of observing the macroscopic Zeno effect for nonlinear waveguides with localized dissipation. We show the existence of stable stationary flows, which are balanced by losses in the dissipative domain. The macroscopic Zeno effect manifests itself in the nonmonotonic dependence of the stationary flow on the strength of the dissipation. In particular, we highlight the importance of the dissipation parameters in observing the phenomenon. Our results are applicable to a large variety of systems, including the condensates of atoms or quasiparticles and optical waveguides.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 21, 2003•0 citations
It is shown that, in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe an optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a counterintuitive enhancement of transparency of the coupler with an increase of the dissipation and represents an optical analog of the quantum Zeno effect. Experimental realization of the phenomenon based on the use of chalcogenide glasses is proposed. The system allows for observation of the crossover between the linear and nonlinear Zeno effects, as well as the effective manipulation of light transmission through the coupler.
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 (1)) and a nonlinear waveguide (χ(2)) 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-Mandal perturbative approach. In the coupler, the linear waveguide acts as a probe on the system (nonlinear waveguide). The effect of the presence of the probe (linear waveguide) on the photon statistics of the second harmonic mode of the system is considered as quantum Zeno and anti-Zeno effects. Further, it is also shown that in the stimulated case, it is easy to switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the asymmetric coupler.
Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear (${\ensuremath{\chi}}^{\left(2\right)}$) waveguides that are interacting with each other via the evanescent waves. Both 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 ${\ensuremath{\chi}}^{\left(2\right)}\ensuremath{-}{\ensuremath{\chi}}^{\left(2\right)}$ symmetric coupler we can obtain momentum operator of ${\ensuremath{\chi}}^{\left(2\right)}\ensuremath{-}{\ensuremath{\chi}}^{\left(1\right)}$ asymmetric coupler with linear (${\ensuremath{\chi}}^{\left(1\right)}$) 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.
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 the nondegenerate hyper-Raman process, while both the pump modes in the system are constantly interacting with the probe waveguide. The effect of the presence of the probe on the spatial evolution of the system in terms of the number of photons in Stokes and anti-Stokes modes as well as the phonon number is quantified as the Zeno parameter. The negative (positive) values of the Zeno parameter in the specific mode are considered as the signatures of the quantum Zeno (anti-Zeno) effect in that mode of the system. It is observed that the initial phase difference between all the coherent amplitudes involved in the Stokes and anti-Stokes generation processes can be controlled to induce a transition between quantum Zeno and anti-Zeno effects for the hyper-Raman process in both cases with and without phase matching. However, in the case of the hyper-Raman process in the system waveguide without a phase matching, the phase mismatch parameters, due to difference in the wave vectors of all the modes involved in the Stokes and anti-Stokes generation processes, can also be used analogously to cause the desired crossover. Further, the general nature of the physical system and the perturbative technique used here allow us to analytically study the possibilities of observing quantum Zeno and anti-Zeno effects in a large number of special cases, including situations where the process is spontaneous or partially spontaneous and/or the system is operated under a degenerate hyper-Raman process, or a simple Raman process.
Frequent observations to a quantum system modify its coherent evolution through the Zeno effect and Zeno dynamics. Generally, the measurement process destroys the evolution environment of the monitored system, making repeated observations remain a challenge. Here, using the quantum analogy experiments, we realize and engineer the Zeno effect and Zeno dynamics in optical waveguide arrays, where the optical modes correspond to distinct quantum states, and the temporal evolution is mapped into the spatial propagation. We propose a new, extensible experimental strategy for realizing an optical analog of stroboscopic measurements, which are performed by the build-in, on-demand segmented waveguide portions. The weak-to-strong stroboscopic measurements are realized, where the monitored system undergoes a transition from free evolution to optical Zeno freezing. Setting the measurements in the strong regime, the optical Zeno effect and optical Zeno dynamics are successfully generated, and their relationship is demonstrated in optics. We then propose a novel quantum Zeno slicing approach, which allows us to dynamically engineer the Hilbert space of the monitored system. This generic approach is verified by generating a series of Zeno subspaces with different measurement projectors, based on the quantum-optical analogy. The complexity of light dynamics is largely increased, providing full control of the propagation via steering Zeno dynamics. Our results pave the way for manipulation of quantum states by harnessing Zeno dynamics in integrated photonics.
We theoretically demonstrate the possibility of observing the macroscopic Zeno effect for nonlinear waveguides with localized dissipation. We show the existence of stable stationary flows, which are balanced by losses in the dissipative domain. The macroscopic Zeno effect manifests itself in the nonmonotonic dependence of the stationary flow on the strength of the dissipation. In particular, we highlight the importance of the dissipation parameters in observing the phenomenon. Our results are applicable to a large variety of systems, including the condensates of atoms or quasiparticles and optical waveguides.