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arXiv:quant-ph/9911018 · Physical Review A

Quantum Zeno effect in a probed down-conversion process

Jaroslav Řeháček, Jan Peřina, Paolo Facchi A, Saverio Pascazio, Ladislav Mišta

Published Jun 9, 2000• 35 citations
arXivHTMLPDF

Abstract

The distortion of a spontaneous down-conversion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the down-conversion in a nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of down-conversion. These effects are interpreted as being manifestations of quantum Zeno and anti-Zeno effects, respectively, and they are understood by using the dressed mode picture of the device. The possibility of using the coupling as a nontrivial phase-matching technique is pointed out.

DOI
10.1103/physreva.62.013804

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The distortion of a spontaneous down-conversion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the down-conversion in a nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of down-conversion. These effects are interpreted as being manifestations of quantum Zeno and anti-Zeno effects, respectively, and they are understood by using the dressed mode picture of the device. The possibility of using the coupling as a nontrivial phase-matching technique is pointed out.
The distortion of a spontaneous downconversion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of the downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the coupling as a nontrivial phase-matching technique is pointed out.
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.
We present a simple multimode analysis of the Zeno and anti-Zeno effects in spontaneous parametric down-conversion. In this process the input vacuum is an unstable state decaying into a reservoir of down-converted modes by emitting a pair of photons. We show that the Zeno and the anti-Zeno effects are two particular examples of quantum propagation depending on the effective spectrum of down-converted modes. We show that this evolution can be easily tailored on demand and that these quantum phenomena admit a very simple explanation in terms of standard interference concepts.
In the framework of the Heisenberg-Langevin theory the dynamical and statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility of controlling the intensity and statistical properties of the light generated in one nonlinear medium by the light entering the other one. Apart from this all-optical switching, behaviour reminiscent of the Zeno and anti-Zeno effects is examined. We also show that the model discussed is an interesting generalization of the famous experiments by Zou et al (Zou X Y, Wang L J and Mandel L 1991 Phys. Rev. Lett. 67 318) on induced coherence without induced emission.
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.