Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0004070 · Journal of Optics B Quantum and Semiclassical Optics

Quantum dynamics and statistics of two coupled down-conversion processes

Ladislav Mišta, JiríHerec, Viktor Jelínek, Jaroslav Řeháček, Jan Peřina

Published Nov 15, 2000• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1464-4266/2/6/304

Related papers

Quantum dynamics and statistics of two-coupled down-conversion processes

Ladislav Mišta, Jiří Herec, Viktor Jelínek +2 more

In the framework of the Heisenberg-Langevin theory the statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility to control the intensity and statistical properties of the light generate din one nonlinear medium by the light entering the other one. We also show that the model discussed is an interesting generalization of the famous experiments by Zou, Wang, and Mandel on the induced coherence without induced emission.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 7, 2001•1 citation

Statistics of light in Raman and Brillouin nonlinear couplers

Jan Peřina, J Perina

Statistical properties of optical fields in nonlinear couplers composed of two waveguides in which Raman or Brillouin processes (with classical pumping) are in operation and which are mutually connected through the mutual Stokes and/or anti-Stokes linear interactions are investigated within the framework of a generalized superposition of coherent fields and quantum noise. Heisenberg equations describing the couplers are solved both analytically under special conditions and numerically in general cases. Regimes for nonclassical properties of optical fields, such as sub-Poissonian photon-number statistics, negative reduced moments of integrated intensity and squeezing of quadrature fluctuations are discussed for the cases of single and compound fields. General results are compared with those from the short-length approximation.

arXiv:quant-ph/9901006•Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1997•19 citations

Quantum Zeno effect in a probed down-conversion process

Jaroslav Řeháček, Jan Peřina, Paolo Facchi A +2 more

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.

arXiv:quant-ph/9911018•Physical Review A•Jun 9, 2000•35 citations

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

Kishore Thapliyal, Anirban Pathak, Jan Peřina

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.

arXiv:1511.02317•Physical Review A•Feb 8, 2016•28 citations

Quantum Statistics of Quadratic Optical Parametric Processes with Intense Coherent or Stochastic Pumping: Equations of motion and their solutions

Vlasta Peřinová

A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed. The Heisenberg-Langevin equations are derived and their solutions are used to obtain the quantum characteristic functions and the corresponding quasidistributions. The Fokker-Planck equation approach is adopted as well and the equivalence of both the approaches is explicitly found.

Optica Acta International Journal of Optics•Jun 1, 1981•32 citations

Interplay between quantum Zeno and anti-Zeno effects in a nondegenerate hyper-Raman nonlinear optical coupler

Moumita Das, Kishore Thapliyal, Biswajit Sen +2 more

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.

arXiv:2005.10467•Physical Review A•Jan 11, 2021•7 citations
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.
In the framework of the Heisenberg-Langevin theory the statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility to control the intensity and statistical properties of the light generate din one nonlinear medium by the light entering the other one. We also show that the model discussed is an interesting generalization of the famous experiments by Zou, Wang, and Mandel on the induced coherence without induced emission.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Statistical properties of optical fields in nonlinear couplers composed of two waveguides in which Raman or Brillouin processes (with classical pumping) are in operation and which are mutually connected through the mutual Stokes and/or anti-Stokes linear interactions are investigated within the framework of a generalized superposition of coherent fields and quantum noise. Heisenberg equations describing the couplers are solved both analytically under special conditions and numerically in general cases. Regimes for nonclassical properties of optical fields, such as sub-Poissonian photon-number statistics, negative reduced moments of integrated intensity and squeezing of quadrature fluctuations are discussed for the cases of single and compound fields. General results are compared with those from the short-length approximation.
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.
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.
A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed. The Heisenberg-Langevin equations are derived and their solutions are used to obtain the quantum characteristic functions and the corresponding quasidistributions. The Fokker-Planck equation approach is adopted as well and the equivalence of both the approaches is explicitly found.
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.