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

Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics

Einstein-Podolsky-Rosen steering and squeezing effect in system two coupled nonlinear oscillators

A. Kowalewska-Kudłaszyk, W. Leoński, Joanna K. Kalaga, Jan Peřina

Published Dec 18, 2018• 0 citations
Publisher

Abstract

We discuss a system consisting of two coupled nonlinear Kerr-like oscillators. For such a model, we study the time-evolution of the steering parameter and the normally ordered variances of the quadratures operators. We discuss the relationships between the generation of steerable and squeezed states.
DOI
10.1117/12.2518265

Related papers

Einstein-Podolsky-Rosen steering and squeezing effect in system two coupled nonlinear oscillators

Joanna K. Kalaga, Jan Peřina, A. Kowalewska-Kudłaszyk +1 more

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 1, 2018•0 citations

Decoherence of Einstein–Podolsky–Rosen steering

L. Rosales-Zárate, Run Yan Teh, Simon Kiesewetter +3 more

We consider two systems A and B that share Einstein–Podolsky–Rosen (EPR) steering correlations and study how these correlations will decay when each of the systems is independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether system A is steered by B, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schrödinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.

arXiv:1508.06383•Journal of the Optical Society of America B•Apr 1, 2015•58 citations

Quantum steering in an asymmetric chain of nonlinear oscillators

Joanna K. Kalaga, W. Leoński, Radosław Szczȩśniak

We discuss here a possibility of generation of steerable states in asymmetric chains comprising three Kerr-like nonlinear oscillators. We show that steering between modes can be generated in the system and it strongly depends on the asymmetry of internal couplings in our model. We can lead to the appearance of new steering effects, which were not present in symmetric models already studied in the literature. Full Text: PDF ReferencesE. Schrödinger, "Discussion of Probability Relations between Separated Systems", Math. Proc. Camb. Phil. Soc. 31, 555 (1935). CrossRef M.D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification", Phys. Rev. A 40, 913 (1989). CrossRef E.G. Cavalcanti, M.D. Reid, "Uncertainty relations for the realization of macroscopic quantum superpositions and EPR paradoxes", Journal of Modern Optics 54, 2373 (2007). CrossRef S.P. Walborn, A. Salles, R.M. Gomes, F. Toscano, P.H. Souto Ribeiro, "Revealing Hidden Einstein-Podolsky-Rosen Nonlocality", Phys. Rev. Lett. 106, 130402 (2011). CrossRef H.M. Wiseman, S.J. Jones, A.C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox", Phys. Rev. Lett. 98, 140402 (2007). CrossRef S.J. Jones, H.M. Wiseman, A.C. Doherty, "Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering", Phys. Rev. A 76, 052116 (2007). CrossRef J.K. Kalaga, W. Leoński, "Quantum steering borders in three-qubit systems", Quantum Inf Process 16, 175 (2017). CrossRef Q. He, Z. Ficek, "Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system", Phys. Rev. A 89, 022332 (2014). CrossRef S. Kiesewetter, Q.Y. He, P.D. Drummond, M.D. Reid, "Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics", Phys. Rev. A 90, 043805 (2014). CrossRef K. Bartkiewicz, A. Cernoch, K. Lemr, A. Miranowicz, F. Nori, "Experimental temporal quantum steering", Scientific Reports 6, 38076 (2016). CrossRef A. Barasiński, B. Brzostowski, R. Matysiak, P. Sobczak, D. Woźniak, In: R. Wyrzykowski, J. Dongarra, K. Karczewski, J. Wasniewski editor, Parallel Processing and Applied Mathematics (PPAM 2013), Lecture Notes in Computer Science, vol 8385. Springer, Berlin, Heidelberg (2014). CrossRef A. Drzewiński, J. Sznajd, "On the real-space renormalization-group study of some 2D quantum spin systems", Physica A 170, 415 (1991). CrossRef G.J. Milburn, C.A. Holmes, "Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity", Phys. Rev. A 44, 4704 (1991). CrossRef W. Leoński, "Quantum and classical dynamics for a pulsed nonlinear oscillator", Physica A 233, 365 (1996). CrossRef A. Kowalewska-Kudłaszyk, J.K. Kalaga, W. Leoński, "Long-time fidelity and chaos for a kicked nonlinear oscillator system", Physics Letters A 373, 1334 (2009). CrossRef J.K. Kalaga, W. Leoński, "Two proposals of quantum chaos indicators related to the mean number of photons: pulsed Kerr-like oscillator case", Proc. SPIE 10142, 101421L (2016). CrossRef A. Barasiński, W. Leoński, T. Sowiński, "Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices", J. Opt. Soc. Am. B 31, 1845 (2014). CrossRef A. Barasiński, W. Leoński, "Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring", Quantum Inf Process 16, 6 (2017). CrossRef D. Woźniak, A. Drzewiński, G. Kamieniarz, "Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy", Acta Physica Polonica A 130, 1395 (2016). CrossRef R. Szczęśniak, D. Szczęśniak, E.A. Drzazga, "Superconducting state in the atomic metallic hydrogen just above the pressure of the molecular dissociation", Solid State Communications 152, 2023 (2012). CrossRef A. P. Durajski, R. Szczęśniak, M.W. Jarosik, "Properties of the superconducting state in compressed sulphur", Phase Transitions 85, 727 (2012). CrossRef R. Szczęśniak, A. P. Durajski, "The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds", Solid State Sciences 25, 45 (2013). CrossRef X. Wang, A. Miranowicz, H.R. Li, F. Nori, "Multiple-output microwave single-photon source using superconducting circuits with longitudinal and transverse couplings", Phys. Rev. A 94, 053858, (2016). CrossRef Y.X. Liu, X.W. Xu, A. Miranowicz, F. Nori, "From blockade to transparency: Controllable photon transmission through a circuit-QED system", Phys. Rev. A 89, 043818 (2014). CrossRef M.K. Olsen, "Spreading of entanglement and steering along small Bose-Hubbard chains", Phys. Rev. A 92, 033627 (2015). CrossRef E.G. Cavalcanti, Q.Y. He, M.D. Reid, H.M. Wiseman, "Unified criteria for multipartite quantum nonlocality", Phys. Rev. A 84, 032115 (2011). CrossRef

Photonics Letters of Poland•Sep 30, 2017•5 citations

Quantum properties of kerr nonlinear directional couplers via phase-space representation / Rafael Julius

Rafael Julius

Quantum statistical properties of interacting optical fields in Kerr nonlinear couplers may be regarded as one of the most fundamental problems yet to be solved in quantum optics. As an analytical solution to this system is not always possible, a semi-analytic or direct numerical solution must be employed in order to obtain a more complete description of their evolution. This study investigates the quantum properties of four-mode couplers composed of two and four Kerr nonlinear waveguides, both with and without cavity set up via phase space representation. In these systems, the electromagnetic fields are described by their Hamiltonians, while the time-evolution of the systems are described by the Von-Neumann equation. Following standard techniques, the master equations for the density matrices of the systems are obtained and further converted to the corresponding classical Fokker- Planck equations using both positive P and Wigner representations. The corresponding set of Langevin Stochastic equations is then obtained from the Fokker-Planck equations by means of Ito rules. Finally, the systems are integrated numerically and averaged over many trajectories to get the relevant information. The effects of self-action nonlinearity, cross-action coupling and the initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Furthermore, the influences of multimode interaction on the dynamics of the squeezed states are discussed. In this research, we show that the system may produce squeezed states in both quadrature variances for all calculated parameters. The multimode two channel model can provide better squeezing in contrast to the conventional device. The amplitude oscillation of maximal squeezing may be amplified by manipulation of the initial state of the coherent light in the first mode, and the range may be extended through multimode interaction. When the model is contained in a cavity, the system is able to generate better amplitude oscillations and squeezing range with leaf-revival-collapse-like behaviour; with the whole oscillation able to evolute below the standard quantum limit Regular photon transition and self trapping effects of the interacting modes in the four channels model are simulated, and squeezing is predicted for various initial intensities of the coherent field and nonlinear coupling parameter g. The cavity setup caused the system to undergo fluctuation amplification and the potential for different types of squeezing to be generated is observed. Depending on how we choose the interaction parameter values, the system may generate better squeezing in comparison to the cavity-less model.

•Jan 1, 2014•0 citations

Quantum squeezing-induced quantum entanglement and EPR steering in a coupled optomechanical system

Shao-xiong Wu, Cheng‐Hua Bai, Gang Li +2 more

We propose a theoretical project in which quantum squeezing induces quantum entanglement and Einstein-Podolsky-Rosen steering in a coupled whispering-gallery-mode optomechanical system. Through pumping the χ (2) -nonlinear resonator with the phase matching condition, the generated squeezed resonator mode and the mechanical mode of the optomechanical resonator can generate strong quantum entanglement and EPR steering, where the squeezing of the nonlinear resonator plays the vital role. The transitions from zero entanglement to strong entanglement and one-way steering to two-way steering can be realized by adjusting the system parameters appropriately. The photon-photon entanglement and steering between the two resonators can also be obtained by deducing the amplitude of the driving laser. Our project does not need an extraordinarily squeezed field, and it is convenient to manipulate and provides a novel and flexible avenue for diverse applications in quantum technology dependent on both optomechanical and photon-photon entanglement and steering.

arXiv:2312.12310•Optics Express•Dec 8, 2023•30 citations

Squeezing in four-mode Kerr nonlinear coupler via phase space representation

Rafael Julius, Abdel-Baset M.A. Ibrahim, Mohd Salleh Mohd Deni +1 more

Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.

AIP conference proceedings•Jan 1, 2013•2 citations
We consider two systems A and B that share Einstein–Podolsky–Rosen (EPR) steering correlations and study how these correlations will decay when each of the systems is independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether system A is steered by B, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schrödinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.
We discuss here a possibility of generation of steerable states in asymmetric chains comprising three Kerr-like nonlinear oscillators. We show that steering between modes can be generated in the system and it strongly depends on the asymmetry of internal couplings in our model. We can lead to the appearance of new steering effects, which were not present in symmetric models already studied in the literature. Full Text: PDF ReferencesE. Schrödinger, "Discussion of Probability Relations between Separated Systems", Math. Proc. Camb. Phil. Soc. 31, 555 (1935). CrossRef M.D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification", Phys. Rev. A 40, 913 (1989). CrossRef E.G. Cavalcanti, M.D. Reid, "Uncertainty relations for the realization of macroscopic quantum superpositions and EPR paradoxes", Journal of Modern Optics 54, 2373 (2007). CrossRef S.P. Walborn, A. Salles, R.M. Gomes, F. Toscano, P.H. Souto Ribeiro, "Revealing Hidden Einstein-Podolsky-Rosen Nonlocality", Phys. Rev. Lett. 106, 130402 (2011). CrossRef H.M. Wiseman, S.J. Jones, A.C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox", Phys. Rev. Lett. 98, 140402 (2007). CrossRef S.J. Jones, H.M. Wiseman, A.C. Doherty, "Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering", Phys. Rev. A 76, 052116 (2007). CrossRef J.K. Kalaga, W. Leoński, "Quantum steering borders in three-qubit systems", Quantum Inf Process 16, 175 (2017). CrossRef Q. He, Z. Ficek, "Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system", Phys. Rev. A 89, 022332 (2014). CrossRef S. Kiesewetter, Q.Y. He, P.D. Drummond, M.D. Reid, "Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics", Phys. Rev. A 90, 043805 (2014). CrossRef K. Bartkiewicz, A. Cernoch, K. Lemr, A. Miranowicz, F. Nori, "Experimental temporal quantum steering", Scientific Reports 6, 38076 (2016). CrossRef A. Barasiński, B. Brzostowski, R. Matysiak, P. Sobczak, D. Woźniak, In: R. Wyrzykowski, J. Dongarra, K. Karczewski, J. Wasniewski editor, Parallel Processing and Applied Mathematics (PPAM 2013), Lecture Notes in Computer Science, vol 8385. Springer, Berlin, Heidelberg (2014). CrossRef A. Drzewiński, J. Sznajd, "On the real-space renormalization-group study of some 2D quantum spin systems", Physica A 170, 415 (1991). CrossRef G.J. Milburn, C.A. Holmes, "Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity", Phys. Rev. A 44, 4704 (1991). CrossRef W. Leoński, "Quantum and classical dynamics for a pulsed nonlinear oscillator", Physica A 233, 365 (1996). CrossRef A. Kowalewska-Kudłaszyk, J.K. Kalaga, W. Leoński, "Long-time fidelity and chaos for a kicked nonlinear oscillator system", Physics Letters A 373, 1334 (2009). CrossRef J.K. Kalaga, W. Leoński, "Two proposals of quantum chaos indicators related to the mean number of photons: pulsed Kerr-like oscillator case", Proc. SPIE 10142, 101421L (2016). CrossRef A. Barasiński, W. Leoński, T. Sowiński, "Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices", J. Opt. Soc. Am. B 31, 1845 (2014). CrossRef A. Barasiński, W. Leoński, "Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring", Quantum Inf Process 16, 6 (2017). CrossRef D. Woźniak, A. Drzewiński, G. Kamieniarz, "Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy", Acta Physica Polonica A 130, 1395 (2016). CrossRef R. Szczęśniak, D. Szczęśniak, E.A. Drzazga, "Superconducting state in the atomic metallic hydrogen just above the pressure of the molecular dissociation", Solid State Communications 152, 2023 (2012). CrossRef A. P. Durajski, R. Szczęśniak, M.W. Jarosik, "Properties of the superconducting state in compressed sulphur", Phase Transitions 85, 727 (2012). CrossRef R. Szczęśniak, A. P. Durajski, "The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds", Solid State Sciences 25, 45 (2013). CrossRef X. Wang, A. Miranowicz, H.R. Li, F. Nori, "Multiple-output microwave single-photon source using superconducting circuits with longitudinal and transverse couplings", Phys. Rev. A 94, 053858, (2016). CrossRef Y.X. Liu, X.W. Xu, A. Miranowicz, F. Nori, "From blockade to transparency: Controllable photon transmission through a circuit-QED system", Phys. Rev. A 89, 043818 (2014). CrossRef M.K. Olsen, "Spreading of entanglement and steering along small Bose-Hubbard chains", Phys. Rev. A 92, 033627 (2015). CrossRef E.G. Cavalcanti, Q.Y. He, M.D. Reid, H.M. Wiseman, "Unified criteria for multipartite quantum nonlocality", Phys. Rev. A 84, 032115 (2011). CrossRef
Quantum statistical properties of interacting optical fields in Kerr nonlinear couplers may be regarded as one of the most fundamental problems yet to be solved in quantum optics. As an analytical solution to this system is not always possible, a semi-analytic or direct numerical solution must be employed in order to obtain a more complete description of their evolution. This study investigates the quantum properties of four-mode couplers composed of two and four Kerr nonlinear waveguides, both with and without cavity set up via phase space representation. In these systems, the electromagnetic fields are described by their Hamiltonians, while the time-evolution of the systems are described by the Von-Neumann equation. Following standard techniques, the master equations for the density matrices of the systems are obtained and further converted to the corresponding classical Fokker- Planck equations using both positive P and Wigner representations. The corresponding set of Langevin Stochastic equations is then obtained from the Fokker-Planck equations by means of Ito rules. Finally, the systems are integrated numerically and averaged over many trajectories to get the relevant information. The effects of self-action nonlinearity, cross-action coupling and the initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Furthermore, the influences of multimode interaction on the dynamics of the squeezed states are discussed. In this research, we show that the system may produce squeezed states in both quadrature variances for all calculated parameters. The multimode two channel model can provide better squeezing in contrast to the conventional device. The amplitude oscillation of maximal squeezing may be amplified by manipulation of the initial state of the coherent light in the first mode, and the range may be extended through multimode interaction. When the model is contained in a cavity, the system is able to generate better amplitude oscillations and squeezing range with leaf-revival-collapse-like behaviour; with the whole oscillation able to evolute below the standard quantum limit Regular photon transition and self trapping effects of the interacting modes in the four channels model are simulated, and squeezing is predicted for various initial intensities of the coherent field and nonlinear coupling parameter g. The cavity setup caused the system to undergo fluctuation amplification and the potential for different types of squeezing to be generated is observed. Depending on how we choose the interaction parameter values, the system may generate better squeezing in comparison to the cavity-less model.
We propose a theoretical project in which quantum squeezing induces quantum entanglement and Einstein-Podolsky-Rosen steering in a coupled whispering-gallery-mode optomechanical system. Through pumping the χ (2) -nonlinear resonator with the phase matching condition, the generated squeezed resonator mode and the mechanical mode of the optomechanical resonator can generate strong quantum entanglement and EPR steering, where the squeezing of the nonlinear resonator plays the vital role. The transitions from zero entanglement to strong entanglement and one-way steering to two-way steering can be realized by adjusting the system parameters appropriately. The photon-photon entanglement and steering between the two resonators can also be obtained by deducing the amplitude of the driving laser. Our project does not need an extraordinarily squeezed field, and it is convenient to manipulate and provides a novel and flexible avenue for diverse applications in quantum technology dependent on both optomechanical and photon-photon entanglement and steering.
Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.