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Photonics Letters of Poland

Kerr nonlinear coupler and entanglement induced by broadband laser light

Quoc Khoa Doan, Long Van Cao, Lanh Chu Van, Thanh Vinh Nguyen, Thi Hai Tran, Kim Quy Ha, Thi Hong Sang Nguyen

Published Sep 30, 2016• 2 citations
Publisher

Abstract

We consider a model of Kerr-like nonlinear coupler linearly excited by a external classical field involving coherent part and white noise and solved a set of coupled stochastic integro-differential equations, deriving exactly analytical formulae for the probability amplitudes of n-photon Fock states. As a consequence, this nonlinear coupler deliberated behaves as a two-qubit system. The effects of dissipation on entanglement of formation parameterised by concurrence are also analyzed and compare these results with that obtained previously in the literature. As a interesting result, initially for a period of time the entanglement is enlarged when the chaotic parameter increases. Full Text: PDF References A. Einstein, B. Podolski, N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Phys. Rev. 47, 777 (1935). CrossRef A. Miranowicz, W. Leoński, "Two-mode optical state truncation and generation of maximally entangled states in pumped nonlinear couplers", J. Phys. B 39, 1683 (2006). CrossRef T.D. Nguyen, W. Leoński, V. Cao Long, "Computer Simulation of Two-Mode Nonlinear Quantum Scissors", Comput. Method. Sci. Tech. 19, 175 (2013). CrossRef N. Korolkova, J. Peřina, "Quantum statistics and dynamics of Kerr nonlinear couplers", Opt. Commun. 136, 135 (1997). CrossRef A. Kowalewska-Kudłaszyk, W. Leoński, "Finite-dimensional states and entanglement generation for a nonlinear coupler", Phys. Rev. A 73, 042318 (2006). CrossRef A. Kowalewska-Kudłaszyk, W. Leoński, T.D. Nguyen, V. Cao Long, "Kicked nonlinear quantum scissors and entanglement generation", Phys. Scr. T 160, 014023 (2014). CrossRef K. Doan Quoc, V. Cao Long, W. Leoński, "Electromagnetically induced transparency for Λ-like systems with a structured continuum and broad-band coupling laser", Phys. Scr. T 147, 014008 (2012). CrossRef K. Doan Quoc, V. Cao Long, W. Leoński, "A broad-band laser-driven double Fano system—photoelectron spectra", Phys. Scr. 86, 045301 (2012). CrossRef K. Doan Quoc, V. Cao Long, L. Chu Van, P. Huynh Vinh, "Electromagnetically induced transparency for Λ-like systems with degenerate autoionizing levels and a broadband coupling laser", Optica Applicata 46, 93 (2016). CrossRef W. Leoński, A. Miranowicz, "Kerr nonlinear coupler and entanglement", J. Opt. B 6, S37 (2004). CrossRef K. Doan Quoc, V. Cao Long, to be Published. W. Leoński, "Finite-dimensional coherent-state generation and quantum-optical nonlinear oscillator models", Phys. Rev. A 55, 3874 (1997). CrossRef

DOI
10.4302/plp.2016.3.02

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We consider a model of Kerr-like nonlinear coupler linearly excited by a external classical field involving coherent part and white noise and solved a set of coupled stochastic integro-differential equations, deriving exactly analytical formulae for the probability amplitudes of n-photon Fock states. As a consequence, this nonlinear coupler deliberated behaves as a two-qubit system. The effects of dissipation on entanglement of formation parameterised by concurrence are also analyzed and compare these results with that obtained previously in the literature. As a interesting result, initially for a period of time the entanglement is enlarged when the chaotic parameter increases. Full Text: PDF References A. Einstein, B. Podolski, N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", Phys. Rev. 47, 777 (1935). CrossRef A. Miranowicz, W. Leoński, "Two-mode optical state truncation and generation of maximally entangled states in pumped nonlinear couplers", J. Phys. B 39, 1683 (2006). CrossRef T.D. Nguyen, W. Leoński, V. Cao Long, "Computer Simulation of Two-Mode Nonlinear Quantum Scissors", Comput. Method. Sci. Tech. 19, 175 (2013). CrossRef N. Korolkova, J. Peřina, "Quantum statistics and dynamics of Kerr nonlinear couplers", Opt. Commun. 136, 135 (1997). CrossRef A. Kowalewska-Kudłaszyk, W. Leoński, "Finite-dimensional states and entanglement generation for a nonlinear coupler", Phys. Rev. A 73, 042318 (2006). CrossRef A. Kowalewska-Kudłaszyk, W. Leoński, T.D. Nguyen, V. Cao Long, "Kicked nonlinear quantum scissors and entanglement generation", Phys. Scr. T 160, 014023 (2014). CrossRef K. Doan Quoc, V. Cao Long, W. Leoński, "Electromagnetically induced transparency for Λ-like systems with a structured continuum and broad-band coupling laser", Phys. Scr. T 147, 014008 (2012). CrossRef K. Doan Quoc, V. Cao Long, W. Leoński, "A broad-band laser-driven double Fano system—photoelectron spectra", Phys. Scr. 86, 045301 (2012). CrossRef K. Doan Quoc, V. Cao Long, L. Chu Van, P. Huynh Vinh, "Electromagnetically induced transparency for Λ-like systems with degenerate autoionizing levels and a broadband coupling laser", Optica Applicata 46, 93 (2016). CrossRef W. Leoński, A. Miranowicz, "Kerr nonlinear coupler and entanglement", J. Opt. B 6, S37 (2004). CrossRef K. Doan Quoc, V. Cao Long, to be Published. W. Leoński, "Finite-dimensional coherent-state generation and quantum-optical nonlinear oscillator models", Phys. Rev. A 55, 3874 (1997). CrossRef
We discuss a model comprising two coupled nonlinear oscillators (Kerr-like nonlinear coupler) with one of them pumped by an external coherent excitation. Applying the method of nonlinear quantum scissors we show that the quantum evolution of the coupler can be closed within a finite set of n -photon Fock states. Moreover, we show that the system is able to generate Bell-like states and, as a consequence, the coupler discussed behaves as a two-qubit system. We also analyse the effects of dissipation on entanglement of formation parametrized by concurrence.
We consider a nonlinear coupler with two Kerr-like oscillators mutually coupled by continuous linear interaction and excited by a series of ultrashort external pulses. We show that the system behaves like nonlinear quantum scissors . It evolves in such a way that it can be treated as a qubit–qubit system. We derive analytic formulas for the probabilities of the states involved in the system's evolution and show that they differ from those already discussed in the literature and corresponding to the continuously excited models. Moreover, for the model discussed here, maximally entangled Bell states can be generated with high efficiency.
We studied a system that has two nonlinear oscillators with different frequencies. These oscillators are coupled via a nonlinear interaction. With the aim of excite the system, we used two external coherent fields. It follows from numerical simulation that evolution of the system which is likely to be a combination of Fock states. THerefore, the deliberated system behaves as so-called nonlinear quantum scissor. However, evolution of the system generates Bell-like states in some times with exact high probability. The system creates a truncation of optical states, which leads to obtain two-qubit states due to the nonlinear properties of oscillators and their interaction.
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled mutually by a nonlinear interaction. The system is excited by an external coherent field that is resonant to the frequency of one of the oscillators. We show that the coupler evolution can be closed within a finite set of nnn-photon states, analogously as in the nonlinear quantum scissors model. Moreover, for this type of evolution our system can be treated as a Bell-like state generator. Thanks to the nonlinear nature of both oscillators and their internal coupling, these states can be generated even if the system exhibits its energy dissipating nature, contrary to systems with linear couplings.
We discuss the simulation method allowing modeling of quantum unitary dynamics for quantum nonlinear scissors systems. In particular, we consider the model of two nonlinear oscillators (Ker-like coupler) excited by an external field. We show that the time-evolution of the system is closed within a finite set of n-photo states and the Bell-like states are generated. Thus, we prove that the numerical method applied can be used as tools of quantum-mechanical simulations leading to the interesting results.