Dynamics and synchronization of linearly coupled Kerr oscillators

Grygiel, K.; Szlachetka, P.

doi:10.1088/1464-4266/3/3/306

Cited by 8 publications

(14 citation statements)

References 20 publications

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“…For instance, NC systems can exhibit such phenomena as: self-modulation, self-switching, self-trapping [9], chaotic systems synchronisation [10] and others. Moreover, NC can exhibit various quantum-optical features such as sub-Poissonian or squeezed light generations [11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Finite-dimensional states and entanglement generation for a nonlinear coupler

Kowalewska-Kudłaszyk

Leoński

2006

Phys. Rev. A

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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 n-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 states 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.

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Section: Introductionmentioning

confidence: 99%

Finite-dimensional states and entanglement generation for a nonlinear coupler

Kowalewska-Kudłaszyk

Leoński

2006

Phys. Rev. A

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“…In the last two decades since the publication of the paper by Pecora and Carroll [10] the phenomenon of synchronization in systems of the coupled oscillators has become a subject of comprehensive investigation. The problem of synchronization of two linearly coupled Kerr oscillators has been studied in [11] and the possibility of synchronization of chaotic motion was proved numerically. Moreover the case of synchronization of two kinds of Kerr couplers having a structure of low-dimensional chains (ring and open) has been analysed [12].…”

Section: Introductionmentioning

confidence: 99%

“…5(a)-(c). InFig.5(a) the phase point starting from the orbit of the radius Lyapunov maps -the values of the maximal Lyapunow exponent λ 1 for the parameters of the system(11): ω = 1, ǫ = 0.01 and for the initial condition: Re a = 10, Im a = 0. The parameter spaces (Ω p , F ) are presented for (a) γ = 0.1 and (b) γ = 0.5.…”

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confidence: 99%

Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators

S̀liwa

Grygiel

2011

Nonlinear Dyn

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Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect, i.e., interaction of optical waves with nonlinear medium with polarizability χ (3) is the basic phenomenon needed to explain, for example, the process of light transmission in fibers and optical couplers. In this paper, we analyze the two Kerr oscillators coupler and we show that there is a possibility to control the dynamics of this system, especially by switching its dynamics from periodic to chaotic motion and vice versa. Moreover, the switching between two different stable periodic states is investigated. The stability of the system is described by the so-called maps of Lyapunov exponents in parametric spaces. Comparison of basins of attractions between two Kerr couplers and a single Kerr system is also presented.

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“…Since the pioneering works of Jensen [9] and Maier [10], the nonlinear couplers attract an increasing interest [11]- [17] (for reviews see [18,19]). As shown in classical [9,10] and quantum [11] models, the Kerr couplers can exhibit self-trapping, self-modulation and self-switching of the energy of the coupled modes.…”

Section: Introductionmentioning

confidence: 99%

“…Among various other quantum statistical properties, it has been shown that the Kerr couplers can be a source of sub-Poissonian and squeezed light [12]- [16]. Another group of papers concerns the correspondences between the quantum and classical dynamics of such systems [11] and their chaotic dynamics, including synchronization effects [17].…”

Section: Introductionmentioning

confidence: 99%

Kerr nonlinear coupler and entanglement

Leoński¹,

Miranowicz²

2004

J. Opt. B: Quantum Semiclass. Opt.

101

104

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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 analyze the effects of dissipation on entanglement of formation parametrized by concurrence.

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Dynamics and synchronization of linearly coupled Kerr oscillators

Cited by 8 publications

References 20 publications

Finite-dimensional states and entanglement generation for a nonlinear coupler

Finite-dimensional states and entanglement generation for a nonlinear coupler

Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators

Kerr nonlinear coupler and entanglement

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