Kerr Nonlinear Coupler Research Articles

Chaos and regularities in cavity assisted two-channel nonlinear coupler

This paper presents a study of the dynamical behavior in a cavity-assisted two-channel Kerr nonlinear directional coupler. Applying a deterministic periodic laser pump to a two-channel coupled system led to a range of dynamic behaviors, encompassing periodicity, quasiperiodicity, chaoticity and hyperchaoticity. This is confirmed by the exploration of the Lyapunov exponents, Poincaré sections and bifurcation diagrams for resonance and low cavity detuning. For low cavity detuning, chaos arises when the laser pump’s amplitude is large. This is due to higher interactions between photons and the cavity, resulting in more photons inside and higher nonlinearity. On the other hand, the reduced interactions in high cavity detuning displayed regular behavior which is explained qualitatively.

Quantum features of nonlinear coupler with competing nonlinearity

In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.

On the Detection of Single-Mode Squeezed States in Kerr Nonlinear Coupler

The generation of squeezed states of light in two guided waves Kerr nonlinear coupler (KNLC) was examined using both the analytical perturbative (AP) and the short-time approximation (STA) method. A comparative analysis between these two methods is provided. We have found that, at certain combinations of input parameters, the STA method may not be able to detect the generation of squeezed states of light in the current KNLC system. Consequently, some essential physics could be lost. On the other hand, for the AP method, all time-dependent terms are included in the mode solutions which improves its sensitivity to detect the generation of squeezed states.

On the perturbative approach to analyse entanglement in two-channel Kerr nonlinear coupler

The intermodal entanglement in a two-channel symmetric nonlinear coupler, operated with Kerr nonlinearity was investigated using the analytical method based on the Heisenberg picture in quantum mechanics. The Heisenberg equations of motion of the propagating modes were solved based on the Baker-Hausdorff (BH) formula. The entanglement expressions were then derived following the Hillery-Zubairy criteria of two-modes state. The time evolution of entanglement was examined at different values of design parameters. Theoretical results from both the HZ-I and HZ-II criteria show that the system exhibits entangled states of light which can be improved by increasing the coupling constants and the initial amplitude of the input field. On the contrary, the increment in frequency mismatch weakens the HZ-I entanglement, while improving the HZ-II entanglement up to a certain mismatch value. The study provides a new theory of entanglement detection in Kerr nonlinear couplers, which opens up the avenues of a new class of applications based on entanglement.

Quantum Kerr nonlinear coupler: analytical versus phase-space method

The generation of squeezed states of light in a two-mode Kerr nonlinear directional coupler (NLDC) was investigated using two different methods in quantum mechanics. First, the analytical method, a Heisenberg-picture-based method where the operators are evolving in time but the state vectors are time-independent. In this method, an analytical solution to the coupled Heisenberg equations of motion for the propagating modes was proposed based on the Baker–Hausdorff (BH) formula. Second, the phase space method, a Schrödinger-picture-based method in which the operators are constant and the density matrix evolves in time. In this method, the quantum mechanical master equation of the density matrix was converted to a corresponding classical Fokker–Planck (FP) equation in positive-P representation. Then, the FP equation was converted to a set of stochastic differential equations using Ito rules. The strengths and weaknesses of each method are discussed. Good agreement between both methods was achieved, especially at early evolution stages and lower values of linear coupling coefficient. On one hand, the analytical method seems insensitive to higher values of nonlinear coupling coefficients. Nevertheless, it demonstrated better numerical stability. On the other hand, the solution of the stochastic equations resulting from the phase space method is numerically expensive as it requires averaging over thousands of trajectories. Besides, numerically unstable trajectories appear with positive-P representation at higher values of nonlinearity.

Quantum Correlations in System of Kerr Nonlinear Coupler

Quantum Correlations in System of Kerr Nonlinear Coupler

Single- and compound-mode squeezing in nonlinear coupler with frequency mismatch

The properties of squeezing, in relation to the different interaction frequencies of the input modes in three-mode Kerr nonlinear coupler consisting of two linearly-coupled Kerr waveguides, were explored. Utilizing the exact representation of a set of noisy-stochastic equations, an investigation was made of the first-order properties of squeezing for two- and three-mode interactions with frequency mismatch. It was observed that enhanced squeezing could be obtained under certain conditions of interactions.

Generation of entangled states by a linear coupling coupler pumped in two modes induced by broadband laser

We research on a Kerr nonlinear coupler comprising two nonlinear oscillations linearly couple with each other. This coupler is pumped by external classical fields, which are supposed to be decomposed into two parts: a coherent part and a randomly fluctuating chaotic component (white noise). We can see that the quantum evolution of the pumped couplers is closed in a Hilbert space of two-qubit spanned by single-photon and vacuum states only. Hence, the pumped couplers can treat as a system of two-qubit. Analysis of time evolution of the quantum entanglement shows that maximally entangled states can be generated in the system and compare these results with that obtained previously by other authors.

Generation of entangled states by a nonlinear coupler pumped in one mode induced by broadband laser

Kerr nonlinear coupler consists of two nonlinear oscillations in which one of them linearly excited by an external classical field. This is assumed to be decomposed into two parts: a coherent part and a randomly fluctuating chaotic component that is a δ-correlated, Gaussian, Markov, stationary process (white noise). We solve a set of coupled stochastic integro-differential equations involved in the problem with all initial conditions and obtain analytical formulae for the complex probability amplitudes of finite n-photon Fock states. Especially, our study shows that the system is also able to generate maximally entangled states and, as a consequence, the coupler discussed behaves as a two-qubit system and the results compared with those derived previously in the literature.

Quantum dynamics of a four-channel Kerr nonlinear directional coupler

Quantum dynamics of a four-channel nonlinear directional coupler, based on Kerr effect, was modeled numerically by a set of stochastic differential equations derived using quasiprobability distribution of positive- $$P$$ representation. The modeling of the system is focused on the properties of quadrature evolution below the standard quantum limit, and its comparison with the conventional two-channel device. The results exhibit that a four-channel Kerr coupler provides an effective way to manipulate squeezing, especially in the mixed-mode basis, as compared with the conventional two-channel system—the theme that would make these to be prudent squeezed light source.

Stationary quantum correlation and coherence of two-mode Kerr nonlinear coupler interdicting with Su(2)-system under intrinsic damping

ABSTRACTA two-level atom interacting with two nonlinear Kerr oscillators pumped by an optical parametric process is studied. An analytical solution for the dynamical evolution of an interaction between Su and Su-systems is derived. The role of intrinsic damping, detuning, and Kerr-like medium on the entanglement evolution, quantum correlation, and coherence is elucidated. It is shown that the intrinsic decoherence leads to the sudden death and sudden birth entanglement, while the detuning eradicates these effects. The quantum coherence growth can be controlled by the detuning and the Kerr-like medium.

Entropy Squeezing of a Qubit Interdicting with Two-Mode Kerr Nonlinear Coupler Due to Intrinsic Damping

An analytical description for the dynamical evolution of a qubit interacting with two nonlinear Kerr oscillators pumped by optical parametric process is derived through Su(1, 1)-algebraic treatment. The role of intrinsic damping, detuning and Kerr-like Medium on the squeezing phenomenon is elucidated via information entropy squeezing. The evolutions of the interaction of the qubit with two-mode Kerr nonlinear coupler lead to the appearance the regular squeezing phenomenon during the chosen time-interval. The preserving and protecting of the qubit components from the squeezing can be controlled by the intrinsic decoherence, detuning and the Kerr-like medium effects. Where the squeezing phenomenon deteriorates with increasing the decoherence rate, whereas, the Kerr-like medium can not protect some qubit components from the squeezing.

Quantum Statistical Properties of the Codirectional Kerr Nonlinear Coupler in Terms of suleft (2right ) Lie Group in Interaction with a Two-level Atom

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of suleft (2right ) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.

Kerr nonlinear coupler and entanglement induced by broadband laser light

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

Stabilizing soliton-based multichannel transmission with frequency dependent linear gain–loss

We report several major theoretical steps towards realizing stable long-distance multichannel soliton transmission in Kerr nonlinear waveguide loops. We find that transmission destabilization in a single waveguide is caused by resonant formation of radiative sidebands and investigate the possibility to increase transmission stability by optimization with respect to the Kerr nonlinearity coefficient γ. Moreover, we develop a general method for transmission stabilization, based on frequency dependent linear gain–loss in Kerr nonlinear waveguide couplers, and implement it in two-channel and three-channel transmission. We show that the introduction of frequency dependent loss leads to significant enhancement of transmission stability even for non-optimal γ values via decay of radiative sidebands, which takes place as a dynamic phase transition. For waveguide couplers with frequency dependent linear gain–loss, we observe stable oscillations of soliton amplitudes due to decay and regeneration of the radiative sidebands.

Thermal atom–atom entanglement in a bichromatic Kerr nonlinear coupler

In this paper thermal entanglement between two identical two-level atoms within a bichromatic cavity including Kerr nonlinear coupler is investigated. In this study, besides atom–field interaction, the field–field (via linear and Kerr-type couplings) and atomic dipole–dipole interactions are also included. It is also assumed that the cavity is held at a temperature T, so that all atom–photon states with probabilities defined by Boltzmann factor are present. Using a canonical transformation, the presented model is converted to a generalized form of Jaynes–Cummings model. After introducing Casimir operators of the system, it is shown that the Hamiltonian representation is block-diagonal. Diagonalizing each block, the thermal (Gibb’s) density matrix, written in the bases of total Hamiltonian, is obtained. The reduced atomic density matrix and consequently the concurrence, as a measure of entanglement, are obtained by partial tracing of thermal density matrix over the bichromatic photonic states. The concurrence vanishes at zero temperature, indicating that the ground state is separable, exhibits a maximal at a critical temperature and terminates at a finite temperature. The influences of coupler nonlinearities and dipole–dipole coupling on the thermal atom–atom entanglement are also addressed in detail.

Quantum state generation in a four-mode Kerr nonlinear directional coupler

The quantum effects in a four-mode Kerr nonlinear directional coupler (NLDC) are investigated using the phase-space representation. The four-mode Kerr NLDC device consists of two closely connected Kerr waveguides where the first channel is traversed by one mode while the second channel is traversed by three modes. The cavity effect on the propagation characteristics of the nonclassical light is also examined. The introduction of a cavity supports amplification of the nonlinearities at the expense of losses in the model. The dynamical quantum behaviour of the system is investigated by integrating the Langevin equations derived in both positive P and Wigner representations numerically. The characteristics of the mean fields and quadrature variances are explored by integrating the stochastic equations numerically over many trajectories. In comparison with a conventional two-mode device, we have found that the cavityless model provides better squeezing and the amplitude oscillation is amplified by controlling the initial state of the coherent light in the first channel. Moreover, the range of squeezing is extended as a result of multimode interaction. In addition, confining the system inside an optical cavity with highly reflective mirrors introduces rapid amplification in the oscillation of the field dynamics.

Thermal entanglement of a two-level atom and bimodal photons in a Kerr nonlinear coupler

In this paper thermally induced entanglement between a two-level atom and photons inside a bimodal nonlinear coupler is studied. The interaction occurs in the presence of a centrosymmetric medium which couples the two photonic modes via the first and third order susceptibilities. Such effects on the atom–photons interaction, however, are assumed negligible so that the linear Jaynes–Cummings model applies. It is further assumed that the coupler is held at a temperature T, so that each of the combined atom–photon states, with a definite, T dependent, probability, is present. The partially transposed density matrix and, consequently, the negativity, as a measure of entanglement, are determined as functions of temperature. The negativity so calculated shows that the system of a two-level atom and photons is separable at zero temperature, becomes more entangled, reaching the maximal at a certain temperature and asymptotically disentangles. Effect of medium characteristics on such behavior is also discussed.

Computer Simulation of Two-Mode Nonlinear Quantum Scissors

We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors’ (NQS) systems. We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses. We show that despite the simplicity of the method one can obtain non-trivial results. In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation.

Entanglement in a nonlinear coupler: the cross-action effect

Three models of Kerr nonlinear couplers are considered as a source of maximally entangled states. The nonlinear properties of the medium are described by both self- and cross-coupling terms, and it is found that such systems can act as nonlinear quantum scissors with fewer requirements concerning the values of nonlinearities than analogous systems described by self-coupling terms alone.