Presence Of Kerr Nonlinearity Research Articles

Optical bistability at lower photon number via photon and phonon interaction in the presence of Kerr nonlinearity

Optical bistability is theoretically analyzed in a hybrid optomechanical system consisting of an optical cavity including a Kerr medium and an optomechanical cavity coupled by direct tunnel coupling. The dynamics of the system is described by Heisenberg–Langevin equations. It is numerically shown that there is a critical value of the Kerr coefficient to observe the bistability of the intracavity intensity for a given coupling rate, and the changing of the Kerr coefficient will lead to the changing of the critical point to observe the bistability as well. In addition, the first critical value to observe bistability becomes larger with the increasing coupling rate between the two cavities. It is also demonstrated that the pump beam required to realize the bistable behavior in the blue sideband regime is significantly smaller than that in the red sideband regime. And the mean intracavity photon number is relatively larger in the red sideband case than that in the blue sideband case. It is remarkable to observe that the mean intracavity photon numbers in both cavities are much lower than that in ordinary situations.

Ultra low-power multistability in [formula omitted]-symmetric periodic structures with saturable coupling, gain and loss

The present work investigates the switching dynamics of conventional fiber Bragg gratings (FBGs) with saturable coupling and parity-time (PT)-symmetric fiber Bragg gratings (PTFBGs) with saturable coupling (SC) and saturable gain-loss (SGL) in the presence of Kerr nonlinearity (KNL) [model - I] and saturable nonlinearity (SNL) [model - II]. Both system models can generate distinct optical multistability (OM) and bistability (OB) curves, including S-shaped, ramp-like, and mixed OM curves in both unbroken and broken PT-symmetric regimes. The impact of each control parameter on controlling switching intensities, hysteresis width, and the number of stable states is thoroughly examined for both of these system models. The direction of right light incidence enables a significant reduction in the switching intensities to below 100 W/cm2, the lowest critical power ever reported in the literature of PTFBGs, thanks to the concept of both saturable coupling, gain and loss.

Entanglement between two charge qubits taking account the Kerr media

Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed.
 Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered.
 Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter.
 Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown.
 Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.

Nondispersive evolution of the pump mode in down-conversion processes and in the presence of Kerr nonlinearity

Nondispersive evolution of the pump mode in down-conversion processes and in the presence of Kerr nonlinearity

Nonequilibrium dynamics of the Jaynes-Cummings dimer.

We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is analyzed systematically to chart out a variety of photonic Josephson oscillations and their regime of stability. Different types of transitions between the dynamical states lead to the self-trapping phenomenon, which results in photon population imbalance between the two cavities. We also study the dynamics quantum mechanically to identify characteristic features of different steady states and to explore fascinating quantum effects, such as spin dephasing, phase fluctuation, and revival phenomena of the photon field, as well as the entanglement of spin qubits. For a particular "self-trapped" state, the mutual information between the atomic qubits exhibits a direct correlation with the photon population imbalance, which is promising for generating photon mediated entanglement between two non interacting qubits in a controlled manner. Under a sudden quench from stable to unstable regime, the photon distribution exhibits phase space mixing with a rapid loss of coherence, resembling a thermal state. Finally, we discuss the relevance of the new results in experiments, which can have applications in quantum information processing and quantum technologies.

Quantum dots interacting with a non-classical field under Kerr-phase modulation as a resource for repeatable quantum algorithms

An analytical solution describing the dynamics of a hybrid system comprising an interacting quantum dot and a quantum electromagnetic field in the presence of Kerr nonlinearity is obtained. A completely new regime of interaction is found. It provides stable periodically repeating dynamics for the total bipartite system and for the quantum dot excitation, accompanied by full and pure revivals. This is even observed when the initial field state is in a squeezed vacuum. Periodical strong entanglement and full disentanglement between the interacting subsystems are demonstrated. The obtained regime forms the basis for the development of quantum information algorithms and photon–matter interfaces involving these hybrid systems. The formation of non-Gaussian field states is revealed. Methods to control and manage the specific features of the found pure and mixed states of the considered subsystems are developed.

Nonclassicality of dissipative cavity optomagnonics in the presence of Kerr nonlinearities

The phenomena of photon and magnon blockade, and nonclassicality which are the key ingredient for quantum enhanced technologies, can be considered as resources in quantum information processing. This paper deals with the study of nonclassicality in a lossy optomagnonic microcavity enclosed by Kerr medium, with considering different sources of dissipation. The system contains a ferromagnetic YIG sphere coupled to two optical modes in a microcavity, with photonic and magnonic Kerr nonlinearity in the presence of magnonic and photonic losses. Considering the Heisenberg-Langevin approach, we obtain the dynamics of the second-order correlation functions (CFs) to observe the phenomenon of photon and magnon blockade (PMB), and the Cauchy-Schwarz inequality (CSI) to find the nonclassicality of the system. We then discuss the effects of magnon-photon coupling strength and different sources of dissipation on the temporal behavior of the mentioned criteria. Looking at the numerical results, we find that the depth and the domain of antibunching behavior significantly depend on the value of the thermal average photon (magnon) number. The phenomenon of perfect PMB may also be observed in the presence of dissipation at the low-temperature regime where the equilibrium thermal photon (magnon) occupation number approaches zero, i.e. T → 0. Moreover, we see a strong anticorrelation between the photonic and magnonic modes and the optical modes, too. Furthermore, it can be found that the phenomenon of PMB blockade as well as antibunching can be observed at cryogenic temperatures.

Effects of Kerr Nonlinearity in Physical Unclonable Functions

We address the question of whether the presence of Kerr nonlinearity in multiple-scattering optical media offers any advantage with respect to the design of physical unclonable functions. Our results suggest that under certain conditions, nonlinear physical unclonable functions can be more robust against the potential cloning of the medium relative to their linear counterparts that have been exploited in the context of various cryptographic applications.

Effect of Kerr nonlinearity on signal and pump intensities in EDFA comprising single-mode step index fiber: Estimation by a simple but accurate mathematical formalism

The paper presents simple but accurate analytical expressions for the estimation of variation of signal and pump intensity with normalised radial distance in case of erbium doped fiber amplifier. Choosing two typical single-mode step index fibers in our investigation, we hereby predict the said variations relating to both pump and signal in presence as well as absence of Kerr nonlinearity. The stated formulation uses power series expression for the fundamental modal field of graded index optical fiber as derived by Chebyshev formalism. Method of iteration is applied for the prediction of concerned parameters in presence of Kerr type nonlinearity. Our results have been shown to be agreeing excellently with the numerical exact ones in absence and also in presence of Kerr nonlinearity. Exact results in case of Kerr nonlinearity are determined using the cumbersome finite element method. It is noteworthy that execution of our proposed method requires very less computation and as such it will be remarkably user friendly for researchers and technologists associated with nonlinear optical engineering.

Broadband resonance-enhanced frequency generation by four-wave mixing in a silicon Floquet topological photonic insulator

Floquet topological photonic insulators, whose light transport properties are dictated by the periodic drive sequence of the lattice, provide more flexibility for controlling and trapping light than undriven topological insulators. This can enable novel nonlinear optics applications in topological photonics. Here, we employ a novel resonance effect called Floquet Defect Mode Resonance (FDMR) in a 2D silicon Floquet microring lattice to demonstrate resonance-enhanced frequency generation by four-wave mixing of Floquet bulk modes in the presence of Kerr nonlinearity. The compact, cavity-less resonance mode, induced through a periodic perturbation of the lattice drive sequence, has the largest reported Q-factor for a 2D topological resonator of ∼105 with low group velocity dispersion, which enables efficient broadband frequency generation over several Floquet–Brillouin zones of the Floquet topological insulator. We achieved wavelength conversion over a 10.1 nm spectral range with an average enhancement of 12.5 dB in the conversion efficiency due to the FDMR. Our work could lead to robust light sources generated directly on a topologically protected photonic platform.

Entanglement of two superconducting qubits induced by a thermal noise of a cavity with Kerr medium taking into account the atomic coherence

The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

Analysis of Kerr type nonlinear single-mode triangular index fiber directional coupler by a simple method

We present the coupling characteristics of directional coupler comprising two identical single-mode triangular index fibers both in the presence and the absence of Kerr nonlinearity. Triangular index fibers of some typical V numbers are chosen for our investigation. Our analysis is based on the simple series expression for the fundamental modal field for triangular index fiber developed by Chebyshev technique. Analytical expression of the coupling length in the absence as well as in the presence of Kerr nonlinearity is prescribed. Using the said expression of coupling length, we apply a method of iteration to evaluate the said coupling parameter in the presence of Kerr nonlinearity. We also show that our results match excellently with the exact results obtainable by rigorous finite-element technique. The execution of our formalism requires little computation. Thus our simple but accurate formalism to study the triangular index directional coupler will prove a suitable alternative to the existing rigorous methods in the field of nonlinear optics. This user-friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.

A simple but accurate method for prediction of splice loss in mono-mode dispersion shifted and dispersion flattened fibers in presence of Kerr nonlinearity

Abstract This paper estimates transmission coefficient at the splice of single-mode dispersion shifted trapezoidal and dispersion flattened graded and step W fibers in presence as well as in absence of Kerr nonlinearity. We restrict our analysis for both angular and transverse offsets only since splices are highly tolerant in respect of longitudinal mismatch. Here, we apply method of iteration involving Chebyshev formalism in order to take care of Kerr nonlinearity. The concerned investigation requires very little computation. It has been shown that our results match excellently with the exact results both in absence as well as in presence of Kerr nonlinearity. Considering that prediction of exact results in presence of Kerr nonlinearity requires application of rigorous finite element technique, our formalism in this context can be treated as a simple alternative to the existing method. Thus, this user friendly method generates ample scope for many useful applications in the field of nonlinear photonics involving such kinds of fiber.

Influence of Kerr nonlinearity on group delay and modal dispersion parameters of single-mode graded index fibers: evaluation by a simple but accurate method

Abstract This paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of V numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering.

A simple but accurate technique for study of single-mode Kerr type nonlinear dispersion-shifted and dispersion-flattened fibers

We employ a simple but accurate power series expression based on Chebyshev technique in order to predict the fundamental modal fields inside the cores as well as the claddings of single-mode dispersion-shifted trapezoidal, dispersion-flattened graded W and step W fibers both in presence and absence of Kerr nonlinearity. Analytical expressions for the concerned parameters are prescribed. In presence of Kerr nonlinearity, our analysis involves the use of a simple iteration method. The formalism developed is executable with little computations. Our results agree excellently with the exact results which can be obtained by employing rigorous finite element technique. Thus our simple and accurate formalism will prove beneficial to the technologists working in the field of nonlinear photonics.

Klein tunneling of Dirac solitons in binary waveguide arrays

We systematically investigate the optical analog of the relativistic quantum Klein tunneling effect in binary waveguide arrays (BWAs) in the presence of Kerr nonlinearity where the Dirac solitons are used to construct the initial beams. The transmission coefficient of Dirac solitons obtained by direct beam propagation simulations in the low-power regime as a function of the potential step height and incidence angle is numerically shown for the first time, to the best of our knowledge, to be in excellent agreement with earlier predicted theoretical results in all ranges of parameters. The conditions for observing Klein tunneling are analytically derived and are also in excellent agreement with simulation-based results. We show that the nonlinearity in BWAs can severely influence the Klein tunneling effect. Our simulations show that initial beams based on Dirac solitons are much better candidates than Gaussian beams to quantitatively study the Klein tunneling effect in detail, especially in the regime where the incidence angle is very close to the Bragg angle.

A Simple but Accurate Method for Estimation of the Effect of Kerr Nonlinearity on Confinement and Excitation of the Fundamental Mode in Single Mode Graded Index Fiber

This paper presents prediction of the fractional modal power and excitation of the fundamental mode inside the core of a single-mode graded index fiber, both in presence and absence of Kerr nonlinearity. Our analysis is based on simple power series expression for fundamental mode of graded index fiber, which has been formulated by applying Chebyshev technique. In absence of nonlinearity, analytical expressions for the concerned propagation parameters are prescribed. Employing these analytical expressions, method of iteration is applied for evaluation of the said parameters in presence of Kerr nonlinearity. In this context, some typical step, parabolic and triangular index fibers are used for our study. In absence of nonlinearity, our results show excellent match with the exact results available in literature. In presence of nonlinearity, the results found by our formalism also agree excellently with the exact results which can be obtained by application of rigorous finite element technique. Thus, this simple but accurate method will prove extremely useful for the system users.

A simple but accurate formalism for study of single-mode graded index fiber directional coupler in presence of Kerr nonlinearity

This paper presents performance of directional coupler consisting of two identical single-mode graded index fibers in presence as well as in absence of Kerr type nonlinearity. In this context, parabolic and step index fibers of some typical V numbers are used. Here, we employ a simple series expression for fundamental modal field for such fibers prescribed by Chebyshev formalism. Analytical expression of the coupling length of the directional coupler is formulated. Here, we apply method of iteration in order to take care of nonlinearity. The concerned evaluation involves little computation. Thus, the formalism developed for study of nonlinear directional coupler can be treated as an accurate but simple alternative to the existing complicated methods available in literature. This user friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.

Prediction of First Higher Order Modal Field for Graded Index Fiber in Presence of Kerr Nonlinearity

AbstractWe report evaluation of first higher order modal field for dual mode optical fiber having step and parabolic index profiles. The study is carried out both in absence as well as in presence of Kerr nonlinearity. The analysis is based on a simple iterative method involving Chebyshev formalism. Taking some typical step- and parabolic-index fibers as examples, we show that our results agree excellently with the exact results which can be obtained by applying rigorous methods. Thus, our simple formalism stands the merit of being considered as an accurate alternative to the existing cumbersome methods. The prescribed formalism provides scope for accurate estimation of different propagation parameters associated with first higher order mode in such kinds of fibers in presence of Kerr nonlinearity. The execution of formalism being user friendly, it will be beneficial to the system engineers working in the field of optical technology.

Bragg solitons in topological Floquet insulators.

We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.