arXiv subjects

Marek Trippenbach

Publications and source records attributed to Marek Trippenbach.

At least 19 recordsLinked to original sources

arXiv2026

Re-entrant parity-time phase transitions in locally coupled ring resonators

We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.

nlin.PS↗

arXiv2026

Degenerate four-wave mixing in a CPT-symmetric coupler with intermodal dispersion

Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels. We study degenerate four-wave mixing in a Kerr dual-core coupler with balanced gain and loss and frequency-dependent intercore coupling. The dispersive coupling changes the symmetry from conventional $\mathcal{PT}$ symmetry to a combined $\mathcal{CPT}$ symmetry and reshapes the two-branch linear spectrum. We determine the unbroken-$\mathcal{CPT}$ domain and classify the branch configurations that can satisfy the degenerate phase-matching condition. In the parameter ranges examined, three resonant channels persist over broad regions, whereas a same-branch channel appears only close to the symmetry-breaking threshold. In this near-threshold regime, a single pump can simultaneously satisfy two distinct nonzero sideband resonances. Direct pulse simulations confirm the predicted resonances and reveal secondary-wave generation and multifrequency cascades near eigenmode coalescence. A reduced three-wave model captures the initial dynamics away from the exceptional point but loses accuracy as the modal basis becomes ill-conditioned. These results show how dispersive coupling reorganizes resonances, group-velocity mismatch, and nonlinear energy exchange in a non-Hermitian wave system, and they identify the exceptional-point region as a regime where a few-mode description can break down.

physics.optics↗

arXiv2026

Hysteresis in the complex nonlinear refractive index of a homogeneous and isotropic medium

We calculate the permittivity, $ε(ω)$, for a medium with a quadratic electro-optic effect, modeling it as a Duffing oscillator. The nonlinear refractive index $n(ω, E(ω))$ and the nonlinear absorption coefficient $α(ω, E(ω))$ exhibit hysteresis when the light intensity is varied [here $E(ω)$ is the electric field strength at angular frequency $ω$], and when the light frequency is varied. $n(ω, E(ω))$ can be negative when the resonances in the permittivity and permeability are close to one another.

physics.optics↗

arXiv2024

Fermionic atoms in a spin-dependent optical lattice potential: topological insulators with broken time-reversal symmetry

We propose a novel approach to study the topological properties of matter. In this approach, fermionic atoms are placed in an external magnetic field and in a two-dimensional spin-dependent optical lattice (SDOL) created by intersecting laser beams with a superposition of polarizations. To demonstrate the utility of the SDOL-based technique we compute the topological invariants (Chern numbers) for the SDOL bands as a function of an external magnetic field, and show the existence of a rich topology of the energy bands for this system which does not have parity-time-reversal symmetry. We explicitly consider $^{6}$Li $F=1/2$ atoms. Using a projection matrix method we observe topological phase transitions between an ordinary insulator, an abelian topological insulator, and a non-abelian topological insulator as the external magnetic field strength is varied. Upon introducing edges for the SDOL we find topological edge states (that are correlated with the band Chern numbers) that simultaneously exhibit non-trivial density and spin currents with both a rotational flow contribution and flow along the edge of the SDOL.

cond-mat.quant-gas↗

arXiv2024

Negative Refraction in isotropic achiral and chiral materials

We show that negative refraction in materials can occur at frequencies $ω$ where the real parts of the permittivity $\veps(ω)$ and the permeability $μ(ω)$ have different sign, and that light with such frequencies can propagate just as well as light with frequencies where they have equal sign. Therefore, for negative refraction one does not need to be in the ``double-negative'' regime. We consider negative refractive index achiral materials using the Drude-Lorentz model and chiral materials using the Drude-Born-Fedorov model. We find that the time-averaged Poynting vector always points along the wave vector, the time-averaged energy-flux density is always positive, and the time-averaged energy density is positive (negative) when the refractive index is positive (negative). The phase velocity is negative when the real part of the refractive index is negative, and the group velocity generally changes sign several times as a function of frequency near resonance.

physics.optics↗

arXiv2023

Analysis of High-Contrast All-Optical Dual Wavelength Switching in Asymmetric Dual-Core Fibers

We systematically present experimental and theoretical results for the dual-wavelength switching of 1560 nm, 75 fs signal pulses (SPs) driven by 1030 nm, 270 fs control pulses (CPs) in a dual-core fiber (DCF). We demonstrate a switching contrast of 31.9 dB, corresponding to a propagation distance of 14 mm, achieved by launching temporally synchronized SP-CP pairs into the fast core of the DCF with moderate inter-core asymmetry. Our analysis employs a system of three coupled propagation equations to identify the compensation of the asymmetry by nonlinearity as the physical mechanism behind the efficient switching performance.

physics.optics↗

arXiv2022

Atoms in a spin dependent optical potential: ground state topology and magnetization

We investigate a Bose-Einstein condensate of $F= 1$ $^{87}$Rb atoms in a 2D spin-dependent optical lattice generated by intersecting laser beams with a superposition of polarizations. For $^{87}$Rb the effective interaction of an atom with the electromagnetic field contains a scalar and a vector (called as fictitious magnetic field, $B_{fic}$) potentials. The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic rotational motion angular momentum and the hyperfine spin. The ground state of the QR is affected upon applying an external magnetic field, $B_{ext}$, perpendicular to the plane of QR motion and a sudden change of its topology occurs as the ratio $B_{ext}/B_{fic}$ exceeds critical value. It is shown that the change of topology of the QR ground state is a result of combined action of Zeeman and Einstein-de Haas effects. The first transfers atoms to the largest hyperfine component to polarize the sample along the field as the external magnetic field is increased. The second sweeps spin to rotational angular momentum, modifying the kinetic energy of the atoms.

quant-ph↗

arXiv2022

Optical Thouless pumping transport and nonlinear switching in a topological low-dimensional discrete nematic liquid crystal array

We theoretically investigate a Thouless pumping scheme in the 1D topological Su-Schrieffer-Heeger (SSH) model for single and multiple band-gaps systems when implemented in a discrete nematic liquid crystal arrangement. For an electrically controlled SSH waveguide array, we numerically demonstrate edge-to-edge light transport at low power levels. On the other hand, at higher powers, the transport is frustrated by light-induced nonlinear defect states, giving rise to robust all-optical switching.

physics.optics↗

arXiv2020

Four-wave mixing in spin-orbit coupled Bose-Einstein condensates

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin-orbit coupled Bose-Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are important source of correlated particles and can be used the experiments testing quantum properties of atomic ensembles.

quant-ph↗

arXiv2020

Reversible ultrafast soliton switching in dual-core highly nonlinear optical fibers

We experimentally investigate a nonlinear switching mechanism in a dual-core highly nonlinear optical fiber. We focus the input beam of femtosecond pulses on one core only, to identify transitions between inter-core oscillations, self-trapping in the cross core, and self-trapping of the pulse in the straight core. A model based in the system of coupled nonlinear Schrodinger equations provides surprisingly good agreement with the experimental findings.

physics.optics↗

arXiv2019

Route to chaos in a coupled microresonator system with gain and loss

We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates, optical waveguides or atomic Bose-Einstein condensates of ultra-cold atoms placed in a circular-shaped trap. From the theoretical point of view this system is attractive due to its modulational instability and rich structure, including various types of spontaneous symmetry breaking, period doubling bifurcations, eventually leading to chaotic regime. It is described by set of partial differential equations but we show that the so called Galerkin approximation can explain most of the system characteristics mapping it on the dynamics of few coupled oscillator modes. The main goal of present study is to investigate various routes to chaos in our non-hermitian system and to show the correspondence between the continuous operator problem and its discrete representation.

physics.optics↗

arXiv2018

Vortex creation without stirring in coupled ring resonators with gain and loss

We present study of the dynamics of two ring waveguide structure with space dependent coupling, linear gain and nonlinear absorption - the system that can be implemented in polariton condensates, optical waveguides, and nanocavities. We show that by turning on and off local coupling between rings one can selectively generate permanent vortex in one of the rings. We find that due to the modulation instability it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with interesting structure of currents flowing between rings, generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as single vortex in one of the channels, that is later alternating between channels.

nlin.PS↗

arXiv2018

Symmetry breakings in dual-core systems with double-spot localization of nonlinearity

We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries.

nlin.PS↗

arXiv2017

Single and double linear and nonlinear flatband chains: spectra and modes

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are studied too, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.

nlin.PS↗

arXiv2016

Super-mode spatial optical solitons in liquid crystals with competing nonlinearities

We study numerically formation of spatial optical solitons in nematic liquid crystals with competing nonlocal nonlinearities. We demonstrate that at the sufficiently high input power the interplay between focusing and thermally induced defocusing may lead to the formation of two-peak fundamental spatial solitons. These solitons have constant spatial phase and hence represent supermodes of the self-induced extended waveguide structure. We show that these two-peak solitons are stable in propagation and exhibit adiabatic transition to a single peak state under weak absorption.

physics.optics↗

arXiv2016

Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials

We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.

physics.optics↗

arXiv2015

Spectroscopy of cross-correlations of environmental noises with two qubits

A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to reconstruct the spectrum of cross-correlations of noises acting at various locations. When the qubits are driven by the same sequence of pulses, real part of cross-correlation spectrum can be reconstructed, while applying two distinct sequence to the two qubits allows for reconstruction of imaginary part of this spectrum. The latter quantity contains information on either causal correlations between environmental dynamics at distinct locations, or on the occurrence of propagation of noisy signals through the environment. We illustrate the former case by modeling the noise spectroscopy protocol for qubits coupled to correlated two-level systems. While entanglement between the qubits is not necessary, its presence enhances the signal from which the spectroscopic information is reconstructed.

cond-mat.mes-hall↗

arXiv2014

Stabilization of solitons under competing nonlinearities by external potentials

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates (BEC) loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations (VA and TFA), and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

nlin.PS↗