arXiv subjects

B. A. Malomed

Publications and source records attributed to B. A. Malomed.

At least 19 recordsLinked to original sources

arXiv2026

Stability of the Quantum Coherent Superradiant States in Relation to Exciton-Phonon Interactions and the Fundamental Soliton in Hybrid Perovskites

The use of macroscopic coherent quantum states at room temperature is crucial in modern quantum technologies. In light of recent experiments demonstrating high-temperature superfluorescence in hybrid perovskite thin films, in this work we investigate the stability of the superradiant state concerning exciton-phonon interactions, taking into account the specifics of perovskites. We focused on quasi-2D Wannier excitons interacting with longitudinal optical (LO) phonons in polar crystals, as well as with acoustic phonons. Our study leads to the derivation of nonlinear equations in the coordinate space that govern the exciton wavefunction's coefficient in the single-exciton basis for the lowest exciton state, which translates to the complex-valued polarization. The resulting equations take the form of a 2D nonlocal nonlinear Schrodinger (NLS) equation. We perform a linear stability analysis of the plane wave solutions for the equations in question, which allows us to establish stability criteria. This analysis is particularly important for evaluating the stability of the superradiant state in the considered quasi-2D structures, as the superradiant state represents a specific case of the plane wave solution. In scenarios involving the weakly nonlocal NLS equation, we find that it transitions into a purely nonlocal form. Furthermore, interactions between the exciton and acoustic phonons reduce the intensity of modulationally stable waves compared to the case without such interactions. Our analytical results are corroborated by numerical calculations. We also numerically solve the 2D nonlocal NLS equation in the polar coordinates and obtain its fundamental soliton solution, which is stable.

nlin.PS↗

arXiv2026

The continuous spectrum of bound states in expulsive potentials

On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive potentials that are steeper than the quadratic ones, give rise to normalizable eigenstates, which may be considered as a manifestation of effective self-trapping in the linear system. These states constitute full continuous spectra in both the 1D and 2D cases. In 1D, they are spatially even and odd eigenstates. The 2D states may carry any value of the vorticity (alias magnetic quantum number). Asymptotic expressions for wave functions of the 1D and 2D eigenstates, valid far from the center, are derived analytically, demonstrating excellent agreement with full numerical solutions. Special exact solutions for vortex states are obtained in the 2D case. These findings suggest an extension of the concept of bound states in the continuum, in quantum mechanics and paraxial photonics. Gross-Pitaevskii equations are briefly considered as the nonlinear extension of the 1D and 2D settings. In 1D, the cubic nonlinearity slightly deforms the eigenstates, maintaining their stability

quant-ph↗

arXiv2026

Stable Quantum Vortices in Lee-Huang-Yang Dipolar Superfluids

The nucleation and dynamics of vortices in the quasi-two-dimensional rotating dipolar Bose-Einstein condensate are explored by taking into account the Lee-Huang-Yang (LHY) correction to the mean-field (MF) theory. Assuming approximate cancellation of the MF interactions, we focus on the formation of a pure LHY superfluid. The effect of rotational frequency $Ω$ is investigated numerically by determining the corresponding number of stable vortices in the superfluid, together with the respective energy per particle $E$ and chemical potential $μ$. The LHY superfluid provides a deep minimum of $E$ and $μ$, indicating that it is a remarkably robust state of quantum matter. By fixing the LHY interaction strength, an exact single-vortex critical frequency is found, along with the respective chemical potential. A notable feature, observed when creating the LHY superfluid with fewer than five vortices, which is understood as being due to the superfluid's nonlinearity and trapping aspect ratio, is the large frequency ranges admitting the production of two and four vortices, as compared to the small frequency ranges to obtain one and three vortices.

cond-mat.quant-gas↗

arXiv2025

Multi-pole solitons and breathers with spatially periodic modulation induced by the helicoidal spin-orbit coupling

We report analytical solutions for diverse multi-pole (MP) soliton and breather states in spatially inhomogeneous binary Bose-Einstein condensates (BECs) with the helicoidally shaped spin-orbit coupling (SOC), including MP stripe solitons on zero background, MP beating stripe solitons on a nonzero plane-wave background, as well as MP beating stripe solitons and MP breathers on periodic backgrounds. The results indicate that modulation effects produced by the helicoidal SOC not only induce stripe patterns in MP solitons, but also generate the spatially-periodic background for the MP beating stripe solitons and breathers. An asymptotic analysis reveals curved trajectories with a logarithmically increasing soliton/breather separation for these MP excitations, fundamentally distinguishing them from periodic trajectories of bound-state solitons/breathers or straight trajectories of conventional multi-soliton/breather sets. With complex periodic structures in individual components, the total density distribution is nonperiodic, due to their configurations which are out-of-phase with respect to the two components. We further examine several degenerate structures of MP solitons and breathers under varying SOC and spectral parameters. Numerical simulations validate the analytical results and demonstrate stability of these MP excitations. These findings may facilitate deeper understanding of soliton/breather interactions beyond conventional multi-soliton systems and bound-state complexes in SOC BEC.

nlin.PS↗

arXiv2025

Nonlinear management of the miscibility-immiscibility transition in binary Bose-Einstein condensates

We investigate application of the nonlinearity management (NM, i.e., periodic variation of the strength of the inter-component repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component BEC, both with and without the linear mixing (Rabi coupling, RC) between the components. To this end, we first identify, by means of a variational approximation and numerical solution, diverse stationary domain-wall (DW) structures supported by the system in the absence of the management. The approximate analytical solutions for the DWs are found to be in excellent agreement with their numerical counterparts. An analytical estimate is also produced for the upshift of the MIM transition caused by the pressure of the trapping potential in the case of a confined system. An exact DW solution is produced for the system including the Pöschl-Teller potential, which is stable (unstable) if the potential is repulsive (attractive). Further, we find the spectrum of linear excitations in the spatially uniform mixed state, and thus establish parameter regions where the system is stable/unstable against demixing. In particular, RC upshifts the critical strength of the inter-component repulsion for the onset of the MIM transition. Eigenfrequencies of excitations on top of DW states are identified from numerical simulations through monitoring the evolution of perturbed states. Weak NM applied at the DW eigenfrequency reveals features of the nonlinear resonance. Stronger NM, under which the system periodically crosses the MIM-transition point, restricts the miscibility.

cond-mat.quant-gas↗

arXiv2025

Beating stripe solitons arising from helicoidal spin-orbit coupling in Bose-Einstein condensates

We demonstrate that the model of a spatially non-uniform two-component Bose-Einstein condensate (BEC) featuring the helicoidal spin-orbit coupling (SOC), gives rise to dark-bright soliton complexes characterized by spatiotemporal periodic oscillations in each component. These solitons are formed by the superposition of dark and bright ones, and exhibit a beating state over time and a striped state across space, earning them the designation of beating stripe solitons. Our analysis demonstrates that helicoidal SOC significantly affects the formation and dynamical properties of these solitons, also serving as the primary driver for spin oscillations. Through the nonlinear superposition of the beating stripe solitons, a range of intricate scenarios of the interaction between multiple solitons emerges, including head-on collisions, bound states, and parallel states.

cond-mat.quant-gas↗

arXiv2024

Ultra-high-amplitude Peregrine solitons induced by helicoidal spin-orbit coupling

In the framework of the model of a spatially non-uniform Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling, we find abnormal Peregrine solitons (PSs) on top of flat and periodic backgrounds, with ultra-high amplitudes. We explore the roles of the SO coupling strength and helicity pitch in the creation of these anomalously tall PSs and find that their amplitude, normalized to the background height, attains indefinitely large values. The investigation of the modulation instability (MI) in the same system demonstrates that these PSs exist in a range of relatively weak MI, maintaining the feasibility of their experimental observation.

cond-mat.quant-gas↗

arXiv2023

Interactions and dynamics of one-dimensional droplets, bubbles and kinks

We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross-Pitaevskii model including the Lee-Huang-Yang correction. Existence regions are identified for the one-dimensional droplets and bubbles in terms of their chemical potential, verifying the stability of the droplets and exposing the instability of the bubbles. The limiting case of the droplet family is a stable kink. The interactions between droplets demonstrate in-phase (out-of-phase) attraction (repulsion), with the so-called Manton's method explicating the observed dynamical response, and mixed behavior for intermediate values of the phase shift. Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink-antikink interactions are repulsive, generating counter-propagating shock waves. Our findings reveal dynamical features of droplets and kinks that can be detected in current experiments.

cond-mat.quant-gas↗

arXiv2022

Self-trapping and switching of solitonic pulses in mismatched dual-core highly nonlinear fibers

We investigate experimentally and theoretically effects of the inter-core propagation mismatch on nonlinear switching in dual-core high-index-contrast soft-glass optical fibers. Incident femtosecond pulses of various energy are fed into a single ("straight") core, to identify transitions between different dynamical regimes, viz., inter-core oscillations, self-trapping in the cross core, and retaining the pulse in the straight core. The transfer between channels, which has solitonic character, is controlled by the pulse's energy. A model based on the system of coupled nonlinear Schrödinger equations reveals the effect of the mismatch parameter and pulse duration on the diagram of the various energy dependent dynamical regimes. Optimal values of the mismatch and pulse width, which ensure stable performance of the nonlinear switching, are identified. The theoretical predictions are in agreement with experimental findings.

physics.optics↗

arXiv2022

Bessel Vortices in Spin-Orbit-Coupled Binary Bose-Einstein Condensates with Zeeman Splitting

We present an analysis of stationary solutions for two-dimensional (2D) Bose-Einstein condensates (BECs) with the Rashba spin-orbit (SO) coupling and Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system can be solved exactly. The solutions are semi-vortices of the Bessel-vortex (BV) and modified Bessel-vortex (MBV) types, in the presence of the weak and strong Zeeman splitting, respectively. The ground states (GSs) of the full nonlinear system are constructed with the help of a specially designed neural network (NN). The GS of the mixed-mode type appears as cross-attraction interaction increases. The spin texture of the GS is produced in detail. It exhibits the Neel skyrmion structure for the semi-vortex GS of the BV type, and the respective skyrmion number is found in an analytical form. On the other hand, GSs of the MBV and mixed-mode types do not form skyrmions.

cond-mat.quant-gas↗

arXiv2021

Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state

Discrete dissipative coupled systems exhibit complex behavior such as chaos, spatiotemporal intermittence, chimera among others. We construct and investigate chimera states, in the form of confined stationary and dynamical states in a chain of parametrically driven sites with onsite damping and cubic nonlinearity. The system is modeled by the respective discrete parametrically driven damped nonlinear Schrodinger equation. Chimeras feature quasi-periodic or chaotic dynamic in the filled area, quantified by time dependence of the total norm (along with its power spectrum), and by the largest Lyapunov exponent. Systematic numerical simulations, in combination with some analytical results, reveal regions in the parameter space populated by stable localized states of different types. A phase transition from the stationary disorder states to spatially confined dynamical chaotic one is identified. Essential parameters of the system are the strength and detuning of the forcing, as well as the lattice's coupling constant.

nlin.PS↗

arXiv2021

Temporal Cavity Solitons in a Laser-based Microcomb: A Path to a Self-Starting Pulsed Laser without Saturable Absorption

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not require saturation of the gain, the results offer an alternative to standard techniques that provide laser mode-locking.

physics.optics↗

arXiv2020

Breather stripes and radial breathers of the two-dimensional sine-Gordon equation

We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. Different families of such solutions are identified. They develop small-amplitude spatially oscillating tails ("nanoptera") through a resonance of higher-order breather's harmonics with linear modes ("phonons") belonging to the continuous spectrum. These results demonstrate the ability of the 2D sG model within our finite domain computations to localize energy in long-lived, self-trapped breathing excitations.

nlin.PS↗

arXiv2020

Stable two-dimensional soliton complexes in Bose-Einstein condensates with helicoidal spin-orbit coupling

We show that attractive two-dimensional spinor Bose-Einstein condensates with helicoidal spatially periodic spin-orbit coupling (SOC) support a rich variety of stable fundamental solitons and bound soliton complexes. Such states exist with chemical potentials belonging to the semi-infinite gap in the band spectrum created by the periodically modulated SOC. All these states exist above a certain threshold value of the norm. The chemical potential of fundamental solitons attains the bottom of the lowest band, whose locus is a ring in the space of Bloch momenta, and the radius of the ring is a non-monotonous function of the SOC strength. The chemical potential of soliton complexes does not attain the band edge. The complexes are bound states of several out-of-phase fundamental solitons whose centers are placed at local maxima of the SOC-modulation phase. In this sense, the impact of the helicoidal SOC landscape on the solitons is similar to that of a periodic two-dimensional potential. In particular, it can compensate repulsive forces between out-of-phase solitons, making their bound states stable. Extended stability domains are found for complexes built of two and four solitons (dipoles and quadrupoles, respectively). They are typically stable below a critical value of the chemical potential.

cond-mat.quant-gas↗

arXiv2020

Modulational instability in binary spin-orbit-coupled Bose-Einstein condensates

We study modulation instability (MI) of flat states in two-component spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in the framework of coupled Gross-Pitaevskii equations for two components of the pseudospinor wave function. The analysis is performed for equal densities of the components. Effects of the interaction parameters, Rabi coupling, and SOC on the MI are investigated. In particular, the results demonstrate that the SOC strongly alters the commonly known MI (immiscibility) condition, $g_{12} > g_{1} g_{2}$, for the binary superfluid with coefficients $g_{1,2}$ and $g_{12}$ of the intra- and interspecies repulsive interactions. In fact, the binary BEC is always subject to the MI under the action of the SOC, which implies that the ground state of the system is plausibly represented by a striped phase.

cond-mat.quant-gas↗

arXiv2020

Interplay of the pseudo-Raman term and trapping potentials in the nonlinear Schroedinger equation

We introduce a nonlinear Schroedinger equation (NLSE) which combines the pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative cubic one with the first spatial derivative, and an external potential, which helps to stabilize solitons against the pseudo-SRS effect. Dynamics of solitons is addressed by means of analytical and numerical methods. The quasi-particle approximation (QPA) for the solitons demonstrates that the SRS-induced downshift of the soliton's wavenumber may be compensated by a potential force, producing a stable stationary soliton. Three physically relevant potentials are considered: a harmonic-oscillator (HO) trap, a spatially periodic cosinusoidal potential, and the HO trap subjected to periodic temporal modulation. Both equilibrium positions of trapped pulses (solitons) and their regimes of motion with trapped and free trajectories are accurately predicted by the QPA and corroborated by direct simulations of the underlying NLSE. In the case of the time-modulated HO trap, a parametric resonance is demonstrated, in the form of motion of the driven soliton with an exponentially growing amplitude of oscillations.

physics.plasm-ph↗

arXiv2019

Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two- and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form. We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers (or norm of the spinor wavefunction) exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point. The zero-threshold point is a boundary between single-peaked and striped states, realizing hybrids combining 2D and 1D structural features. In a vicinity of such point, an asymptotic equation describing the bifurcation of the solitons from the linear spectrum is derived and investigated analytically. We show that striped 3D solitary states are as well stabilized by 2D SOC, albeit in a limited range of chemical potentials and norms.

cond-mat.quant-gas↗

arXiv2019

Solitons in a chain of charge-parity-symmetric dimers

We consider an array of dual-core waveguides, which represent an optical realization of a chain of dimers, with an active (gain-loss) coupling between the cores, opposite signs of discrete diffraction in the parallel arrays, and a phase-velocity mismatch between them (which is necessary for the stability of the system). The array provides an optical emulation of the charge-parity ($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearity gives rise to several species of fundamental discrete solitons, which exist in continuous families, although the system is non-Hermitian. The existence and stability of the soliton families are explored by means of analytical and numerical methods. An asymptotic analysis is presented for the case of weak intersite coupling (i.e., near the anticontinuum limit), as well as weak coupling between cores in each dimer. Several families of fundamental discrete solitons are found in the semi-infinite gap of the system's spectrum, that have no counterparts in the continuum limit, as well as a branch which belongs to the finite band gap and carries over into a family of stable gap solitons in that limit. One branch develops an oscillatory instability above a critical strength of the intersite coupling, others being stable in their entire existence regions. Unlike solitons in conservative lattices, which are controlled solely by the strength of the intersite coupling, here fundamental-soliton families have several control parameters, one of which, viz., the coefficient of the intercore coupling in the active host medium, may be readily adjusted in the experiment by varying the gain applied to the medium.

nlin.PS↗