arXiv subjects

Li-Chen Zhao

Publications and source records attributed to Li-Chen Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Superheavy dark-bright soliton as a signature of spatial symmetry breaking transition in harmonically trapped Bose mixtures

We investigate the dynamics of a dark-bright soliton in harmonically trapped two-component Bose-Einstein condensates and reveal an interesting spontaneous spatial symmetry breaking driven by nonlinear interactions. When the interaction parameter crosses a threshold value, we find that the dark-bright soliton's motion demonstrates a transition from symmetric periodic oscillation about the origin to asymmetric oscillations offset from the origin. In particular, at the transition point, the effective soliton mass, determined by the ratio of inertial mass to physical mass, diverges. The underlying mechanism is uncovered by constructing trial wave functions and employing the Lagrangian variational method to obtain an effective potential in the quasiparticle picture, which changes from a single well to a double well. The anomalous ``superheavy soliton'' phenomenon is a direct consequence of the dark-bright soliton's physical mass vanishing at the transition point. We obtain the phase diagram of this spatial symmetry-breaking transition. Possible implications of our finding for quantum metrology are discussed.

cond-mat.quant-gas↗

arXiv2026

Controllable Thouless Pumping Switching Dynamics of Gap Solitons Mediated by Finite Bogoliubov Excitations

We investigate the Thouless pumping dynamics of nonlinear gap solitons and attempt to realize topological Chern number switching by modulating nonlinear parameters and varying the ramping rate of the relative phase between periodic potentials. We find that gap solitons can undergo nonlinear instabilities accompanied by finite Bogoliubov excitations under near-adiabatic ramping. Such finite Bogoliubov excitations induce the particle loss of the solitons, leading to reversed propagation directions that signals the occurrence of Chern number switching with analyzing the correspondence between soliton chemical potential and Bloch topological energy band. Our findings offer a feasible strategy for manipulating the Thouless pump dynamics of gap solitons mediated by finite Bogoliubov excitations, with implications for topological quantum transport and quantum computing applications.

nlin.PS↗

arXiv2026

Controllable excitation of vector Akhmediev breather patterns

In the focusing Manakov system, multiple modulation instability (MI) branches coexist on the same plane wave background, so the usual weak periodic modulation cannot selectively excite a single vector Akhmediev breather (AB). Here we propose an eigenvector-based initial perturbation scheme that constructs the initial condition as a plane wave plus Fourier modes whose coefficients follow the perturbation eigenvector of a selected MI branch, enabling controllable high-fidelity excitation of desired vector ABs. Numerical simulations show near-100\% fidelity with the exact AB solution. The underlying mechanism is eigenvector-controlled mode selection. The initial seeding of the target MI branch through the chosen eigenvector, together with the non-Hermitian coupling inherent in the linearized MI dynamics, ensures that the targeted unstable mode dominates the early linear stage and thereby dictates the breather type. This eigenvector-based control succeeds in gain-balanced regimes and when the targeted branch has a sufficient gain advantage. The proposed method provides a simple and robust framework for controllable generation of vector ABs over a broad parameter range, highlighting the key role of eigenvector selectivity in multi-component nonlinear systems.

nlin.PS↗

arXiv2026

Dirac monopole potentials with high charges underlying nonlinear waves

We investigate topological vector potentials underlying the phases of nonlinear waves by performing Dirac's magnetic monopole theory in an extended complex plane, taking into account self-steepening effects while ignoring the usual cubic nonlinearities. We uncover that the simple poles and third-order poles of the density function constitute virtual monopole fields with higher charges $\pm3/2$ and $\pm5/2$, respectively. These results are in sharp contrast to the previous findings, where the simple zeros of the density function yield charges $\pm1/2$. We choose scalar and vector rogue waves as well as bright solitons to demonstrate the Dirac monopole potentials. These results confirm a series of quantized magnetic charges for virtual monopoles underlying nonlinear waves, and reveal new relations between poles of density functions and topological charges.

nlin.PS↗

arXiv2026

Dissipation-induced Nonlinear Topological Gear Switching

Nonlinear interaction enables topological phenomena impossible in linear systems. A paradigm is nonlinear Thouless pump, where the transport of solitons can be topologically quantized even when band occupation is nonuniform. Such nonlinear quantization traditionally requires a time-periodic Hamiltonian with static nonlinearity and, much as in the linear case, is inherently independent of pumping speed. Instead, we demonstrate a dissipation-induced topological gear switching, where quantized soliton transport can be switched on and off via the adiabatic pumping speed itself. This phenomenon has no counterpart in prior conservative nonlinear pumps, nor in linear non-Hermitian pumps. Crucially, quantization here no longer requires a time-periodic nonlinear Hamiltonian; it stems from a genuinely non-equilibrium mechanism captured by an effective conservative model whose \textit{nonlinearity varies aperiodically in time}. Remarkably, a quantized nonlinear transport can be induced even when this nonlinear aperiodic driving is such that the system is pumped from the linear to nonlinear regimes. Our results open a route toward nonequilibrium nonlinear topological matter, where topological effect is dynamically reconfigurable via time-varying nonlinearities, with experimental implications for photonic, atomic, or superconducting platforms and beyond.

cond-mat.quant-gas↗

arXiv2026

Soliton Thouless pumping engineered by inter-site nonlinearities

We study soliton Thouless pumping in an extended diagonal Aubry-Andr\'e-Harper model with on-site nonlinearities and inter-site nonlinearities. We show that the inter-site nonlinearities can make solitons acquire anomalous transport distances far beyond the ones predicted by the linear bands, and the quantized displacements can be engineered well. We uncover that nonlinear instabilities require lower limits on sweeping rates for soliton pumping, challenging the common notion that slower modulation enables a more favorable realization of topological transport. The nonlinear interactions between solitons make multi-soliton pumping generally lack the robustness characteristic of Thouless pumping as linear systems. Our results provide many possibilities to engineer topological pumping by nonlinearities, and further make a step for applications of soliton pumping.

nlin.PS↗

arXiv2025

Varied Branches of Nondegenerate Vector Solitons

Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given soliton velocity, the nondegenerate dark-bright-bright solitons exhibit four distinct branches with different density profiles and phase distributions, comprising two positive mass branches and two negative mass branches. The energy-velocity dispersion relation of each pair of positive- and one negative-mass branches form a closed loop, resulting in two mutually independent loops for the soliton's overall dispersion. All soliton branches share a common maximal velocity, which is determined by the larger bright soliton particle number. Linear stability analysis shows that all these branches are stable against weak perturbations. Extending to an $N$-component Manakov system, the nondegenerate solitons have $2^{N-1}$ distinct branches, of which $2^{N-2}$ branches solitons is positive mass and $2^{N-2}$ branches solitons is negative mass. Each pair of positive- and negative-mass branches form a closed dispersion relation loop, so that the vector solitons have $2^{N-2}$ disjoint loops. These results uncover the rich branches and interesting dispersion relations of nondegenerate vector solitons in multi-component models.

nlin.PS↗

arXiv2025

Anomalous Trajectory Drift and Geometric Phases of Cyclic Spinor Solitons Induced by Virtual Magnetic Monopoles

We investigate the dynamics of a two-component Bose-Einstein condensate with spin-orbit coupling numerically and analytically. Under the drive of a weak segmented rotational external field, we observe that the system exhibits cyclic soliton motion; however, in contrast to the predictions of quasi-particle theory, the trajectory of the soliton center shows a distinct drift. The underlying mechanism of this anomalous drift is revealed: the moving soliton experiences a Lorentz force induced by a virtual magnetic monopole field in momentum space. We further calculate the phase evolution of the soliton during this cyclic motion and find that its geometric component comprises both an adiabatic Berry phase and a nonadiabatic Aharonov-Anandan phase. Notably, the Berry phase can be expressed in terms of the magnetic flux of the aforementioned virtual monopole field. Our findings hold implications for geometric phase theory and experiments on two-component Bose-Einstein condensates, and may establish a novel link between quantum geometry and soliton dynamics.

cond-mat.quant-gas↗

arXiv2025

Dirac monopole magnets in non-Hermitian systems

We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation $\Delta \phi_d = \Delta \phi_g$, which quantifies how cumulative minute energy differences ($\Delta \phi_d$) manifest as geometric phase shifts ($\Delta \phi_g$) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.

quant-ph↗

arXiv2025

A corresponding relationship between nonlinear Hermitian systems and linear non-Hermitian models

We note that the non-orthogonality of states and their coincidence at the degeneracy point are both admitted by nonlinear Hermitian systems and linear non-Hermitian systems. These striking characteristics motivate us to re-investigate the localized waves of nonlinear Hermitian systems and the eigenvalue degeneracies of linear non-Hermitian models, based on several well-known Lax integrable systems that have wide applications in nonlinear optics. We choose nonlinear Schrodinger equation integrability hierarchy to demonstrate the quantitative relations between dynamics of nonlinear Hermitian systems and eigenvalue degeneracies of linear non-Hermitian models. Specifically, the degeneracies of the real or imaginary spectrum of the linear non-Hermitian matrices are uncovered to clarify several essential characteristics of nonlinear localized waves, such as breathers, rogue waves, and solitons. We find that the exceptional points generally correspond to rogue waves for modulational instability cases and dark solitons with maximum velocity for the modulational stability cases. These insights provide another interesting perspective for understanding nonlinear localized waves, and hint that there are closer relations between nonlinear Hermitian systems and linear non-Hermitian systems.

nlin.PS↗

arXiv2025

Self-Adapted Josephson Oscillation of Dark-Bright Solitons under Constant Forces

We study the propagation of dark-bright solitons in two-component Bose-Einstein condensates (BECs) with general nonlinear parameters, and explore how nonlinear interactions enrich the soliton dynamics giving rise to nonsinusoidal oscillations under constant forces. Treating the bright soliton as an effective barrier, we reveal that such oscillations are characterized by the Josephson equations with self-adapted critical current and bias voltage, whose explicit analytic expressions are derived using the Lagrangian variational method. The dynamical phase diagram in nonlinear parameter space is presented, identifying oscillation regions with different skewed sinusoidal dependence, and diffusion regions with irreversible soliton spreading due to instability of the barrier. Furthermore, we obtain periodic dispersion relations of the solitons, indicating a switch between positive and negative inertial masses, consistent with the oscillation behaviors. Our results provide a general and comprehensive theoretical framework for soliton oscillation dynamics and pave the way for investigating various nonlinear transports and their potential applications.

cond-mat.quant-gas↗

arXiv2024

Manipulating topological charges via engineering zeros of wave functions

Topological charges are typically manipulated by managing their energy bands in quantum systems. In this work, we propose a new approach to manipulate the topological charges of systems by engineering density zeros of localized wave excitations in them. We demonstrate via numerical simulation and analytical analysis that the winding number of a toroidal Bose condensate can be well manipulated by engineering the relative velocities between the dark solitons and their backgrounds. The crossing of relative velocities through zero makes a change in winding number by inducing density zeros during acceleration, with the direction of crossing determining whether charge increases or decreases. Possibilities of observing such winding number manipulation are discussed for current experimental settings. This idea may also be to higher dimensions. These results will inspire new pathways in designing topological materials using quantum simulation platforms.

cond-mat.quant-gas↗

arXiv2024

Note on Dirac monopole theory and Berry geometric phase

This work reveals the intrinsic connection between Dirac monopole theory and Berry geometric phases by extending Dirac's theory to the parameter space. Using the simplest two-mode Hamiltonian model, we explicitly visualize Dirac strings with endpoints in the parameter space, demonstrating that these endpoints correspond to accidental degeneracy points of energy eigenvalues in Hermitian systems. We show that non-integrable phase factors, induced by such Dirac strings, directly give rise to the well-known Berry connection and curvature, which can be derived rigorously via Dirac's monopole framework. Our results indicate that the Berry geometric phase is essentially the non-integrable phase factor induced by Dirac strings with endpoints in the parameter space. This establishes a unified and effective approach to study monopoles and geometric phases, particularly applicable when Berry's framework fails.

quant-ph↗

arXiv2024

One family of dark-bright solitons with striking width differences

Most of previously reported dark-bright solitons admit identical width for the two components in both theoretical and experimental studies. We report dark-bright solitons can admit strikingly different widths, and derive a family of analytical solutions for them by Lagrangian variational method. The existence regimes for these solitons become much more widespread in the space of nonlinear parameters, than the ones for the previously known dark-bright solitons with identical width. Our analysis indicates that the effective quantum wells are quite different in the two components, in sharp contrast to the ones for all previously known vector solitons. Especially, the particle number of bright soliton can be used to control the generation of dark-bright solitons with varied ratios of solitons' widths. Based on the current experimental technologies, we propose an experimental scheme for observing these novel dark-bright solitons. The results suggest that abundant vector solitons with difference widths exist in multi-components coupled systems, and would inspire experiments to observe them in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

nlin.PS↗

arXiv2023

Controlling dark solitons on the healing length scale

While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.

cond-mat.quant-gas↗

arXiv2022

The optical rogue wave patterns in coupled defocusing systems

We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and defocusing cases. We establish the quantitative correspondence between modulation instability and rogue wave patterns, which develops the previously reported inequality relation into an equation correspondence. As an example, we demonstrate phase diagrams for rogue wave patterns in a two-component coupled system, based on the complete classification of their spatial-temporal structures. The phase diagrams enable us to predict various rogue wave patterns, such as the ones with a four-petaled structure in both components. These results are meaningful for controlling the rogue wave excitations in two orthogonal polarization optical fibers.

nlin.PS↗

arXiv2022

Phase Characters of Optical Dark Solitons with the Third-order Dispersion and Delayed Nonlinear Response

Dark soliton is usually seen as one of the simplest topological solitons, due to the phase jump across its density dip. We investigate the phase jump properties of dark solitons in a single mode optical fiber with the third-order dispersion and delayed nonlinear response, based on exact analytical solutions of Hirota equation. Our analysis indicates that a single-valley dark soliton (SVDS) can admit two distinct phase jumps at the same velocity, in sharp contrast to the dark soliton with only the second-order dispersion and self-phase modulation, which admits a one-to-one match between the velocity and phase jump. We further uncover the different topological vector potentials underlying the distinct phase jumps. The relations between phase jump and velocity of the SVDS can explain the generation of the previously reported double-valley dark soliton (DVDS). The detailed analysis on the two phase jumps characters of the DVDS with one identical velocity enables us to obtain U-shaped type or double-step type phase distribution. We further explore collision properties of the DVDSs by analyzing their topological phase, which can be considered as the generalization of topological phase (Phys. Rev. E 103, L040204). Strikingly, the inelastic collision can lead to the conversion between the two types of phase distributions for DVDS. The results reveal that inelastic or elastic collision can be judged by analyzing the magnetic monopole fields.

nlin.PS↗

arXiv2022

Non-degenerate Kuznetsov-Ma solitons of Manakov equations and their physical spectra

We study the dynamics of Kuznetsov-Ma solitons (KMS) in the framework of vector nonlinear Schr\"odinger (Manakov) equations. Exact multi-parameter family of solutions for such KMSs is derived. This family of solutions includes the known results as well as the previously unknown solutions in the form of the non-degenerate KMSs. We present the existence diagram of such KMSs that follows from the exact solutions. These non-degenerate KMSs are formed by nonlinear superposition of two fundamental KMSs that have the same propagation period but different eigenvalues. We present the amplitude profiles of new solutions, their exact physical spectra, their link to ordinary vector solitons and offer easy ways of their excitation using numerical simulations.

nlin.PS↗