arXiv subjects

Zhaoxin Liang

Publications and source records attributed to Zhaoxin Liang.

At least 19 recordsLinked to original sources

arXiv2026

Transdimensional quantum droplets in an optically trapped Bose mixture

We study quantum droplets in a symmetric two-component Bose mixture with interspecies $p$-wave interactions and a two-dimensional transverse optical lattice. The lattice drives a crossover from an anisotropic three-dimensional gas to weakly coupled one-dimensional tubes. We calculate the ground-state energy and quantum depletion at the Gaussian level and derive their limiting forms. At $y=g_{12}/g=-0.95$, where the bare mean field is repulsive and no free-space droplet exists, the calculated bulk equation of state supports a self-bound minimum across the crossover: a negative lattice contribution at order $n^{2}$ supplies the attraction in the three-dimensional regime, and attractive fluctuations do so in the quasi-one-dimensional regime, with the intermediate, transdimensional range described quantitatively by neither limit. The interspecies $p$-wave interaction modifies only the spin branch. In the parameter range studied, increasing its strength lowers the equilibrium density across the crossover, consistently with a weakening of the induced binding.

cond-mat.quant-gas↗

arXiv2026

Anisotropic dynamical reconstruction of quantum geometry in quenched Chern insulators

Under unitary dynamics, the Chern number of an evolving quantum state remains conserved even when a quench drives the Hamiltonian across a topological phase transition. In sharp contrast, we reveal an anisotropic dynamical reconstruction of the quantum metric. Following a sudden quench in a two-dimensional Chern insulator, the metric develops a principal frame in which one eigenvalue grows in time whereas the other remains nearly unchanged. At long times, the associated axes align with the energy-gradient direction and the tangent direction of the constant-energy contours of the post-quench Hamiltonian, respectively. This dynamically selected frame is distinct from that of the static post-quench ground-state metric. We identify momentum-dependent relative dynamical phases as its origin: they enhance the distinguishability of neighboring states separated along the energy-gradient direction, while states along an equal-energy contour remain nearly phase locked. Consequently, local and global metric observables acquire characteristic long-time signatures of the post-quench Hamiltonian. Our results establish a nonequilibrium mechanism by which coherent dynamics reorganizes quantum geometry, suggesting new possibilities for its dynamical control.

quant-ph↗

arXiv2026

Universal quantum corrections of two-body correlation in a weakly interspecies interacting binary Bose mixture

We investigate universal quantum corrections to two-body correlations in a zero-temperature binary Bose mixture using the Cornwall-Jackiw-Tomboulis two-particle-irreducible effective action formalism. In the weak interspecies-coupling regime, a saddle-point treatment based on Hubbard-Stratonovich transformations can be combined with a two-loop expansion and a gapless Hartree-Fock correction, thereby preserving the Goldstone theorem and reducing the coupled two-component problem to two analytically solvable single-component theories. Within this framework, we derive the ground-state energy density as a low-density expansion in the gas parameter, together with the quantum depletion and chemical potentials. The results exhibit a simple mapping to the single-component case: the universal quantum corrections of the mixture are obtained by evaluating the known single-component series at an effective scattering length $a_{\sigma\sigma}-a_{12}$ for each species, where $a_{\sigma\sigma}$ and $a_{12}$ are the intra- and interspecies $s$-wave scattering lengths. This reproduces Petrov's equation of state at one-loop order in the weak-coupling limit and yields beyond-Lee-Huang-Yang corrections at two-loop order. We also analyze the role of mass imbalance, which enters the energy density through the exact rescaling factor $(1+m_{1}/m_{2})/2$.

cond-mat.quant-gas↗

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

Nonreciprocity Induced Fractional Nonlinear Thouless Pumping

Recent interest has surged in eigenvalue's nonlinearity-based topological transport governed by the equation of auxiliary eigenvalues $H\Psi=\omega S(\omega)\Psi$ [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024); C. Bai and Z. Liang, 111, 042201 (2025); Phys. Rev. A 112, 052207 (2025)] rather than the conventional Schrodinger equation $H\Psi=E\Psi$ in conservative settings, yet non-Hermitian generalizations remain uncharted. In this work, we are motivated to investigate the nonlinear Thouless pumping in a non-Hermitian and nonlinear Rice-Mele model. In particular, we uncover how non-Hermiticity parameters can induce fractional topological phases--even in the presence of quantized topological invariants as predicted by conventional linear approaches. Crucially, these fractional phases are naturally explained within the framework of the equation of auxiliary eigenvalues, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and non-Hermiticity, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in the real world.

cond-mat.quant-gas↗

arXiv2025

Self-consistent effective field theory to nonuniversal Lee-Huang-Yang term in quantum droplets

Quantum droplets (QDs) in weakly interacting ultracold quantum gases are typically characterized by mean-field theories incorporating Lee-Huang-Yang (LHY) quantum fluctuations under simplified zero-range interaction assumptions. However, bridging these models to broader physical regimes like superfluid helium requires precise understanding of short-range interatomic interactions. Here, we investigate how finite-range interactions--next-order corrections to zero-range potentials--significantly alter QDs mechanics. Using a consistent effective theory, we derive an analytical equation of state (EOS) for three-dimensional bosonic mixtures under finite-range interactions at zero temperature. Leveraging the Hubbard-Stratonovich transformation, we demonstrate that interspecies attraction facilitates bosonic pairing across components characterized by the non-perturbative parameter of $\Delta$, leading to nonuniversal LHY terms that encode short-range interaction details while recovering previous universal QDs EOS in the zero-range limit. Extending superfluid hydrodynamic equations for two-component systems, we predict fractional frequency shifts in breathing modes induced by these nonuniversal terms. Experimental observation of these shifts would reveal critical insights into QDs dynamics and interatomic potential characteristics.

cond-mat.quant-gas↗

arXiv2025

Quench Dynamics and Stability of Dark Solitons in Exciton Polariton Condensates

Exciton polariton condensates (EPCs) have emerged as a paradigmatic platform for investigating nonequilibrium quantum many-body phenomena, particularly due to their intrinsic open-dissipative nature and strong nonlinear interactions governed by the interplay between stimulated scattering and reservoir-mediated damping. Recent advances in Feshbach resonance engineering now enable precise tuning of interaction strengths, opening new avenues to explore exotic nonlinear excitations in these driven-dissipative systems. In this work, we systematically investigate the quench dynamics and stability of dark solitons in repulsive one-dimensional EPCs under sudden parameter variations in both nonlinear interaction strength g and pump intensity P. Through a Hamiltonian variational approach that incorporates reservoir damping effects, we derive reduced equations of motion for soliton velocity evolution that exhibit remarkable qualitative agreement with direct numerical simulations of the underlying open-dissipative Gross Pitaevskii equation. Our results reveal three distinct dynamical regimes: (i) stable soliton propagation at intermediate pump powers, (ii) velocity-dependent soliton breakup above critical pumping thresholds, and (iii) parametric excitation of soliton trains under simultaneous interaction quenches. These findings establish a quantitative framework for understanding soliton dynamics in nonresonantly pumped EPCs, with implications for quantum fluid dynamics and nonequilibrium Bose Einstein condensates.

cond-mat.quant-gas↗

arXiv2025

Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems

Recent foundational studies have established the bulk-edge correspondence for nonlinear eigenvalue problems using auxiliary eigenvalues $\hat{H}\Psi=\omega S(\omega)\Psi$, spanning both linear [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024)] and nonlinear [Chenxi Bai and Zhaoxin Liang, Phys. Rev. A. 111, 042201 (2025)] Hamiltionians. This progress prompts a fundamental question: Can eigenvalue nonlinearity generate observable physical phenomena absent in conventional approaches ($\hat{H}\Psi=E\Psi$)? In this work, we address this question by demonstrating the first uniquely nonlinear manifestation of the bulk-edge correspondence: fractional Thouless pumping of solitons. Through systematic investigation of nonlinear Thouless pumping in an extended Rice-Mele model incorporating next-nearest-neighbor (NNN) couplings, we uncover that NNN interaction parameters can induce fractional topological phases|even in the presence of quantized topological invariants as predicted by conventional linear approaches. Crucially, these fractional phases are naturally explained within the auxiliary eigenvalue framework, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and NNN couplings, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in nonlinear regimes.

cond-mat.mes-hall↗

arXiv2025

Tuning spin-density separation via finite-range interactions: Dimensionality-driven signatures in dynamic structure factors

Spin-density (charge) separation, marked by distinct propagation velocities of spin and density excitations, epitomizes strong correlations, historically confined to one-dimensional (1D) systems. The recent experimental work of S. Dhar, B. Wang, M. Horvath, et al. Nature 642, 53 (2025), using a weakly interacting 3D Bose-Einstein condensate of $^{133}$Cs atoms confined in a 2D optical lattice to realize spin-density separation and demonstrate boson anyonization, motivates a deeper exploration into how dimensionality and interactions govern quantum correlations. In this work, we investigate this in two-component bosonic mixtures with finite-range interactions, probing 1D and 3D dynamics. Using path integral effective field theory within the one-loop approximation, we derive analytical expressions for zero-temperature ground-state energy and quantum depletion, seamlessly recovering contact interaction results in the contact limit. By crafting an effective action for decoupled density and spin modes, we compute dynamic structure factors (DSFs), revealing how finite-range interactions sculpt spin-density separation. A pivotal finding is the dimensionality-driven divergence in DSF peak dynamics: in 1D, peaks ascend to higher frequencies with increasing interaction strength, yielding sharp responses; in 3D, peaks descend to lower frequencies, with broader density wave profiles. These insights highlight dimensionality's critical role in collective excitations and provide a robust theoretical blueprint for probing interaction-driven quantum phenomena via Bragg spectroscopy, paving new pathways for exploring dimensionally tuned quantum correlations in ultracold quantum gases.

cond-mat.quant-gas↗

arXiv2025

Probing $p$-wave effects in spin-density separation of Bose mixtures with the dynamic structure factor

Quantum mixtures of Bose gases with tunable $s$- and $p$-wave interactions offer a versatile platform to explore strongly correlated phases and exotic phenomena. While repulsive interactions often drive phase separation, the interplay of $p$-wave interactions with spin-density decoupling remains underexplored. In this work, we employ the path integal field theory to investigate the role of $p$-wave interactions in three-dimensional two-component Bose gas. We derive the Lee-Huang-Yang corrections to the ground-state energy and quantum depletion, revealing how $p$-wave interactions modify equations of state of the model system. Furthermore, we demonstrate that $p$-wave interactions predominantly renormalize the spin-sector effective mass in the language of decoupling the density and spin-density degrees of freedom. This effect manifests in the dynamic structure factor, computed via hydrodynamic theory, where Bragg spectroscopy can detect a tunable splitting between spin and density modes. Our results bridge theoretical predictions with experimental observables, offering insights into anisotropic interaction effects in quantum gases and their implications for probing emergent phases.

cond-mat.quant-gas↗

arXiv2025

Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover

Equation of state (EOS) for a pure two-dimensional (2D) Bose gas exhibits a logarithmic dependence on the s-wave scattering length [L. Salasnich, Phys. Rev. Lett. 118, 130402 (2017)]. The pronounced disparity between the EOS of a 2D Bose gas and its 3D counterpart underscores the significance of exploring the dimensional crossover between these two distinct dimensions. In this work, we are motivated to deduce nonuniversal corrections to EOS for an optically trapped Bose gas along the dimensional crossover from 3D to 2D, incorporating the finite-range effects of the interatomic potential. Employing the framework of effective field theory, we derive the analytical expressions for both the ground state energy and quantum depletion. The introduction of the lattice induces a transition from a 3D to a quasi-2D regime. In particular, we systematically analyze the asymptotic behaviors of both the 2D and 3D aspects of the model system, with a specific focus on the nonuniversal effects on the EOS arising from finite-range interactions. The nonuniversal effects proposed in this study along the dimensional crossover represent a significant stride toward unraveling the intricate interplay between dimensionality and quantum fluctuations.

cond-mat.quant-gas↗

arXiv2025

Anomalous bulk-edge correspondence of nonlinear Rice-Mele model

Bulk-edge correspondence (BEC) constitutes a fundamental concept within the domain of topological physics, elucidating the profound interplay between the topological invariants that characterize the bulk states and the emergent edge states. A recent highlight along this research line consists of establishing BEC under the eigenvalue's nonlinearity in a linear Hamiltonian by introducing auxiliary eigenvalues [\href{https://doi.org/10.1103/PhysRevLett.132.126601}{ T. Isobe {\it et al.,} Phys. Rev. Lett. 132, 126601 (2024)}]. The purpose of this work aims to extend Isobe's analysis to uncover BEC of eigenvalue's nonlinearity in intrinsic nonlinear Hamiltonians. To achieve this, we numerically solve the nonlinear Rice-Mele (RM) model and identify two distinct types of nonlinear eigenvalues: the intrinsically nonlinear eigenvalues and the eigenvalue's nonlinearity introduced through the incorporation of auxiliary eigenvalues. Furthermore, we establish a novel form of BEC based on these auxiliary nonlinear eigenvalues, which we term the anomalous BEC of a nonlinear physical system. The concept of the anomalous BEC defined herein provides a novel perspective on the intricate interplay between topology and nonlinearity in the context of BEC.

cond-mat.quant-gas↗

arXiv2024

Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps

In nonlinear topological physics, Thouless pumping of nonlinear excitations is a central topic, often illustrated by scalar solitons. Vector solitons, with the additional spin degree of freedom, exhibit phenomena absent in scalar solitons due to enriched interplay between nonlinearity and topology. Here, we theoretically investigate Thouless pumping of vector solitons in a two-component Bose-Einstein condensate confined in spin-dependent optical superlattices, using both numerical solutions of the Gross-Pitaevskii equation and the Lagrangian variational approach. The spin-up and spin-down components experience superlattice potentials that are displaced by a tunable distance $d_r$, leading to a vector soliton state with a relative shift between its components. We demonstrate that $d_r$, as an independent degree of freedom, offers a novel control parameter for manipulating the nonlinear topological phase transition of vector solitons. Specifically, when $d_r=0$, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying $d_r$, remarkably, we find that an arrested vector soliton can re-enter the pumped regime and exhibits a quantized shift. As $d_r$ continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in $d_r$, the quantized shift revives. Our work paves new routes for engineering nonlinear topological pumping of solitons in spinor systems by utilizing the relative motion degrees of freedom between different spin components.

cond-mat.quant-gas↗

arXiv2024

Dissipative Nonlinear Thouless Pumping of Temporal Solitons

The interplay between topology and soliton is a central topic in nonlinear topological physics. So far, most studies have been confined to conservative settings. Here, we explore Thouless pumping of dissipative temporal solitons in a nonconservative one-dimensional optical system with gain and spectral filtering, described by the paradigmatic complex Ginzburg-Landau equation. Two dissipatively induced nonlinear topological phase transitions are identified. First, when varying dissipative parameters across a threshold, the soliton transitions from being trapped in time to quantized drifting. This quantized temporal drift remains robust, even as the system evolves from a single-soliton state into multi-soliton state. Second, a dynamically emergent phase transition is found: the soliton is arrested until a critical point of its evolution, where a transition to topological drift occurs. Both phenomena uniquely arise from the dynamical interplay of dissipation, nonlinearity and topology.

cond-mat.quant-gas↗

arXiv2024

Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas

The equation of state (EOS) serves as a cornerstone in elucidating the properties of quantum many-body systems. A recent highlight along this research line consists of the derivation of the nonuniversal Lee-Huang-Yang (LHY) EOS for an ultracold quantum bosonic gas with finite-range interatomic interactions using one-loop effective path-integral field theory. The purpose of this work is to extend Salasnich's pioneering work to uncover beyond-LHY corrections to the EOS by employing the Cornwall-Jackiw-Tomboulis (CJT) effective field theory, leveraging its two-loop approximation. In this end, we expand Salasnich's remarkable findings of EOS to the next leading order characterized by $\left(\rho a_{\text{s}}^{3}\right)^{2}$, with $\rho$ and $a_{\text{s}}$ being the density and the $s$-wave scattering length. Notably, we derive analytical expressions for quantum depletion and chemical potential, representing the next-to-LHY corrections to nonuniversal EOS induced by finite-range effects. Moreover, we propose an experimental protocol of observing the nonuniversal next-to-LHY corrections to the EOS by calculating fractional frequency shifts in the breathing modes. The nonuniversal beyond-LHY EOS in this work paves the way of using LHY effects in quantum simulation experiments and for investigations beyond the LHY regime.

cond-mat.quant-gas↗

arXiv2024

Nonlinear Thouless Pumping of Solitons Across an Impurity

The nonlinear Thouless pumping is an exciting frontier of topological physics. While recent works have revealed the quantized motion of solitons in Thouless pumps, the interplay between the topology, nonlinearity and disorder remains largely unexplored. Here, we investigate the nonlinear Thouless pumping of solitons in the presence of an impurity in the context of a Bose-Einstein condensate. Using both the Gross-Pitaevskii equation and Lagrangian variational approach, we analyze the interaction between a moving soliton and an impurity. Without the pump, the soliton can pass through a light impurity, but gets trapped by the impurity with large mass. In marked contrast, we find the soliton in Thouless pumps can always transit through the impurity, and its motion is topologically quantized. Our result explicitly showcases the robustness of topological soliton pumping against microscopic imperfections, and opens a new perspective in the information processing with solitons.

cond-mat.quant-gas↗

arXiv2024

Interaction-Induced Dimensional Crossover through Full 3D to 1D

The exploration of dimensional crossover carries profound fundamental significance, serving as a crucial bridge in comprehending the remarkable disparities observed in transitional phenomena across the two distinct dimensions of a physical system. The prevalent strategy for manipulating the dimensionality involves meticulously controlling the external trapping geometry, thereby restricting the degrees of freedom of the kinetic energy from three-dimensional (3D) to lower-dimensional spaces, while maintaining the 3D nature of the interaction energy degrees of freedom. The aim of this work is to introduce an innovative scenario to achieve dimensional crossover, characterized by lower-D nature of both the kinetic and the interaction energy degrees of freedom. To accomplish this objective, we delve deeply into the realm of a 2D optically trapped Bose gas, focusing specifically on its finite-range interaction. Our emphasis lies in exploring the lattice-induced dimensional crossover from full 3D to 1D in both kinetic and interaction terms. Utilizing the functional path integral method, we derive the equation of states of the model system, encompassing crucial quantities such as the ground state energy and quantum depletion. These equations enable us to analyze the combined effects of finite range interaction and an optical lattice on quantum fluctuations of the BEC system. Notably, our analytical findings reconcile the Lee-Huang-Yang (LHY) correction to the ground state energy in 3D and Lieb-Liniger (LL) ones in 1D limit, thereby providing fresh insights into the intriguing disparities between LHY and LL corrections.

cond-mat.quant-gas↗

arXiv2024

Noisy Demkov-Kunike model

The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J~\text{sech}(t/T)$ and on-site detuning $Δ_0+Δ_1\tanh(t/T)$, has one of the most general forms of an exactly solvable two-state quantum system, and, therefore, it provides a paradigm for coherent manipulations of a qubit's quantum state. Despite its extensive applications in the noise-free cases, the exploration of the noisy DK model remains limited. Here, we extend the coherent DK model to take into account of a noisy coupling term $J\rightarrow J_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by the telegraph noise and Gaussian noise. We present exact solutions for the survival probability $Q^{\text{noisy}}_{\text{DK}}$ of the noisy DK model, namely the probability of the system to remain in its initial state. For the slow telegraph noise, we identify parameter regimes where the survival probability $Q^{\text{noisy}}_{\text{DK}}$ is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability $Q^{\text{noisy}}_{\text{DK}}$, due to the absorption of noise quanta across the energy gap. This study not only complements the existing research on the noisy Landau-Zener model, but also provides valuable insights for the control of two-level quantum systems.

quant-ph↗