arXiv subjects

Enhong Cheng

Publications and source records attributed to Enhong Cheng.

6 recordsLinked to original sources

arXiv2026

Fate of moir\'e flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional $\mathcal{PT}$-symmetric bichromatic optical lattices

One-dimensional (1D) superlattices provide one simplified platform for exploring moir\'e physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here, we propose a 1D $\mathcal{PT}$-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moir\'e flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the $\mathcal{PT}$-symmetric imaginary potential due to the distinct $\mathcal{PT}$ pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the $\mathcal{PT}$-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the $\mathcal{PT}$-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moir\'e bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moir\'e systems.

cond-mat.quant-gas↗

arXiv2025

Electric circuit analog of Landau-Zener tunneling using time-varying elements

Landau-Zener tunneling (LZT) is a fundamental dynamical phenomenon, ubiquitous in various quantum systems. Here, we propose a time-varying electric circuit to address the question of whether the quantum LZT can occur in classical systems. Although the underlying differential equation of motion is quite different from the Schr\"odinger equation and the instantaneous frequency spectrum of the proposed circuit is not linear, the probability of the LZT in circuits (circuit LZT for short), based on our generalized definition for norm-unconserved systems, still follows the laws of the LZT in quantum systems, codetermined by the linear sweeping rate $\alpha'$ and the frequency gap $\Delta$, i.e., approaching the analytical value $\exp(-\pi\Delta^2/2\alpha')$, regardless of whether the coupling is reciprocal or nonreciprocal. The deep relationship between the circuit LZT and its quantum counterpart can be established through a linearization and block-diagonalization process. Our proposal provides a general method for simulating time-dependent quantum models using time-varying electric circuits, which has been lacking in previous studies, and paves the way for studying more complicated LZT and other dynamical phenomena in circuits and other classical systems.

cond-mat.mes-hall↗

arXiv2024

Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals

The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal hopping can lead to the manifestation of two distinct Lyapunov exponents on opposite sides of the localization center. Building on this observation, we here introduce a comprehensive approach for examining the localization characteristics and mobility edges of non-reciprocal quasicrystals, referred to as asymmetric transfer matrix analysis. We demonstrate the application of this method to three specific scenarios: the non-reciprocal Aubry-Andr\'e model, the non-reciprocal off-diagonal Aubry-Andr\'e model, and the non-reciprocal mosaic quasicrystals. This work may contribute valuable insights to the investigation of non-Hermitian quasicrystal and disordered systems.

cond-mat.dis-nn↗

arXiv2022

Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity. Notably, We find a class of discrete breathers that aggregate to one boundary, here named as skin discrete breathers (SDBs). The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP. Specifically, the response of nonlinear energy to the perturbation is given by $E_m\propto \varGamma^{\alpha_{m}}$, where $\alpha_m=3^{m-1}$ is the power with $m=1,\cdots,L$ labeling the nonlinear energy bands. This is in sharp contrast to the $L$-th root of a linear perturbation in general. These SDBs decay in a double-exponential manner, unlike the edge states or skin modes in linear systems, which decay exponentially. Furthermore, these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity. They are also stable, as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis. As nonreciprocal nonlinear models may be experimentally realized in various platforms, such as the classical platform of optical waveguides, where Kerr nonlinearity is naturally present, and the quantum platform of optical lattices with Bose-Einstein condensates, our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity, particularly on high-order EPs, and benchmark the relevant simulations.

quant-ph↗

arXiv2022

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.

cond-mat.quant-gas↗

arXiv2020

Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions

For non-Hermitian quantum models, the dynamics is apparently not reflected by the static properties, e.g., the complex energy spectrum, because of the nonorthogonality of the right eigenvectors, the nonunitarity of the time evolution, the breakdown of the adiabatic theory, etc., but in experiments the time evolution of an initial state is commonly used. Here, we pay attention to the dynamics of an initial end state in nonreciprocal Su-Schrieffer-Heeger models under open boundary conditions, and we find that it is dynamically more robust than its Hermitian counterpart, because the non-Hermitian skin effect can suppress the part leaking to the bulk sites. To observe this, we propose a classical electric circuit with only a few passive inductors and capacitors, the mapping of which to the quantum model is established. This work explains how the non-Hermitian skin effect enhances the robustness of the topological end state, and it offers an easy way, via the classical electric circuit, of studying the nonreciprocal quantum dynamics, which may stimulate more dynamical studies of non-Hermitian models in other platforms.

quant-ph↗