arXiv subjects

Gao Xianlong

Publications and source records attributed to Gao Xianlong.

At least 55 records · Page 3Linked to original sources

arXiv2024

Linear-scale simulations of quench dynamics

The accurate description and robust computational modeling of the nonequilibrium properties of quantum systems remain a challenge in condensed matter physics. In this work, we develop a linear-scale computational simulation technique for the non-equilibrium dynamics of quantum quench systems. In particular, we report a polynomial-expansion of the Loschmidt echo to describe the dynamical quantum phase transitions of noninteracting quantum quench systems. An expansion-based method allows us to efficiently compute the Loschmidt echo for infinitely large systems without diagonalizing the system Hamiltonian. To demonstrate its utility, we highlight quantum quenching dynamics under tight-binding quasicrystals and disordered lattices in one spatial dimension. In addition, the role of the wave vector on the quench dynamics under lattice models is addressed. We observe wave vector-independent dynamical phase transitions in self-dual localization models.

cond-mat.dis-nn↗

arXiv2024

Effects of reservoir squeezing on the amplification of quantum correlation

The dynamics of quantum discord is studied in a system of two identical noninteracting qubits coupled to a common squeezed vacuum bath through non-demolition interactions. We concern on how reservoir squeezing influences the dynamical behaviors of quantum discord when both qubits are initially prepared in $X$-type states. We find that the critical time exhibits the sudden change of quantum discord, which is of great significance for the quantum discord amplification. Furthermore, depending on the initial parameters of the system, we numerically calculate the interval when the critical time is finite or infinite. For the finite critical time, we show that the squeezing phase of the bath can prolong the critical time while the squeezing strength exhibits the opposite effect. For infinite critical time, even if there is no sudden transition point, reservoir squeezing still has an effect on the amplification of quantum discord, and the time to reach steady-state quantum discord can be changed by adjusting the squeezing parameters. Fianlly, we investigate the quantum speed limit time for a two-qubit system under squeezed reservoir, and find that the quantum speed limit time can be reduced via the adjustment of the squeezing parameters and the initial parameters. Remarkably, in the short time limit, reservoir squeezing has an obvious influence on the degree of amplification of quantum discord. Our study presents a promising approach to controlling the amplification of quantum correlation.

quant-ph↗

arXiv2023

Bulk-edge correspondence for the nonlinear eigenvalues problem of the Haldane model

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalues problems in a two-dimensional topological system with spin-orbit coupling. By introducing auxiliary eigenvalues, the nonlinear bulk-edge correspondence was established. In this paper, taking the Haldane model as an example, we address that such a correspondence will appear in two dimensional topological system without spin-orbit coupling. The resulting edge states are characterized by the Chern number of the auxiliary energy band. A full phase diagram containing topological nontrivial phase, topological trivial phase, and metallic phase is obtained. Our work generalizes the study of the bulk-edge correspondence for nonlinear eigenvalue problems in two-dimensional system.

cond-mat.dis-nn↗

arXiv2023

Persisting quantum effects in the anisotropic Rabi model at thermal equilibrium

Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this work, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling.

quant-ph↗

arXiv2023

Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states

The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work, we introduce compass-like states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that, when a significant quantity of photons is added (or subtracted), the Wigner function of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.

quant-ph↗

arXiv2023

The failure of semiclassical approach in the dissipative fully-connected Ising model

We solve the fully-connected Ising model in the presence of dissipation and time-periodic field, with the corresponding Lindblad equation having a time-periodic Liouvillian. The dynamics of the magnetizations is studied by using both the semiclassical approach and the numerical simulation with the help of permutation symmetry. The semiclassical approach shows a transition from the periodic response for small field amplitude to the chaotic dynamics for large amplitude. The trajectory of the magnetizations and the Lyapunov exponents are calculated, which support the existence of a chaotic phase. But in the exact numerical simulation, the response is periodic for both small and large amplitude. The scaling analysis of Floquet Liouvillian spectrum confirms the periodic response in the thermodynamic limit. The semiclassical approximation is found to fail as the field amplitude is large.

nlin.CD↗

arXiv2023

Multi-Stability in Cavity QED with Spin-Orbit Coupled Bose-Einstein Condensate

We investigate the occurrence of steady-state multi-stability in a cavity system containing spin-orbit coupled Bose-Einstein condensate and driven by a strong pump laser. The applied magnetic field splits the Bose-Einstein condensate into pseudo-spin states, which then became momentum sensitive with two counter propagating Raman lasers directly interacting with ultra-cold atoms. After governing the steady-state dynamics for all associated subsystems, we show the emergence of multi-stable behavior of cavity photon number, which is unlike with previous investigation on cavity-atom systems. However, this multi-stability can be tuned with associated system parameters. Further, we illustrate the occurrence of mixed-stability behavior for atomic population of the pseudo spin-$\uparrow$ amd spin-$\downarrow$ states, which are appearing in so-called bi-unstable form. The collective behavior of these atomic number states interestingly possesses a transitional interface among the population of both spin states, which can be enhance and controlled by spin-orbit coupling and Zeeman field effects. Furthermore, we illustrate the emergence of secondary interface mediated by increasing the mechanical dissipation rate of the pseudo-spin states. These interfaces could be cause by the non-trivial behavior of synthetic spin state mediated by cavity. Our findings are not only crucial for the subject of optical switching, but also could provide foundation for future studies on mechanical aspect of synthetic atomic states with cavity quantum electrodynamics.

cond-mat.quant-gas↗

arXiv2023

Engineering chaos in a four-mirror cavity-optomechanics with mechanical drives

We study occurrence of chaos in a four-mirror optomechanical cavity with mechanical drives externally interacting with two transversely located moving-end mirrors of the cavity. The strong cavity mode, driven by the pump laser, excites mechanical oscillations in both moving-end mirrors with its radiation pressure. These radiation-pressure-induced mechanical effects then lead to the indirect coupling between two transverse mirrors, where intra-cavity field mimics as a spring between two mechanical objects. By computing Poincaré surface of sections for both mirrors over a wide interval of initial conditions, we illustrate the transition from stable to mixed -- containing stable islands and chaotic seas -- Poincaré surface of sections with external mechanical drives. To further explore the occurrence of chaos with mechanical drives, we measure the spatio-temporal responses of moving-end mirrors initially located in mixed Poincaré sections. We find that both of the mirrors follow chaotic temporal evolution with external mechanical drives, even in the absence of any one of the mechanical drives. To quantitatively measure the occurrence of chaos, we computed the possible Lyapunov exponents and collective Kolmogorov-Sinai Entropy of the system. We find that the largest Lyapunov exponent, and corresponding Kolmogorov-Sinai Entropy, not only gains positive values with increase in external drives but also crucially depends on the initial conditions chosen from the Poincaré surface of sections. Furthermore, we show the enhancement in chaotic dynamics of mirrors in the presence of mechanical damping rates associated with the oscillatory motion of the mirrors.

quant-ph↗

arXiv2023

Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals

In this paper, a non-Hermitian Aubry-André-Harper model with power-law hoppings ($1/s^{a}$) and quasiperiodic parameter $β$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $β$ is a member of the metallic mean family. We find that under the weak non-Hermitian effect, there preserves $P_{\ell=1,2,3,4}$ regimes where the fraction of ergodic eigenstates is $β$-dependent as $β^{\ell}$L ($L$ is the system size) similar to those in the Hermitian case. However, $P_{\ell}$ regimes are ruined by the strong non-Hermitian effect. Moreover, by analyzing the fractal dimension, we find that there are two types of edges aroused by the power-law index $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal edge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge for the short-range hopping case ($a>1$). Meanwhile, the existence of these two types of edges is found to be robust against the non-Hermitian effect. By employing the Simon-Spence theory, we analyzed the absence of the localized states for $a<1$. For the short-range hopping case, with the Avila's global theory and the Sarnak method, we consider a specific example with $a=2$ to reveal the presence of the intermediate phase and to analytically locate the intermediate regime and the ergodic-to-multifractal edge, which are self-consistent with the numerically results.

cond-mat.dis-nn↗

arXiv2023

A rotational-cavity optomechanical system with two revolving cavity mirrors: optical response and fast-slow light mechanism

We investigate the optical behavior of a single Laguerre-Gaussian cavity optomechanical system consisting of two mechanically rotating mirrors. We explore the effects of various physical parameters on the double optomechanically induced transparency (OMIT) of the system and provide a detailed explanation of the underlying physical mechanism. We show that the momentum is not the cause of the current double-OMIT phenomena; rather, it results from the orbital angular momentum between the optical field and the rotating mirrors. Additionally, the double-OMIT is simply produced using a single Laguerre-Gaussian cavity optomechanical system rather than by integrating many subsystems or adding the atomic medium as in earlier studies. We also investigate the impact of fast and slow light in this system. Finally, we show that the switching between ultrafast and ultraslow light can be realized by adjusting the angular momentum, which is a new source of regulating fast-slow light.

quant-ph↗

arXiv2022

From topological phase to Anderson localization in a two-dimensional quasiperiodic system

In this paper, the influence of the quasidisorder on a two-dimensional system is studied. We find that there exists a topological phase transition accompanied by a transverse Anderson localization. The topological properties are characterized by the band gap, the edge-state spectra, the transport conductance, and the Chern number. The localization transition is clearly demonstrated by the investigations of the partial inverse participation ratio, the average of level spacing ratio, and the fraction dimension. The results reveal the topological nature of the bulk delocalized states. Our work facilitates the understanding on the relationship between the topology and the Anderson localization in two-dimensional disordered systems.

cond-mat.dis-nn↗

arXiv2022

Topological Floquet-bands in a circularly shaken dice lattice

The hoppings of non-interacting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasi-energy bands in the quasi-energy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasi-energy band shows that when the hopping strengths of the nearest-neighboring hoppings are isotropic, the system persists in the topologically non-trivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighboring hopping strengths, a topological phase transition occurs, making Chern number change from $C=2$ to $C=1$. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the non-trivially topological characteristics of optical dice lattices by applying the periodic shaking, and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.

cond-mat.quant-gas↗

arXiv2022

Quantum criticality driven by the cavity coupling in Rabi-dimer model

The superradiant phase transition (SPT) controlled by the interacting strength between the two-level atom and the photons has been a hot topic in the Rabi model and the Rabi-dimer model. The latter describes two Rabi cavities coupled with an inter-cavity hopping parameter. Moreover, the SPT in the Rabi-dimer model is found to be the same universal class that in the Rabi model by investigating the correlation-length critical exponent. In this paper, we are concerned about whether the inter-cavity hopping parameter between two Rabi cavities (i.e., the Rabi-dimer model) will induce the SPT and to which the universal class of the phase transition belongs. We analytically derive the phase boundary of the SPT and investigate the ground-state properties of the system. We uncover that the inter-cavity induced SPT can be apparently understood from the ground-state energy and the ground-state photon population, as well as the ground-state expectation value of the squared anti-symmetric mode. From the scaling analysis of the fidelity susceptibility, we numerically verify that the SPT driven by the cavity coupling belongs to the same universal class as the one driven by the atom-cavity interaction. Our work enriches the studies on the SPT and its critical behaviors in the Rabi-dimer model.

quant-ph↗

arXiv2022

Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals

The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the PT-symmetry.

cond-mat.dis-nn↗

arXiv2022

Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model

We investigate the transition from PT-symmetry to PT-symmetry breaking and vice versa in the non-Hermitian Landau-Zener (LZ) models. The energy is generally complex, so the relaxation rate of the system is set by the absolute value of the gap. To illustrate the dynamics of phase transitions, the relative population is introduced to calculate the defect density in nonequilibrium phase transitions instead of the excitations in the Hermitian systems. The result shows that the adiabatic-impulse (AI) approximation, which is the key concept of the Kibble-Zurek (KZ) mechanism in the Hermitian systems, can be generalized to the PT-symmetric non-Hermitian LZ models to study the dynamics in the vicinity of a critical point. Therefore, the KZ mechanism in the simplest non-Hermitian two-level models is presented. Finally, an exact solution to the non-Hermitian LZ-like problem is also shown.

quant-ph↗

arXiv2022

Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states

We investigate the sub-Planck-scale structures associated with the SU(1,1) group by establishing that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Our discussion involves SU(1,1) versions of Wigner functions, and the quantum-interference effect is easily visualized through plots of these Wigner functions. Specifically, the superpositions of four Perelomov SU(1,1) coherent states (compass state) yield nearly isotropic sub-Planck structures in phase space scaling as $\frac1{k}$ compared with $\frac1{\sqrt{k}}$ scaling for individual SU(1,1) coherent states and anisotropic quadratically improved scaling for superpositions of two SU(1,1) coherent states (cat state). We show that displacement sensitivity exhibits the same quadratic improvement to scaling.

quant-ph↗

arXiv2022

Territories of Parrondo's paradox and its relation with entanglement in quantum walks

Parrondo's paradox is a well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones. In this paper, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of different periods for distinct choices of the relative phase. Furthermore, we investigate the regimes of the relative phase of the initial state of coins where Parrondo games exist. Moreover, we also analyze the relationships between Parrondo's game and quantum entanglement and show regimes where the Parrondo sequence may generate a maximal entangler state in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.

quant-ph↗

arXiv2021

Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice

We aim to study a one-dimensional $p$-wave superconductor with quasiperiodic on-site potentials. A modified real-space-Pfaffian method is applied to calculate the topological invariants. We confirm that the Majorana zero mode is protected by the nontrivial topology the topological phase transition is accompanied by the energy gap closing and reopening. In addition, we numerically find that there are mobility edges which originate from the competition between the extended $p$-wave pairing and the localized quasi-disorder. We qualitatively analyze the influence of superconducting pairing parameters and on-site potential strength on the mobility edge. In general, our work enriches the research on the $p$-wave superconducting models with quasiperiodic potentials.

cond-mat.dis-nn↗