arXiv subjects

Liang-Liang Wan

Publications and source records attributed to Liang-Liang Wan.

9 recordsLinked to original sources

arXiv2025

Universal Manipulation of Quantum Synchronization in Spin Oscillator Networks

Quantum synchronization (QS) in open many-body systems offers a promising route for controlling collective quantum dynamics, yet existing manipulation schemes often rely on dissipation engineering, which distorts limit cycles, lacks scalability, and is strongly system-dependent. Here, we propose a universal and scalable method for continuously tuning QS from maximal synchronization under isotropic interactions to complete synchronization blockade (QSB) under fully anisotropic coupling in spin oscillator networks. Our approach preserves intrinsic limit cycles and applies to both few-body and macroscopic systems. We analytically show that QS arises solely from spin flip-flop processes and their higher-order correlations, while anisotropic interactions induce non-synchronizing coherence. A geometric QS measure reveals a macroscopic QSB effect in the thermodynamic limit. The proposed mechanism is experimentally feasible using XYZ interactions and optical pumping, and provides a general framework for programmable synchronization control in complex quantum networks and dynamical phases of matter.

quant-ph↗

arXiv2024

Proof of bulk-edge correspondence for band topology by Toeplitz algebra

We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index. Specifically, an essential formula is discovered that links the quantity expressed by Toeplitz algebra, i.e., hopping terms on the lattice with an edge, to the Fourier series on the bulk Brillouin zone. We then apply it to chiral models and utilize exterior differential calculations, instead of the sophisticated \emph{K}-theory, to show that the winding number of bulk system equals to the Fredholm index of 1D edge Hamiltonian, or to the sum of edge winding numbers for higher odd dimensions. Moreover, this result is inherited to the even-dimensional Chern insulators as each of them can be mapped to an odd-dimensional chiral model. It is revealed that the Chern number of bulk system is identical to the spectral flow of 2D edge Hamiltonian, or to the negative sum of edge Chern numbers for higher even dimensions. Our methods and conclusions are friendly to physicists and could be easily extended to other physical scenarios.

cond-mat.mes-hall↗

arXiv2024

Topological bosonic Bogoliubov excitations with sublattice symmetry

Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with non-vanishing particle-number-nonconserving terms. Specifically, we show that such systems well described by the bosonic Bogoliubov-de Gennes Hamiltonian can be in general reduced to particle-number-conserving (single-particle) ones. Building upon this observation, the sublattice symmetry is uncovered with respect to an excitation energy, which is usually hidden in the bosonic Bogoliubov-de Gennes Hamiltonian. Thus, we obtain an additional topological class, i.e., class AIII, which enriches the framework for the topological threefold way of free-boson systems. Moreover, a construction is proposed to show a category of systems respecting such a symmetry. For illustration, we resort to a one-dimensional (1D) prototypical model to demonstrate the topological excitation characterized by a winding number or symplectic polarization. By introducing the correlation function, we present an approach to measure the topological invariant. In addition, the edge excitation together with its robustness to symmetry-preserving disorders is also discussed.

quant-ph↗

arXiv2023

Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect

We theoretically predict the squeezing-induced point-gap topology together with a {\it symmetry-protected $\mathbb{Z}_2$ skin effect} in a one-dimensional (1D) quadratic-bosonic system (QBS). Protected by a time-reversal symmetry, such a topology is associated with a novel $\mathbb{Z}_2$ invariant (similar to quantum spin-Hall insulators), which is fully capable of characterizing the occurrence of $\mathbb{Z}_2$ skin effect. Focusing on zero energy, the parameter regime of this skin effect in the phase diagram just corresponds to a {\it real-gap and point-gap coexisted topological phase}. Moreover, this phase associated with the {\it symmetry-protected $\mathbb{Z}_2$ skin effect} is experimentally observable by detecting the steady-state power spectral density. Our work is of fundamental interest in enriching non-Bloch topological physics by introducing quantum squeezing, and has potential applications for the engineering of symmetry-protected sensors based on the $\mathbb{Z}_2$ skin effect.

cond-mat.mes-hall↗

arXiv2023

Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an experimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and non-trivial phases due to the topological locality. In the long-time limit, the OTOC undergoes a {\it zero-to-finite-value transition} at the critical point of the TPTs. This transition is robust to the choices of the initial state of the system and the used operators in OTOC. The proposed OTOC witness can be applied into the systems with and without chiral symmetry, e.g., the lattices described by the SSH model, Creutz model, and Haldane model. Moreover, our proposal, as a physical witness in real space, is still valid even in the presence of disorder. Our work fundamentally offers a new prospect of exploring topological physics with quantum correlations.

quant-ph↗

arXiv2020

Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations

We investigate the role of squeezing interaction in inducing topological Bogoliubov excitations of a bosonic system. We introduce a squeezing transformation which is capable of reducing the corresponding Bogoliubov-de Gennes Hamiltonian to an effective non-interacting one with the spectra and topology unchanged. In the weak interaction limit, we apply the perturbation theory to investigate the squeezing-induced topological gap opening on bosonic Bogoliubov excitations and find that the squeezing interaction plays an equivalent role as a spin-orbit or Zeeman-like coupling in the effective Hamiltonian. We thus apply this formalism to two existed models for providing deeper understandings of their topological structures. We also construct minimal models based on the elegant Clifford algebra for realizing bosonic topological Bogoliubov excitations. Our construction is potentially applicable for experiments in bosonic systems.

cond-mat.quant-gas↗

arXiv2020

Topological Classification of Excitations in Quadratic Bosonic Systems

We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry classification. We find a specific decomposition of the quadratic bosonic Hamiltonian and use it to prove that each quadratic bosonic system is homotopic to a direct sum of two single-particle subsystems. The topological classification table is thus derived via inheriting from that of Atland-Zirnbauer classes and unique topological phases of bosons are predicted. Finally, concrete topological models are proposed to demonstrate the peculiarity of bosonic excitations.

cond-mat.quant-gas↗

arXiv2018

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Herewe investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

quant-ph↗

arXiv2018

Hybrid Interference Induced Flat Band Localization in Bipartite Optomechanical Lattices

The flat band localization, as an important phenomenon in solid state physics, is fundamentally interesting in the exploration of exotic ground property of many-body system. Here we demonstrate the appearance of a flat band in a general bipartite optomechanical lattice, which could have one or two dimensional framework. Physically, it is induced by the hybrid interference between the photon and phonon modes in optomechanical lattice, which is quite different from the destructive interference resulted from the special geometry structure in the normal lattice (e.g., Lieb lattice). Moreover, this novel flat band is controllable and features a special local density of states (LDOS) pattern, which makes it is detectable in experiments. This work offers an alternative approach to control the flat band localization with optomechanical interaction, which may substantially advance the fields of cavity optomechanics and solid state physics.

cond-mat.mes-hall↗