Generalized Kibble-Zurek mechanism for defects formation in trapped ions

The Kibble-Zurek(KZ)mechanism has played a fundamental role in defect formation with universal scaling laws in nonequilibrium phase transitions.However,this theory may not accurately predict the scaling laws in inhomogeneous systems and slow quenching processes.Here,we present a generalized KZ mechanism for the defect formation in trapped ions with the freeze-out condition gt=b0τ(t),where g is a universal quenching velocity function and b0 is a constant.We derived a differential equationφ(x,t)to account for the frozen correlation length of a kink in an inhomogeneous system and demonstrated a smooth crossover from a fast quenching process to a slow quenching process,which agrees well with the experiments performed by Ulm et al.[Nat.Commun.4,2290(2013)]and Pyka et al.[Nat.Commun.4,2291(2013)].Furthermore,we confirmed our theoretical model using molecular dynamics simulation by solving the stochastic differential equation,showing excellent agreement with the results from the differential equation.Our theory provides a general theoretical framework for studying KZ physics in inhomogeneous systems,which has applications in other nonequilibrium platforms studied experimentally.

Quench dynamics in 1D model with 3rd-nearest-neighbor hoppings

The non-equilibrium dynamics of a one-dimensional(1 D)topological system with 3 rd-nearest-neighbor hopping has been investigated by analytical and numerical methods.An analytical form of topological defect density under the periodic boundary conditions(PBC)is obtained by using the Landau-Zener formula(LZF),which is consistent with the scaling of defect production provided by the Kibble-Zurek mechanism(KZM).Under the open boundary conditions(OBC),quench dynamics becomes more complicated due to edge states.The behaviors of the system quenching across different phases show that defect production no longer satisfies the KZM paradigm since complicated couplings exist under OBC.Some new dynamical features are revealed.

Learning topological defects formation with neural networks in a quantum phase transition

Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body systems.While they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural networks.To address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising model.Specifically,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength.The excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink numbers.Moreover,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the kinks.Finally,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

玻色凝聚原子气体跨越自发对称性破缺的普适非平衡动力学研究进展

自发对称性破缺是自然界中普遍存在的物理现象,从宇宙星系的形成到超流涡旋的产生,它广泛存在于宇宙学、凝聚态物理以及原子分子光物理等各个领域之中.自发对称性破缺过程中的普适临界动力学可用KibbleZurek机制描述,该机制描述了体系非绝热激发和淬火速率之间的普适标度关系.研究普适临界动力学既可以加深人们对早期宇宙中复杂结构形成和演化的理解,又可以帮助人们找出更快的绝热路径,缩短量子态制备和量子调控的时间.超冷原子体系具有洁净的环境、较长的相干时间以及高度可控等优点,是研究普适临界动力学的理想平台之一.本文从自发对称性破缺相变出发,介绍了玻色凝聚原子气体跨越自发对称性破缺的两类普适非平衡动力学:(1)由无能隙Higgs模诱导的普适非平衡动力学;(2)由软化声子模诱导的普适非平衡动力学.

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems.We study the topological and dynamical properties of the quasiperiodic SuSchrier-Heeger model with long-range hoppings.It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with nonzero winding numbers ω=1,2,and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length.We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths.The critical exponents extracted from the dynamical behavior agree with the Kibble-Zurek mechanic prediction for the path with W=0.90.In particular,the dynamical exponent of the path crossing the multicritical point is numerical obtained as 1/6~0.167,which agrees with the unconventional finding in the previously studied XY spin model.Besides,we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.