On periodically kicked quantum systems

The time evolution of a multi-dimensional system which is kicked periodically with a potential is obtained. The most interesting aspects of the investigation are (i) if the operator corresponding to the potential has invariant subspaces (a characteristic property of multi-dimensional systems), the states belonging to these subspace in its evolution are confined to these invariant subspaces respectively and there cannot be any mixing of states between these subspaces. Further, (ii) it leads to the existence of quasi-stationary states (determined again by the potential) which evolves independent of other similar quasi-stationary states. The method followed in the paper is the direct integration of the Schrödinger equation and then to construct the wave function from the initial wave function.     

Spectral properties of a periodically kicked quantum Hamiltonian

We study the spectral properties of the Floquet operator for the periodically kicked HamiltonianH(t) =H ₀+ ₊ ^– (t–nT),H ₀ being self-adjoint and pure point. We show that the Floquet operator is pure point for almost every , if is cyclic forH ₀ and has absolutely convergent expansion in the basis of eigenstates ofH ₀. When this last condition is not satisfied, the Floquet operator can have a continuous spectrum, as we show by an example.     

Floquet bands and photon-induced topological edge states of graphene nanoribbons

Floquet theorem is widely used in the light-driven systems. But many 2 D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work,we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies(including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.     

Classical and quantum dynamics of a kicked relativistic particle in a box

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.     

The periodically kicked rotator: Recurrence and/or energy growth

We explore the properties of the quantum kicked rotator, its classical equivalent being the standard map. Its behavior, as found by computer studies, depends very much on the strength of the external forcing. At low strength it is seemingly recurrent in the sense of Hogg and Huberman. However, its energy increases with time at large forcings. For quantum systems, a unitary map defines the evolution over one period of time. The spectrum of this map in an infinite space does not seem to change continuously when one approaches the ratio of the frequencies of the external and of the unperturbed system by rational approximations of the golden mean.     

Floquet topological phase transitions and chiral edge states in a kagome lattice

The Floquet topological phases and chiral edge states in a kagome lattice under a circularly-polarized driving field are studied. In the off-resonant case, the system exhibits the similar character as the kagome lattice model with staggered magnetic fluxes, but the total band width is damped in oscillation. In the on-resonant case, the degeneracy splitting at the Γ point does not always result in a gap. The positions of the other two gaps are influenced by the flat band. With the field intensity increased, these two gaps undergo closing-then-reopening processes, accompanied with the changing of the winding numbers.     

Hopping between localized Floquet states in periodically driven quantum dots

The dynamic localization in energy space, suppression of the absorption of energy from an external microwave field due to quantum interference, was analyzed recently for a closed quantum dot in the absence of electron-electron interactions. Here a weak interaction is shown to lead to a finite absorption and heating, which may be viewed as hopping between localized Floquet states. The heating rate grows together with the electronic temperature, eventually destroying the localization.     

Probing (topological) Floquet states through DC transport

We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed numerical study we relate the differential conductances of such a system in two and three terminal geometries to the spectrum of quasi-energies of the Floquet operator. Moreover these differential conductances are found to provide an accurate probe of the existence of gaps in this quasi-energy spectrum, being quantized when topological edge states occur within these gaps. Our analysis opens the perspective to describe the intermediate time dynamics of driven mesoscopic conductors as topological Floquet filters.     

周期变截面波导中的多缺陷态*

设计了一种具有对称结构的多缺陷周期变截面波导,并在其Bragg禁带中实现了多缺陷态的产生。研究表明,通过调整缺陷的个数和长度可实现对缺陷态数目的选择和缺陷态中心频率的调谐。另外,改变重复周期个数可对缺陷态的带宽进行调节。通过对各缺陷态的声场分布进一步分析,我们发现声压沿波导中心轴呈对称或反对称分布。对称缺陷态的最大声能量总是向长度较小的缺陷处偏移,而反对称缺陷态则相反,总是向长度较大的缺陷处偏移。利用这种偏移特性可实现对多缺陷态的声场调控。这不仅使我们对声缺陷态的认识更加深入,更有利于功能型声波导器件的发展与应用。     

周期驱动的Harper模型的量子计算鲁棒性与量子混沌

以周期驱动的量子Harper(quantum kicked Harper, QKH)模型为例，研究复杂量子动力系统的量子计算在各种干扰下的稳定性.通过对Floquet算子本征态的统计遍历性及其Husimi函数的分析，比较随机噪声干扰和静态干扰对量子计算不同程度的影响.进一步的保真度摄动分析表明，在随机噪声干扰下保真度随系统演化呈指数衰减，而静态干扰下的保真度为高斯衰减，并通过数值计算得到了干扰下的可信计算时间尺度.与经典混沌仿真中误差使状态产生指数分离不同，量子计算对状态干扰的稳定性和仿真模型的动力学特性无关. 关键词： 量子Harper模型 量子计算 量子混沌 保真度     

Floquet Majorana fermions in superconducting quantum dots

We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.     

“Escape” of a periodically driven particle from a metastable state in a noisy system

We consider the statistical properties of the escape time of a particle initially sitting in a potential well subject to a combination of white noise and a periodic forcing term. As one finds in the case of the much-studied bistable potential, different kinds of resonant effects can occur, as measured by the survival probability and the average residence time. When this time is considered as a function of the noise strength, then we show that for small amplitudes of the forcing term there are no resonant effects, while for large amplitudes such effects can appear. We also show that a resonant phenomenon is possible in terms of the amplitude of a periodic forcing term.     

Topological invariants for anomalous Floquet higher-order topological insulators

We review the recent development in constructing higher-order topological band insulators under strong periodic drivings. In particular, we focus on various approaches in formulating the anomalous Floquet topological invariants beyond (quasi-)static band topology, and compare their different physical consequences.     

Ergodic properties of a kicked damped particle

We investigate a class of nonlinear dynamical systems describing the movement of a particle in a viscous medium under the influence of a kick force. These systems can be regarded as a generalization of the Langevin approach to Brownian motion in the sense that the fluctuating force on the particle is not Gaussian white noise but an arbitrary non-gaussian process generated by a nonlinear dynamical system. We investigate how certain properties of the force (periodicity, ergodicity, mixing property) transfer to the velocity of the particle. Moreover, the relaxation properties of the system are analysed.Address after October 1, 1989: Institut für Theoretische Physik, RWTH, D-5100, Aachen, FRG     

High-order quantum resonances observed in a periodically kicked Bose-Einstein condensate

We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.     

Resonant nonlinear quantum transport for a periodically kicked bose condensate

Our realistic numerical results show that the fundamental and higher-order quantum resonances of the delta-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.     

Photonic Floquet topological insulators in atomic ensembles

The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated. The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one.

     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法，研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明，一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比，在干扰强度小于某一阈值时，耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降；而在干扰强度大于该阈值时，静态干扰下的可信计算时间尺度下降更快.