Recent studies have established that, in addition to the well-known kicked Harper model (KHM), an on-resonance double kicked rotor model (ORDKR) also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter's spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasi-energy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2*pi and (ii) will be different if the same parameter takes rational multiples of 2*pi. This work makes some detailed comparisons between these two models, with an effective Planck constant given by 2*pi M/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and $N-1$ non-flat bands whose largest width decays in power law as K to the power of N+2, where K is a kicking strength parameter. The existence of a flat band is strictly proven and the power law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its band width scales linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in KHM. Finally, we show that despite these differences, there exist simple extensions of KHM and ORDKR (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR are actually topologically equivalent, i.e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided.
The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance of periodic driving to the generation of unconventional topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1/2 degree of freedom. The latter has been ex…
The dynamics of chaotic Hamiltonian systems such as the kicked rotor continues to guide our understanding of transport and localization processes. The localized states of the quantum kicked rotor decay due to decoherence effects if subjected to stationary noise. The associated quantum diffusion increases monotonically as a function of a parameter characterising the noise distribution. In this work, for the Levy kicked atom-optics rotor, it is experimentally shown that by tuning a parameter characterizing the Levy distribution, quantum diffusion displays non-monotonic behaviour. The parameters …
Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?
我们研究了深量子体系中开放版本的δ-kicked转子模型的量子生存概率的参数涨落。光谱参数[Guarneri I and Terraneo M 2001 Phys. Rev. E vol. 65 015203（R）]预测了参数分形波动的存在，这是由于被踢转子的本征态的强动力学局部化。我们讨论了观察这种动态诱导分形的量子生存概率作为踢周期的函数的原子光学实现踢转子的可能性。原子的初始动量分布的影响进行了研究，以及预期的分形维数对实验的有限尺寸效应，如有限的检测窗口和短的测量时间的依赖。我们的研究结果表明，在周期性闪烁的光晶格中，冷原子可以观察到清晰的分形特征，这对相互作用时间和初始原子系综提供了很好的控制。
We study the dynamics of a Bose-Einstein condensate in the quasiperiodic kicked rotor described by a Gross-Pitaevskii equation with periodic boundary conditions. As the interactions are increased, Bogoliubov excitations appear and deplete the condensate; we characterize this instability by considering the population of the first Bogoliubov mode, and show that it does not prevent, for small enough interaction strengths, the observation of the transition. However, the predicted subdiffusive behavior is not observed in the stable region. For higher interaction strengths, the condensate may be str…
The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays ballistic mean energy growth due to coherent momentum transfer. Secondly, the sharp quantum resonance peaks are useful in the context of measurement of Talbot time, one of the parameter that helps in precise measurement of fine structure constant. Most of the earlier works rely on fidelity based approach and have proposed Talbot time measurement through experimenta…
We study the breaking of time-reversal invariance (TRI) by the application of a magnetic field in the quantum kicked rotor (QKR), using Izrailev's finite-dimensional model. There is a continuous crossover from TRI to time-reversal non-invariance (TRNI) in the spectral and eigenvector fluctuations of the QKR. We show that the properties of this TRI $\rightarrow$ TRNI transition depend on $α^2/N$, where $α$ is the chaos parameter of the QKR and $N$ is the dimensionality of the evolution operator matrix. For $α^2/N \gtrsim N$, the transition coincides with that in random matrix theory. For $α^2/N…
Exponential Quantum Spreading in a Class of Kicked Rotor Systems near High-Order Resonances
最近在一个简单但非常丰富的动力学模型中发现了长时间的量子指数扩展，即共振双踢转子模型[J. Wang，I。瓜尔内里湾Casati和J. B. Gong，Phys. Rev. Lett. 107，234104（2011）]。潜在的机制，无关的混沌运动的经典极限，但在准可积运动的伪经典极限休息，被确定为一个特殊的情况。通过对同一模型的详细研究，这项工作提供了一个框架来解释更一般条件下的长期量子指数传播。特别是，我们采用所谓的“旋量”表示处理的kicked-rotor动力学高阶共振条件下，然后利用Born-Oppenheimer近似理解的动力学演化。研究发现，平坦带（或有效平坦带）的存在是指数动力学为什么以及如何出现的一个重要特征。研究还发现，基于有趣且简单的伪经典映射来定量预测指数扩展速率可能是不准确的。除了关于量子系统中的指数行为如何持续很长时间的问题的普遍兴趣之外，我们的研究结果应该激励进一步的研究，以更好地理解delta-kicked量子系统中的高阶共振行为。
We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In this way we can apply exact diagonalization up to quite large system sizes and confirm that the system tends to ergodicity in the large-size limit. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian. These equations give rise to a power-law increase in time of the energy with exponent $γ\sim 2/3$ in a wide range of parameters. We explain this finding by means of a master-…
We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength…
The quantum kicked rotor (QKR) model is a prototypical system in the research of quantum chaos. In a spin-$1/2$ QKR, tuning the effective Planck parameter realizes a series of transitions between dynamical localization phases, which closely resembles the integer quantum Hall (IQH) effect and the plateau transitions. In this work, we devise and apply the finite-size scaling analysis to the transitions in the spin-$1/2$ QKR model. We obtain an estimate of the critical exponent at the transition point, $ν=2.62(9)$, which is consistent with the IQH plateau transition universality class. We also gi…
Unconventional quantum criticality in the kicked rotor
$d$非公度频率驱动的量子反冲转子（QKR）实现了$d$维无序金属的普适类.对于$d>3$，该系统表现出安德森金属-绝缘体转变，已观察到的原子光学实现的框架内。然而，在QKR中缺乏真正的随机性反映在安德森普适类之外的临界现象中。具体地说，该系统表现出很强的敏感性，其有效普朗克常量$\tilde h \equiv 4π/q$的代数性质。对于整数$q$，系统可能处于全局可积状态，处于以发散响应系数为特征的“超金属”构型，安德森局域化，金属化，或表现出这些相之间的转变。我们提出了不同的$q$值和有效的维数的数值数据，重点是参数配置，可以访问实验研究。
Finite-time effects in periodically kicked systems
Universidad Politécnica de Madrid（马德里理工大学）；Universidad de Extremadura（埃斯特雷马杜拉大学）；Instituto de Computación Científica Avanzada (ICCAEx)（高级科学计算研究所 (ICCAEx)）；Universidad Autónoma de Madrid（马德里自治大学）
