This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered, those satisfying the classical Kolmogorov-Arnol'd-Moser scenario and those which not. The experimental realization of some of these systems using atom-optics methods will be mentioned.
Impact of thermal and dissipative effects in a periodically-kicked quantum battery
Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所）；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物理理论系）
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）
We consider quantum maps induced by periodically-kicked scattering systems and discuss the computation of their resonance spectra in terms of complex scaling and sufficiently weak absorbing potentials. We also show that strong absorptive and projective openings, as commonly used for open quantum maps, fail to produce the resonance spectra of kicked scattering systems, even if the opening does not affect the classical trapped set. The results are illustrated for a concrete model system whose dynamics resembles key features of ionization and exhibits a trapped set which is organized by a topolog…
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。
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 introduce kicked $p$-spin models describing a family of transverse Ising-like models for an ensemble of spin-$1/2$ particles with all-to-all $p$-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top ($p$=2)[Haake, Kuś, and Scharf, Z. Phys. B 65, 381 (1987)]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between $p=2$ and $p>…
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…
We investigate the onset of chaos in a periodically kicked Dicke model (KDM), using the out-of-time-order correlator (OTOC) as a diagnostic tool, in both the oscillator and the spin subspaces. In the large spin limit, the classical Hamiltonian map is constructed, which allows us to investigate the corresponding phase space dynamics and to compute the Lyapunov exponent. We show that the growth rate of the OTOC for the canonically conjugate coordinates of the oscillator is able to capture the Lyapunov exponent in the chaotic regime. The onset of chaos is further investigated using the saturation…
We study the quantum dynamics of the kicked Dicke model(KDM) in terms of the Floquet operator and analyze the connection between the chaos and thermalization in this context. The Hamiltonian map is constructed by taking the classical limit of the Heisenberg equation of motion suitably to study the corresponding phase space dynamics which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed point analysis and calculation of the Lyapunov exponent(LE) provides us a complete picture of the onset of chaos in phase space dynamics. We carry out the spectral analy…
We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pa…
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 …
Quantum directed transport can be realized in non-interacting, deterministic, chaotic systems by appropriately breaking the spatio-temporal symmetries in the potential. In this work, the focus is on the class of interacting quantum systems whose classical limit is chaotic. In this limit, one subsystem effectively acts as a source of "noise" to the other leading to temporal symmetry breaking. Thus, the quantum directed currents can be generated with two ingredients -- broken spatial symmetry in the potential and presence of interactions. This is demonstrated in two-body interacting kicked rotor…
Classical "kicked Hall systems" (KHSs), i.e., periodically kicked charges in the presence of uniform magnetic and electric fields that are perpendicular to each other and to the kicking direction, have been introduced and studied recently. It was shown that KHSs exhibit, under generic conditions, the phenomenon of "superweak chaos" (SWC), i.e., for small kick strength $κ$ a KHS behaves as if this strength were effectively $κ^2$ rather than $κ$. Here we investigate quantum-dynamical and spectral manifestations of this generic SWC. We first derive general expressions for quantum effective Hamilt…
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 for 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 pe…
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties close to an ideal disordered quantum system, opening new windows into the study of Anderson physics.
We investigate the quantum diffusion of a periodically kicked particle subjecting to both nonlinearity induced self-interactions and $\mathcal{PT}$-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of mean square of momentum scales with time in a super-exponential form $\langle p^2(t)\rangle\propto\exp[β\exp(αt)]$, which is faster than any known rates of quantum diffusion. In the $\mathcal{PT}$-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the i…
