Martina Abb, Italo Guarneri, Sandro Wimberger
Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.
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We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical moments on the shape of the initial distribution. For the secondary resonances we obtain numerically a similar dependence. This allows us to devise an extended initial condition which produces an average angular momentum pointing in a preset direction which increases with time with a preset ratio.
We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked Rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to the nonlinear pert…
We examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor…
We develop a system consisting of a quantum kicked rotor with an additional degree of freedom. This models a single two-level atom with internal ground and excited states, and it is characterized by its quantum resonances with ballistic spreading and by the entanglement between the internal and momentum degrees of freedom. These behaviors establish an equivalence between our model and the usual quantum walk on the line.
We study the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, we show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior, however the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential law decay for the coherence.
We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the standard deviation and the external kick strength. For the secondary resonances we obtain essentially the same result numerically. Selecting the time sequence of the kick allows to obtain a variety of asymptotic wave-function spreadings: super-ballistic, ballistic, sub-ballistic, diffusive, sub-diffusive and localized.
We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation.
It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.
A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model
本研究提出适用于受激转子模型的广义赝经典理论，突破原有理论仅适用最低两个量子共振邻域的限制，经模拟验证可预测深量子区域波包动力学，还探讨了其在PT对称受激转子中的应用。
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, epsilon-classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamica…
The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical-quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from t…
Near-Resonance-Induced Caustics and Scaling Laws in a Quantum Kicked Rotor
本研究通过分析量子踢动转子在近共振区域的动力学，揭示了 caustic 结构的形成机制，并推导了与波幅放大、踢动强度和共振偏移参数相关的幂律关系。
We review the theoretical model and experimental realization of the atom optics $δ-$kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy $<p^{2}>/2m$ in units of the re…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting quantum exponential spreading under much more general conditions. In p…
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 present a quantum localization phenomenon that exists in periodically kicked 3D rotors, but is absent in the commonly studied 2D ones: edge localization. We show that under the condition of a fractional quantum resonance there are states of the kicked rotor that are strongly localized near the edge of the angular momentum space at $J=0$. These states are analogs of surface states in crystalline solids, and they significantly affect resonant excitation of molecular rotation by laser pulse trains.
A linear rotor trapped and coupled to the vibrational modes of an ion crystal
该研究针对共囚禁于保罗阱的分子离子与原子离子，确定了考虑分子超精细结构的共振偶极-声子耦合条件，提出用边带分辨激光光谱和退相干测量探测该耦合的方案，为量子控制提供了可行路径。
A simple analytical alignment model for laser-kicked molecular rotors
本文提出一种简洁准确的解析模型，用于描述线性分子热系综在单脉冲非共振激光冲激下的取向，并揭示温度、脉冲强度与时间取向形状之间的直观关系。
We present experimental observations of diffusion resonances for the quantum kicked rotor with weak decoherence. Cold caesium atoms are subject to a pulsed standing wave of near-resonant light, with spontaneous emission providing environmental coupling. The mean energy as a function of the pulse period is determined during the late-time diffusion regime for a constant probability of spontaneous emission per unit time. Structure in the late-time energy is seen to increase with physical kicking strength. The observed structure is related to Shepelyansky's predictions of the initial quantum diffu…
We show that the quantum fidelity is accessible to cold atom experiments for a large class of evolutions in periodical potentials, properly taking into account the experimental initial conditions of the atomic ensemble. We prove analytically that, at the fundamental quantum resonances of the atom-optics kicked rotor, the fidelity saturates at a constant, time-independent value after a small number of kicks. The latter saturation arises from the bulk of the atomic ensemble, whilst for the resonantly accelerated atoms the fidelity is predicted to decay slowly according to a power law.
Feedback-Induced Dynamical Phases in a Self-Adaptive Quantum Kicked Rotor
我们提出自适应量子 kicked rotor 模型，通过腔反馈使 kicking 强度成为动力学变量，揭示共振下的双 kick 弹道输运和反共振，以及不可公度下的周期加倍局域化，建立反馈重塑量子输运与时间序的通用框架。
The Quantum Kicked Rotor: A Paradigm of Quantum Chaos. Foundational aspects and new perspectives
本文通过量子踩踏转子模型探讨经典与量子混沌的核心概念，分析从规则到混沌运动的过渡，介绍动态局域化与量子共振等现象，并讨论其在量子技术中的应用与最新发展。
Probing rotational decoherence with a trapped-ion planar rotor
本研究首次实验观测了转动退相干标度律，利用双离子阱平面转子制备角动量叠加态并测量退相干速率，结果与理论高度吻合，对转子量子应用具有重要意义。
Bose-Einstein condensates subject to short pulses (`kicks') from standing waves of light represent a nonlinear analogue of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability (ie exponential proliferation of non-condensate particles) suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the excitation of Bogoliubov modes for both the quantum kicked rotor (QKR) and a variant, the double kicked …
As demonstrated in our previous work [J. Chem. Phys. 149, 174109 (2018)], the kinetic energy imparted to a quantum rotor by a non-resonant electromagnetic pulse with a Gaussian temporal profile exhibits quasi-periodic drops as a function of the pulse duration. Herein, we show that this behaviour can be reproduced with a simple waveform, namely a rectangular electric pulse of variable duration, and examine, both numerically and analytically, its causes. Our analysis reveals that the drops result from the oscillating populations that make up the wavepacket created by the pulse and that they are …
Anomalous multi-gap topological phases in periodically driven quantum rotors
周期驱动量子旋转子可实现非平衡多间隙拓扑相，通过非阿贝尔编织产生异常狄拉克弦相。
We study the electronic resonant states of H3 with energies above the potential energy surface of the H3+ ground state. These resonant states are important for the dissociative recombination of H3+ at higher collision energies, and previous studies have indicated that these resonant states exhibit a triple intersection. We introduce a complex generalization of the pseudo-Jahn-Teller model to describe these resonant states. The potential energies and the autoionization widths of the resonant states are computed with electron scattering calculations using the complex Kohn variational method, and…
We experimentally investigate the atom optics kicked particle at quantum resonance using finite duration kicks. Even though the underlying process is quantum interference it can be well described by an $ε$-pseudoclassical model. The $ε$-pseudoclassical model agrees well with our experiments for a wide range of parameters. We investigate the parameters yielding maximal momentum transfer to the atoms and find that this occurs in the regime where neither the short pulse approximation nor the Bragg condition is valid. Nonetheless, the momentum transferred to the atoms can be predicted using a simp…
The quantum resonances (QRs) of the kicked particle are studied in a most general framework by also considering {\em arbitrary} periodic kicking potentials. It is shown that QR can arise, in general, for {\em any rational} value of the Bloch quasimomentum. This is illustrated in the case of the main QRs for arbitrary potentials. In this case, which is shown to be precisely described by the linear kicked rotor, exact formulas are derived for the diffusion coefficients determining the asymptotic evolution of the average kinetic energy of either an incoherent mixture of plane waves or a general w…
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