Kicked Rotor Research Articles

Localization-Delocalization Transition in a System of Quantum Kicked Rotors

The quantum dynamics of atoms subjected to pairs of closely spaced delta kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single delta-kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power L approximately h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation summation2(L) approximately or equal to chi(L) approximately 1/2 (1-nu)L, where nu approximately 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximately 0.75 exponent is analyzed.

Reversible Destruction of Dynamical Localization

Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown that deviation from strict periodicity in the driving rapidly destroys dynamical localization. We report experimental results showing that this destruction is partially reversible when the deterministic perturbation that destroyed it is slowly reversed. We also provide an explanation for the partial character of the reversibility.

Ballistic and Localized Transport for the Atom Optics Kicked Rotor in the Limit of a Vanishing Kicking Period

We present mean energy measurements for the atom optics kicked rotor as the kicking period tends to zero. A narrow resonance is observed marked by quadratic energy growth, in parallel with a complete freezing of the energy absorption away from the resonance peak. Both phenomena are explained by classical means, taking proper account of the atoms' initial momentum distribution.

Numerical solution of classical kicked rotor and local Lyapunov exponents

We calculate a local Lyapunov exponent for the kicked rotor that is constant for a duration that depends on the initial separation between two trajectories, but then decreases asymptotically as O ( t −1 ln t ) . This behavior is consistent with an upper bound that is determined analytically.

Observation of robust quantum resonance peaks in an atom optics kicked rotor with amplitude noise

The effect of pulse train noise on the quantum resonance peaks of the atom optics kicked rotor is investigated experimentally. Quantum resonance peaks in the late time mean energy of the atoms are found to be surprisingly robust against all levels of noise applied to the kicking amplitude, while even small levels of noise on the kicking period lead to their destruction. The robustness to amplitude noise of the resonance peak and of the fall-off in mean energy to either side of this peak are explained in terms of the occurrence of stable, epsilon classical dynamics [Nonlinearity 16, 1381 (2003)]] around each quantum resonance.

Directed anomalous diffusion without a biased field: a ratchet accelerator.

Directed classical current that increases linearly with time without using a biased external field is obtained in a simple model Hamiltonian system derived from a modified kicked rotor model, by breaking the spatial symmetry of the transporting regular islands in the classical phase space. A parallel study of the corresponding quantum dynamics suggests that although quantum coherence effects suppress the directed current and can even induce a current reversal, directed quantum current that increases linearly with time can nonetheless be realized in a quantum system that is far from the classical limit.

A transition from conservative to quasi-dissipative

A special kicked rotor moving in a piecewise continuous force field is suggested and studied. When adjusting a control parameter,the rotor displays a transition from conservative to quasi-dissipative, and a change of a stochastic web formed by the set of the images of the discontinuous borderlines to a transient stochastic web. This transition and change can be described by a logarithmic rule of the fractal dimension of the transient stochastic web versus the control parameter, or a rule of the averaged lifetime of the iterations in the transient stochastic web versus the control parameter.

Control of dynamical localization.

Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of the dynamical localization length, the introduction of classical anomalous diffusion assisted control for systems far from the semiclassical regime, and the observation of a variety of strongly nonexponential line shapes for dynamical localization. The results provide excellent examples of controlled quantum dynamics in a system that is classically chaotic and offer opportunities to explore quantum fluctuations and correlations in quantum chaos.

Coherent manipulation of quantum delta-kicked dynamics: faster-than-classical anomalous diffusion.

Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system parameters and over long time scales, is shown to display energy absorption that is significantly faster than that associated with the underlying classical anomalous diffusion. The results are of interest to areas of both quantum chaos and quantum control.

Strange Quasi-Repeller in a Kicked Rotor

A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the end-results of the images of the discontinuous borderlines of the system function. In the crisis, a strange quasi-repeller can be defined. When changing the controlling parameter, the variation of the fractile dimension of the quasi-repeller obeys a logarithmic rule.

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

We investigate how the dynamical production of quantum entanglement for weakly coupled mapping systems is influenced by the chaotic dynamics of the corresponding classical system. We derive a general perturbative formula for the entanglement production rate which is defined by using the linear entropy of the subsystem. This formula predicts that {\it the increment of the strength of chaos does not enhance the production rate of entanglement} when the coupling is weak enough and the subsystems are strongly chaotic. The prediction is confirmed by numerical experiments for coupled kicked tops and rotors. We also discuss the entanglement production using the Husimi representation of the reduced density matrix.

Estimates on Green's Functions, Localization and the Quantum Kicked Rotor Model

and phase space L2(1r). It has been conjectured by a number of authors (cf. [FGP], [Bel]) that for typical parameter values for a, b, the wave function t satisfying equations (0.1), (0.2) will be almost periodic in time; hence f(t) (the Fourier transform) remains localized. We will prove this here, assuming the parameter S in (0.2) small. Thus we have: THEOREM. For K stnall and (a,b) o?>tside a set of small rneasure ( > O for K > 0), the following holds. Let 4! = W(t, x) solve (0 1), (0 2) and let to = 4!(0, x) be a suJgciently smooth function on T. Then @ is an alrnost periodic function of timbe, say as an Hl(T)-valued map. In particular supt ll@(t)llHl

Experimental demonstration of localization in the frequency domain of mode-locked lasers with dispersion

Mode-locked lasers with intracavity dispersion are experimentally shown to exhibit localization behavior in their frequency domain. The localization, with its typical exponential spectrum structure, is analogous to that which occurs for the quantum kicked rotor. The experimental demonstration of our optical kicked rotor is done with a long mode-locked dispersive fiber laser. The localization effect sets a basic limit on the spectrum bandwidth and the minimum pulse width in such lasers. It also provides a special experimental test bed for the study of optical kicked rotors and localization effects.

Dynamic simulation of random packing of spherical particles

Kicked rotor is a paradigmatic model for classical and quantum chaos in time-dependent Hamiltonian systems. More than fifty years since the introduction of this model, there is an increase in the number of works that use kicked rotor model as a fundamental template to study a variety of questions in nonlinear dynamics, quantum chaos, condensed matter physics and quantum information. This is aided by the experimental approaches that have implemented many variants of the quantum kicked rotor model. The problems addressed using kicked rotor and its variants include the basic phenomenology of classical and quantum chaos, transport and localization in one- and higher dimensional kicked systems, effects of disorder and interactions, resonant dynamics and the relation between quantum correlations and chaos. This would also include a range of applications such as for constructing ratchet dynamics and for atom-optics based interferometry. This article reviews the current status of theoretical and experimental research devoted to exploring these ideas using the framework of kicked rotor model.

Relaxation and diffusion for the kicked rotor

The dynamics of the kicked rotor, which is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular, is studied statistically. The evolution operator of phase space densities in the chaotic component is calculated in the presence of noise, and the limit of vanishing noise is taken in the end. The relaxation rates to the equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. A global picture is presented of relaxation to the equilibrium density in the chaotic component when the system is bounded and to diffusive behavior when it is unbounded.

Entropy production, dynamical localization and criteriafor quantum chaos in the open quantum kicked rotor

The von Neumann entropy production for a quantum mechanical kicked rotor coupled to a thermal environment is calculated. This rate of entropy increase is shown to be a good criterion to distinguish between quantum mechanical counterparts of chaotic and regular classical motion. We show that for high temperatures the entropy production rate increases linearly with the Kolmogorov-Sinai entropy of the classical system. However, for lower temperatures we also show that there are fluctuations in this linear behaviour due to dynamical localization. PACS Numbers: 0545, 0365

Quantum suppression of chaos in the Fermi accelerator

We address the question of how a quantum particle exchanges energy with a moving wall with an imposed smooth, periodic motion law. In the semiclassical region of parameter space, the energy gain of the particle is initially consistent with the classical result. This correspondence is maintained for some time, until quantum localization effects suppress the classical diffusion. We discuss similarities with the well studied case of the Quantum Kicked Rotor.

Quantum-classical correspondence of entropy contours in the transition to chaos

Von Neumann entropy production rates of the quantized kicked rotor interacting with an environment are calculated. A significant correspondence is found between the entropy contours of the classical and quantized systems. This is a quantitative tool for describing quantum-classical correspondence in the transition to chaos.

Limited sensitivity to analyticity: a manifestation of quantum chaos

Classical Hamiltonian systems generally exhibit an intricate mixture of regular and chaotic motions on all scales of phase space. As a nonintegrability parameter K (the “strength of chaos”) is gradually increased, the analyticity domains of functions describing regular-motion components [e.g., Kolmogorov-Arnol’d-Moser (KAM) tori] usually shrink and vanish at the onset of global chaos (breakup of all KAM tori). It is shown that these phenomena have quantum-dynamical analogs in simple but representative classes of model systems, the kicked rotors and the two-sided kicked rotors. Namely, as K is gradually increased, the analyticity domain ℛQE of the quantum-dynamical eigenstates decreases monotonically, and the width of ℛQE in the global-chaos regime vanishes in the semiclassical limit. These phenomena are presented as particular aspects of a more general scenario: As K is increased, ℛQE gradually becomes less sensitive to an increase in the analyticity domain of the system.

Antiresonance and localization in quantum dynamics.

The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for $\eta$ (a scaled $\hbar$) in the infinitesimal vicinity of QAR points $\eta_0$. The localization length $\xi_0$ is determined from the analytical properties of the kicking potential. This ``QAR-localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR-localization to DL in a semiclassical regime, as $\eta$ is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.