Quantum fractal fluctuations

Multifractal Conductance Fluctuations in High-Mobility Graphene in the Integer Quantum Hall Regime

We present the first experimental evidence for the multifractality of a transport property at a topological phase transition. In particular, we show that conductance fluctuations display multifractality at the integer quantum Hall plateau-to-plateau transitions in high-mobility mesoscopic graphene devices. The multifractality gets rapidly suppressed as the chemical potential moves away from these critical points. Our combination of experimental study and multifractal analysis provides a novel method for probing the criticality of wave functions at phase transitions in mesoscopic systems, and quantum criticality in several condensed-matter systems.

Interplay between quantum diffusion and localization in the atom-optics kicked rotor

Atom-optics kicked rotor represents an experimentally reliable version of the paradigmatic quantum kicked rotor system. In this system, a periodic sequence of kicks are imparted to the cold atomic cloud. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this paper, to explore the interplay between localized and diffusive phases, we experimentally implement a modification to this system in which the sign of the kick sequence is flipped after every M kicks. This is achieved in our experiment by allowing free evolution for half the Talbot time after every M kicks. Depending on the value of M, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes-localization induced by standard kicked rotor type kicks, and diffusion induced by the half Talbot time evolution. The experimental and numerical simulations agree with one another. The evolving states display localized but nonexponential wave function profiles. This provides another route to quantum control in the kicked rotor class of systems.

Fractal dynamics in chaotic quantum transport

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter's butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.

Quantum localization in open chaotic systems

We study a quasibound state of a delta -kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths xi of lossy quasibound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates Gamma are dramatically enhanced. We find the relation xi approximately Gamma(-1/2) and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.

Current relaxation in nonlinear random media

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as P(t) approximately 1/t(alpha). For intermediate times t<t(*), the exponent alpha satisfies a scaling law alpha=f(Lambda=chi/l(infinity)), where chi is the nonlinearity strength and l(infinity) is the localization length of the corresponding random system with chi=0. For t>>t(*) and chi>chi(cr) we find a universal decay with alpha=2/3 which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.

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.

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.

Isolated resonances in conductance fluctuations and hierarchical states

We study the isolated resonances occurring in conductance fluctuations of quantum systems with a classically mixed phase space. We demonstrate that the isolated resonances and their scattering states can be associated with eigenstates of the closed system. They can all be categorized as hierarchical or regular, depending on where the corresponding eigenstates are concentrated in the classical phase space.

Fractal fluctuations in quantum integrable scattering

We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with scattering processes in the presence of strong dynamical localization, thus explaining recent numerical observations of fractality in the latter class of systems.