Low-energy properties of aperiodic quantum spin chains

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that, in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.     

Quantum well behavior without confining barrier observed via dynamically screened photon field

Angle-resolved photoemission spectra from Na adlayers on Al(111) reveal features which behave like quantum well resonances although the substrate provides no confining barrier. These features are observed in a narrow photon energy range where overlayer collective excitations cause resonant enhancement of the photoemission intensity. The quantum well behavior is shown to be due to surface resonances of the Na/Al system. The resonances are observable using photoemission because of spatial confinement and dynamical enhancement of the local electric field within the Na films.     

Kondo effect in a quantum antidot

We report Kondo-like behavior in a quantum antidot (a submicron depleted region in a two-dimensional electron gas) in the quantum-Hall regime. When both spins of the lowest Landau level are present all around the antidot, the resonances between extended edge states via antidot bound states show an abnormal feature in alternate Coulomb-blockaded regions. The feature becomes suppressed when the temperature or source-drain bias is raised as for Kondo resonances in quantum dots. Although the exact mechanism is unknown, Kondo-like correlated tunneling may arise from a Skyrmion-type edge reconstruction. This observation demonstrates the generality of the Kondo phenomenon.     

Quantum interference effects in the magnetopiezoresistance of InAs/AlGaSb quasi-one-dimensional electron systems

We measured the low temperature magnetopiezoresistance of a quasi-one-dimensional electron system by fabricating an InAs/AlGaSb micromechanical cantilever. The magnetopiezoresistance curve showed aperiodic but reproducible oscillation, which was similar to the differential magnetoresistance curve obtained for the same device. A detailed comparison with model calculations strongly suggests that the quantum interference effects that cause the conductance fluctuations in the magnetoresistance are responsible for the peculiar behavior of the magnetopiezoresistance.     

Multiband diffraction and refraction control in binary arrays of periodically curved waveguides

The possibility of controlling discrete diffraction and refraction in a multiband waveguide array by periodic waveguide bending is theoretically demonstrated. Resonance effects, leading to the enhancement or inhibition of discrete diffraction, are found and related to the quantum analog of field-induced n-photon resonances in semiconductor superlattices. A very distinct behavior for light refraction is found for odd or even resonances. In particular, for even resonances, the two-band behavior of the straight binary array is quenched, resulting in the inhibition of double refraction.     

Quantum fingerprints of classical ruelle-pollicott resonances

Quantum and classical correlations are studied experimentally in model n-disk microwave billiards. The wave vector kappa autocorrelation C(kappa) of the quantum spectrum displays nonuniversal oscillations for large kappa, comparable to the universal random matrix theory behavior observed for small kappa. The nonuniversal behavior is shown to be completely determined by the classical Ruelle-Pollicott resonances, arising from the complex eigenvalues of the Perron-Frobenius operator, and calculated using periodic orbit theory. This work establishes a fundamental connection between the quantum and classical correlations of an open system.     

Controlling the ratchet effect for cold atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.     

A Study of Resonances in a One-Dimensional Model with Singular Hamiltonian and Mass Jumps

We study the resonances produced in a one dimensional quantum system with an infinite potential on the negative real line plus two Dirac delta barriers centered at the points a,b>0. The system mass is not constant but undergoes jumps at the singular points a and b of the potential. We study the behavior of the resonances under the change of parameters such that the weight of the deltas or the heights of mass jumps. Possible degeneration of these resonances is also considered.     

Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity

We study linear transmission and nonlinear soliton transport through quasiperiodic structures, where the lattice profiles are described by multiple modulation frequencies. We show that resonant scattering at mixed-frequency resonances limits transmission efficiency of localized wave packets, leading to radiation and possible trapping of solitons. We obtain an explicit analytical expression for optimal quasiperiodic lattice profiles, where additional aperiodic modulations suppress mixed-frequency resonances, resulting in dramatic enhancement of soliton mobility. Our results can be applied to the design of photonic waveguide structures, and arrays of magnetic micro-traps for atomic Bose-Einstein condensates.     

Electronic excitations and transport in aperiodic sequences of quantum dots in external electric and magnetic fields

The energy spectra and transport of electronic excitations in one-dimensional aperiodic sequences of quantum dots of Thue-Morse and double-periodic type are studied. The influence of external magnetic and electric fields on the energy spectra and transport is considered. For aperiodic sequences of quantum dots, in contrast to aperiodic sequences of atoms, the influence of relatively small magnetic and electric fields is essential, but localization occurs at finite values of the perturbations. The transmission coefficient is determined using the quasiclassical approximation with the Coulomb blockade taken into account. The resonance tunneling is studied.     

Classical decays in decoherent quantum maps

The linear entropy and the Loschmidt echo have proved to be of interest recently in the context of quantum information and of the quantum to classical transitions. We study the asymptotic long-time behavior of these quantities for open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse graining, and for chaotic maps, these decay rates are given by the Ruelle-Pollicott resonances of the classical map.     

Subdiffusive Quantum Transport for 3D Hamiltonians with Absolutely Continuous Spectra

We exhibit a class of Hamiltonians in dimension D3, describing a quantum particle in an aperiodic medium with absolutely continuous spectrum and subdiffusive behavior. The diffusion exponent, which characterizes the time growth of the mean square displacement, can be chosen slightly bigger than Guarneri's lower bound. These models are built out of 1D Hamiltonians with well-understood spectral and transport properties.     

光学简并三波混频中的量子非破坏测量

运用半经典量子理论方法建立了光学简并三波混频在两输入场均不为零的情况下的理论模型 ,讨论了在两输入场均不为零时系统的动力学行为以及相应的量子非破坏测量 (QND)特性。研究结果表明 ,该系统的最佳量子非破坏测量工作点与以往的情况不同 ,不是出现在非线性共振点处而是在双稳转变点     

Mesoscopic to universal crossover of the transmission phase of multilevel quantum dots

Transmission phase alpha measurements of many-electron quantum dots (small mean level spacing delta) revealed universal phase lapses by pi between consecutive resonances. In contrast, for dots with only a few electrons (large delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multilevel quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of alpha for small delta follows from Fano-type antiresonances of the renormalized single-particle levels.     

Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.     

Arnol’d diffusion in a system with 2.5 degrees of freedom: Classical and quantum mechanical approaches

Arnol’d diffusion, a universal phenomenon in nonlinear dynamics, is analyzed for a model system with 2.5 degrees of freedom. Only the three primary order resonances are taken into account, and the results obtained by using classical and quantum mechanical approaches are compared. It is shown that the parameter dependence of the rate of quantum Arnol’d diffusion is similar to the classical one, but the quantum diffusion coefficient is smaller by approximately an order of magnitude. It is found that the existence of a threshold with respect to perturbation parameters, pointed out earlier, is not an indispensable feature of quantum Arnol’d diffusion. It is shown that a quantum system with weakly overlapping resonances can exhibit mixed dynamics that has no classical counterpart (diffusion along a resonance superimposed by oscillations across the overlapped resonances).     

Conductance fluctuations and quantum chaotic scattering in semiconductor microstructures

We review recent experiments on aperiodic conductance fluctuations in ballistic GaAs/AlGaAs microstructures in the shape of a stadium billiard and a circle with point-contact leads, measured at millikelvin temperatures. Much of the observed behavior can be analyzed within a semiclassical approach to quantum chaotic scattering. After a brief review of the Landauer-Buttiker formulation of coherent transport, a variety of novel experimental phenomena and comparisons to semiclassical theory are presented. In particular, we discuss quantum-enhanced backscattering, the power spectrum of conductance fluctuations, crossover to the high-magnetic-field and tunneling regimes, and an application allowing the rate of phase-randomizing scattering to be measured in chaotic ballistic microstructures.