Quantum contact interactions

The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is identified.     

Exponential speedup with a single bit of quantum information: measuring the average fidelity decay

We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation. Thus for those maps admitting an efficient gate decomposition, it provides an exponential speedup over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of eigenvector statistics. Our result also illustrates the role of chaos in the process of decoherence.     

Time-reversal characteristics of quantum normal diffusion

This paper concerns the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain period is time-reversed for the same period after applying a small perturbation at the reversal time, and the separation between the time-reversed perturbed and unperturbed states is measured as a function of perturbation strength, which characterizes sensitivity of the time reversed system to the perturbation and is called the time-reversal characteristic. Time-reversal characteristics are investigated for various quantum systems, namely, classically chaotic quantum systems and disordered systems including various stochastic diffusion system. When the system is normally diffusive, there exists a fundamental quantum unit of perturbation, and all the models exhibit a universal scaling behavior in the time-reversal dynamics as well as in the time-reversal characteristics, which leads us to a basic understanding of the nature of quantum irreversibility.     

Tolerance of edge cascades with coupled map lattices methods

This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.     

The dynamical entropy of the quantum Arnold cat map

We present a rigorous computation of the dynamical entropyh of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents ± 1n ⁺, ⁺ > 1. We show that, for all values of the quantum deformation parameter,h coincides with the positive Lyapunov exponent of the dynamics.     

The periodically kicked rotator: Recurrence and/or energy growth

We explore the properties of the quantum kicked rotator, its classical equivalent being the standard map. Its behavior, as found by computer studies, depends very much on the strength of the external forcing. At low strength it is seemingly recurrent in the sense of Hogg and Huberman. However, its energy increases with time at large forcings. For quantum systems, a unitary map defines the evolution over one period of time. The spectrum of this map in an infinite space does not seem to change continuously when one approaches the ratio of the frequencies of the external and of the unperturbed system by rational approximations of the golden mean.     

Border between regular and chaotic quantum dynamics

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power-law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with [1+(q-1)(t/tau)2](1/(1-q)) (with the nonextensive entropic index q and tau depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.     

Gravitation as Anholonomy

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenböck connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.     

Space curves,anholonomy and nonlinearity

Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.     

Modeling an adiabatic quantum computer via an exact map to a gas of particles

We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than |lambda|gamma, where |lambda| is the adiabaticity parameter. The scaling exponent for the escape probability is gamma=1/2 for all levels, except the edge (bottom and top) ones, where gamma approximately < 1/3. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.     

Quantum features in atomic nanofabrication using exactly resonant standing waves

We report on the first fabrication of nanostructures with exactly resonant light revealing the quantum character of the atom-light interaction. Classically the formation of nanostructures is not expected; thus, the observed formation of complex periodic line patterns can be explained only by treating atom-light interaction and propagation of the atoms quantum mechanically. Our numerical quantum calculations are in quantitative agreement with this experimental finding. Moreover, the theory predicts that for small detunings nanostructures with lambda/4 period can be produced, which beats the standard nanofabrication limit of lambda/2. Our experiments confirm this prediction.     

Oscillatory electron phonon coupling in Pb/Si（111）deduced by temperature-dependent quantum well states

Photoemission study of atomically flat Pb films with a thickness from 15 to 24 monolayers （ML） have been performed within a temperature range 75-270K. Well-defined quantum well states （QWSs） are observed, which exhibit interesting temperature-dependent behaviours. The peak position of the QWSs shifts towards higher binding energy with increasing substrate temperature, whereas the peak width broadens linearly due to enhanced electron-phonon coupling strength （λ）. An oscillatory A with a period of 2ML is deduced. Preliminary analysis shows that the oscillation can be explained in terms of the interface induced phase variations, and is thus a manifestation of the quantum size effects.     

Quantum reversibility: is there an echo?

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time t(r) for maximum return probability is in general shorter. We find that t(r) depends on lambda=epsilon(evol)/epsilon(prep), being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.     

Multiple-scale analysis of open quantum systems

In this work, we present a multiple-scale perturbation technique suitable for the study of open quantum systems, which is easy to implement and in few iterative steps allows us to find excellent approximate solutions. For any time-local quantum master equation, whether markovian or non-markovian, in Lindblad form or not, we give a general procedure to construct analytical approximations to the corresponding dynamical map and, consequently, to the temporal evolution of the density matrix. As a simple illustrative example of the implementation of the method, we study an atom-cavity system described by a dissipative Jaynes-Cummings model. Performing a multiple-scale analysis we obtain approximate analytical expressions for the strong and weak coupling regimes that allow us to identify characteristic time scales in the state of the physical system.     

Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities

The insertion of a metal-coated tip on the surface of a photonic crystal microcavity is used for simultaneous near field imaging of electric and magnetic fields in photonic crystal nanocavities, via the radiative emission of embedded semiconductor quantum dots (QD). The photoluminescence intensity map directly gives the electric field distribution, to which the electric dipole of the QD is coupled. The magnetic field generates, via Faraday's law, a circular current in the apex of the metallized probe that can be schematized as a ring. The resulting magnetic perturbation of the photonic modes induces a blue shift, which can be used to map the magnetic field, within a single near-field scan.     

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.     

Quantumlike dynamics of classical particles in ponderomotive potentials

The average dynamics of a classical particle under the action of a high-frequency radiation resembles quantum particle motion in a conservative field with an effective de Broglie wavelength lambda equal to the particle average displacement on the oscillation period. In a quasiclassical field, with a spatial scale large compared to lambda, the guiding-center motion is adiabatic. Otherwise, a particle exhibits quantized eigenstates in ponderomotive potential wells, tunnels through "classically forbidden" regions, and experiences stochastic reflection from attractive potentials.     

Quantization of the kicked rotator with dissipation

The effect of dissipation on a quantum system exhibiting chaos in its classical limit is studied by coupling the kicked quantum rotator to a reservoir with angular momentum exchange. A master equation is derived which maps the density matrix from one kick to the subsequent one. Several limiting cases are investigated. The limits of 0 and of vanishing dissipation serve as tests of consistency, in reproducing the maps of the classical kicked damped rotator and of the kicked quantum rotator, respectively. In the limit of strong dissipation the classical map reduces to a circle map. A quantum map corresponding to the circle map is therefore obtained in this limit. In the limit of infinite dissipation the density matrix becomes independent of the initial condition after a single application of the map, allowing for a simple analytical solution for the density matrix. In the semi-classical limit the quantum map reduces to a classical map with quantum mechanically determined classical noise terms, which are evaluated. For sufficiently small dissipation the physical character of the leading quantum corrections changes. Quantum mechanical interference effects then render the Wigner distribution negative in some parts of phase space and prevent its interpretation in classical terms. Numerical results will be presented in a subsequent paper.     

光学-射频场双驱动原子系统中的透明与吸收特性的调控

光与物质的相互作用可以产生许多奇特的量子光学现象,电磁诱导透明和电磁诱导吸收是其中最典型的现象.本文在通常的Λ型三能级系统中引入射频场作用于激发态的精细结构能级之间,组成光学-射频双驱动场共同激发原子的相干跃迁,使系统的吸收特性出现电磁诱导透明和电磁诱导吸收两种量子相干效应.通过讨论双驱动场开启后直到系统达到稳定的量子相干过程,分析电磁诱导透明和电磁诱导吸收随时间的产生和转化,得到两种量子相干现象之间的关联性及对其进行量子调控的方法.