Unusual quantum states: nonlocality, entropy, Maxwell's daemon, and fractals

This paper analyses the mathematical properties of some unusual quantum states that are constructed by inserting an impenetrable barrier into a chamber confining a single particle.Comment: 9 Figure

Anomalies of the infrared-active phonons in underdoped YBCO as an evidence for the intra-bilayer Josephson effect

The spectra of the far-infrared c-axis conductivity of underdoped YBCO crystals exhibit dramatic changes of some of the phonon peaks when going from the normal to the superconducting state. We show that the most striking of these anomalies can be naturally explained by changes of the local fields acting on the ions arising from the onset of inter- and intra-bilayer Josephson effects.Comment: Revtex, epsf, 6 pages, 3 figures encapsulated in tex

Geometry of PT-symmetric quantum mechanics

Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem associated with such Hamiltonians have shown that in many cases the entire energy spectrum is real and positive and that the eigenfunctions form an orthogonal and complete basis. Furthermore, the quantum theories determined by such Hamiltonians have been shown to be consistent in the sense that the probabilities are positive and the dynamical trajectories are unitary. However, the geometrical structures that underlie quantum theories formulated in terms of such Hamiltonians have hitherto not been fully understood. This paper studies in detail the geometric properties of a Hilbert space endowed with a parity structure and analyses the characteristics of a PT-symmetric Hamiltonian and its eigenstates. A canonical relationship between a PT-symmetric operator and a Hermitian operator is established. It is shown that the quadratic form corresponding to the parity operator, in particular, gives rise to a natural partition of the Hilbert space into two halves corresponding to states having positive and negative PT norm. The indefiniteness of the norm can be circumvented by introducing a symmetry operator C that defines a positive definite inner product by means of a CPT conjugation operation.Comment: 22 Page

Faster than Hermitian Quantum Mechanics

Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi_I> to |psi_F> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.Comment: 4 page

Non-Locality of Experimental Qutrit Pairs

The insight due to John Bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day. We describe an experiment, and its analysis, displaying non-locality of entangled qutrit pairs. The non-locality of such systems, as compared to qubit pairs, is of particular interest since it potentially opens the door for tests of bipartite non-local behavior independent of probabilistic Bell inequalities, but of deterministic nature

Tunable reflection minima of nanostructured antireflective surfaces

Broadband antireflection schemes for silicon surfaces based on the moth-eye principle and comprising arrays of subwavelength-scale pillars are applicable to solar cells, photodetectors, and stealth technologies and can exhibit very low reflectances. We show that rigorous coupled wave analysis can be used to accurately model the intricate reflectance behavior of these surfaces and so can be used to explore the effects of variations in pillar height, period, and shape. Low reflectance regions are identified, the extent of which are determined by the shape of the pillars. The wavelengths over which these low reflectance regions operate can be shifted by altering the period of the array. Thus the subtle features of the reflectance spectrum of a moth-eye array can be tailored for optimum performance for the input spectrum of a specific application

Classical Concepts in Quantum Programming

The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the increasing hardware complexity and fully exploit its potential. This paper investigates, how classical concepts like hardware abstraction, hierarchical programs, data types, memory management, flow of control and structured programming can be used in quantum computing. The experimental language QCL will be introduced as an example, how elements like irreversible functions, local variables and conditional branching, which have no direct quantum counterparts, can be implemented, and how non-classical features like the reversibility of unitary transformation or the non-observability of quantum states can be accounted for within the framework of a procedural programming language.Comment: 11 pages, 4 figures, software available from http://tph.tuwien.ac.at/~oemer/qcl.html, submitted for QS2002 proceeding