Showing papers on "Quantum published in 1987"

Quantum-classical crossover of the transition rate in the damped double well

Abstract: The author studies the barrier-crossing rate Gamma for a particle in a symmetric double well coupled to a sluggish bath; the aim is to justify the quantum simulation procedure used in related work on the diffusion of hydrogen in metals. He uses path-integral methods to discuss the transition between the low-temperature tunnelling and the high-temperature barrier-jumping regimes, and suggests a unifying formula valid for both, which relates Gamma to the probability of finding the centroid of the quantum path at the barrier top. Numerical results for Gamma are presented for the case of the quartic double well.

The Physics of Time Reversal

Abstract: The notion that fundamental equations governing the motions of physical systems are invariant under the time reversal transformation ("T") has been an important, but often subliminal, element in the development of theoretical physics. It serves as a powerful and useful tool in analyzing the structure of matter at all scales, from gases and condensed matter to subnuclear physics and the quantum theory of fields. The assumption of invariance under "T" was called into question, however, by the 1964 discovery that a closely related assumption, that of "CP" invariance (where "C" is charge conjugation and "P" is space inversion), is violated in the decay of neutral "K" mesons. In "The Physics of Time Reversal," Robert G. Sachs comprehensively treats the role of the transformation "T," both as a tool for analyzing the structure of matter and as a field of fundamental research relating to "CP" violation. For this purpose he reformulates the definitions of "T, P, " and "C" so as to avoid subliminal assumptions of invariance. He summarizes the standard phenomenology of "CP" violation in the "K"-meson system and addresses the question of the mysterious origin of "CP" violation. Using simple examples based on the standard quark model, Sachs summarizes and illustrates how these phenomenological methods can be extended to analysis of future experiments on heavy mesons. He notes that his reformulated approach to conventional quantum field theory leads to new questions about the meaning of the transformations in the context of recent theoretical developments such as non-Abelian gauge theories, and he suggests ways in which these questions may lead to new directions of research.

Interpreting the anholonomy of coiled light

Abstract: Circular birefringence of purely geometric origin was recently predicted1 and observed2 in helically coiled monomode optical fibres, and widely reported3–5 as a successful application to photons of a general theory6,7 for phase shifts in adiabatically transported quantum states. However, earlier similar observations8–10 had been interpreted not by quantum mechanics but simply as a classical anholonomy, namely parallel transport of the polarization11. Indeed, because the magnitude of the effect is independent of the wavelength of the light as well as Planck's constant, it might seem that 'classical' here means that not only quantum but also wave effects can be neglected. Here, I argue that these experiments, and their discrete analogues, are most appropriately described at the level of classical electromagnetism; the parallel transport law can then be derived (rather than assumed8–11) and nonadiabatic polarization changes calculated.

Squeezing of quantum solitons.

Abstract: We develop a quantum theory of propagation in dispersive nonlinear media. Quantum fluctuations are handled via the coherent-state positive-P representation. A stochastic nonlinear Schr\"odinger equation in the field variables is obtained which predicts wide band squeezing in the region of anomalous dispersion. For soliton inputs, fluctuations are reduced over the soliton bandwidth. This leads to quantum solitons which have quadrature fluctuations less than the level of vacuum fluctuations.

Finite-Q cavity electrodynamics: dynamical and statistical aspects

Abstract: Solutions of the basic equations of a simplified model of the cavity quantum electrodynamics are presented under the condition that the single-photon Rabi frequency is much larger than the cavity decay rate. Such solutions are used to calculate the quantum-statistical properties of the field and atomic observables under a variety of initial conditions involving the states of the field and atom. Effects of increasing cavity damping and of the addition of thermal photons on collapse and revival phenomena are discussed. Phase-sensitive aspects of the cavity field are also treated. Quantum effects are shown to be most easily isolated by sending an atom initially prepared in a dressed state for such a state does not evolve further under the influence of a classical field. The appearance of squeezing in the cavity field is demonstrated. The squeezing is most prominent for a coherently prepared atom passing through an empty cavity. The quantum features of the complex dipole moment and their detectability are also discussed in detail.

Conformal anomaly and surface energy for Potts and Ashkin-Teller quantum chains

Abstract: Exact equivalences between the critical quantum Potts and Ashkin-Teller chains and a modified XXZ Heisenberg chain have recently been derived by Alcaraz et al (1987). The leading finite-size corrections to the ground-state energies of these chains are derived using the methods of de Vega and Woynarovich (1985) and Eckle. Exact results are then obtained for the conformal anomaly of each model, and for the surface energy in the case of free boundaries.

Semiclassical quantization using classical perturbation theory: Algebraic quantization of multidimensional systems

Abstract: The method of algebraic quantization, a semiclassical analog of Van Vleck perturbation theory, is applied to multidimensional resonant, nonresonant, and nearly resonant systems. perturb, a special purpose program written in C, is utilized to implement classical perturbation theory efficiently to high order. States corresponding to both regular and chaotic classical regimes are quantized, and accurate eigenvalues obtained in both cases. Various quantization rules are compared, and a novel symmetry preserving rule is given which leads to good agreement with quantum mechanics. The method is able to reproduce purely quantum mechanical splittings to very good accuracy. Algebraic quantization combined with Pade resummation is used to determine energy eigenvalues for a resonant system with five degrees of freedom.

Obtainment of thermal noise from a pure quantum state

Abstract: It is shown that if one has access to only one mode of a two-mode squeezed-vacuum state, the photon statistics of this mode is indistinguishable from that of a thermal distribution. Parametric interactions that give rise to two-mode squeezing thus provide a mechanism for thermalization that is intrinsically quantum mechanical.

Quantised Hall effect

Abstract: A review of the quantised Hall effect is given. The author surveys experiments and theories on the normal and fractional quantum Hall effect including recent developments. As a background to the effect, which is a most remarkable manifestation of the Landau quantisation, the author starts with the description of the two-dimensional electron system in magnetic fields. As a closely related topic, the author also discusses the singular localisation of states specific to systems under the Landau quantisation in two dimensions. The determination of the fine-structure constant including the quantum Hall method is also briefly reviewed. In giving a self-contained account of the effect we emphasise the special features of the quantised Hall effect, which has an aspect of macroscopic quantum phenomenon on the one hand, and invokes, in the presence of electron-electron interactions, a new quantum liquid state on the other.

Quantum Theory of Multiport Optical Homodyning

Abstract: Multiport optical homodyning concerns the combining of a local oscillator with N − 1 signals of the same frequency in a lossless 2N-port junction or an N × N directional coupler. An operator representation is derived for quantum measurements made on these signals in the limit of a strong local oscillator. The local oscillator may otherwise be in an arbitrary quantum state.

Connection between long-range correlations in quantum spectra and classical periodic orbits.

Abstract: We analyze long-range correlations in quantum spectra within the framework of periodic-orbit theory and find excellent agreement between level clustering in quantum spectra and semiclassical predictions. The analysis demonstrates how classical chaotic motion is reflected in the spectral properties of the corresponding quantum system.

Theory of light detection in the presence of feedback

Abstract: The usual open-loop quantum and semiclassical theories of light detection are extended to include closed-loop operation in which there is feedback from the detector to the source. It is shown that the unmistakable signatures of nonclassical light associated with open-loop detection, such as sub-shot-noise spectra and sub-Poisson photo-counts, do not carry over to closed-loopsystems. This behavior is illustrated through quantitatively indistinguishable quantum and semiclassical analyses of two recent closed-loop experiments in which sub-Poisson photocount statistics were produced. It turns out that if the open-loop illumination does not require the use of quantum photodetection theory, then neither does the closed-loop illumination. Conversely, if the open-loop illumination is nonclassical, then the closed-loop behavior must be analyzed quantum mechanically. The use of nonclassical field correlations to obtain light beams that give sub-Poisson open-loop photocounts from these closed-loop arrangements is discussed and generalized into a synthesis procedure for producing light beams with arbitrary open-loop photocount statistics.

Random-Matrix Theory and Universal Statistics for Disordered Quantum Conductors

Abstract: An Ansatz is proposed for the joint probability distribution of the eigenvalues of the transfer matrix in the quantum transport problem, based on symmetry arguments and a "maximum entropy" hypothesis. The local statistical behavior of the distribution is predicted to be that of the well-known random-matrix ensembles of Wigner and Dyson; and this result is confirmed by independent numerical calculations. For metals this behavior leads to size- and disorder-independent conductance fluctuations, and this approach suggests an alternative framework for the scaling theory of localization.

Integral quantum Hall effect for nonspecialists

Abstract: An attempt is made to develop a description of the multielectron quantum state responsible for the integral quantum Hall effect. One goal is to provide intuitive support for the very powerful and general argument of Laughlin that the theoretical relationship is insensitive to complicating details in the interior of the sample. The model the author uses is somewhat more realistic than heretofore in that it is three dimensional, does not ignore the atomic structure of the bulk matter, and does not use an effective-mass approximation. In order to treat the problem quantum mechanically, the complete system, including circuitry external to the system of interest, is replaced by a model closed system consisting of a finite number of electrons. In this model, states with a finite Hall current and voltage are metastable against decay caused by interactions outside the model, such as those with bulk matter excitations. Such states describe the true situation well only in the conductivity plateaus; between plateaus, there would be current flow between the Hall voltage probes corresponding to decaying states. Experimental constraints replace this transverse current by a voltage drop along the direction of current flow. The interactions between the electrons are expressed in terms of a self-consistent potential which gives an independent-particle description as a starting point, and residual interactions which are treated by perturbation theory. The self-consistent potential is found to be important in understanding the properties of the quantum state of the system, such as the existence of the plateaus in conductivity and how the electrons in the (effective) two-dimensional region come to equilibrium with the different Fermi levels in the voltage probes. To all finite orders of perturbation theory, the residual interactions are found not to alter the quantized Hall conductivity.

Quantum-mechanical derivation of the equations of motion for Davydov solitons.

Abstract: The equations of the Davydov model, which describe energy propagation along linear-chain molecules by a soliton mechanism, have heretofore been derived by a combination of quantum-mechanical and classical techniques. We give here a derivation which is completely based on quantum mechanics.

Resonant excitation transfer: A quantum electrodynamical study

Abstract: A new quantum electrodynamical (QED) method is presented, based in the Schrodinger representation, for the calculation of the rate of energy transfer between identical molecules. In contrast to existing methods in this representation, the new treatment gives explicitly causal and energy‐conserving results. By returning to perturbation theory the correct, complex form for the electric dipole–electric dipole interaction tensor is obtained, without recourse to the physical, ‘‘outgoing wave’’ arguments of quantum scattering theory necessary if the Fermi rule is used. This method also allows a new interpretation for the role of the time‐ordered diagrams involved, which may be useful in the rigorous treatment of higher order cooperative processes. The QED treatment uses virtual photon coupling, and incorporates both the Coulombic, R−6 dependence, and the R−2 dependence characteristic of two‐step radiative transfer.

Hydrogen transfer in double minimum potential: Kinetic properties derived from quantum dynamics

Abstract: The interaction of hydrogen transfer in a double minimum potential with a condensed phase environment is studied. For a symmetric double minimum system, the tunneling motion in the vibrational ground state is retarded efficiently by fluctuation as well as by rearrangement of the lattice consisting of harmonic oscillators. Environmental displacements with large inertia cause dynamic asymmetry by failing to cooperate with the transfer motion and favor a thermally activated process even at low temperatures. To describe such processes, an effective Hamiltonian is derived, which consists of a leading term referring to a one‐dimensional transfer motion along an asymmetric potential profile and of a random perturbation term linear in the transfer coordinate. The power spectral density is derived for the perturbation given as a superposition of the time‐dependent quantum mechanical expectation values of the vibrational displacements in the environment. A master equation treatment is proposed to describe the kinet...

Superlocalization of Electrons and Waves in Fractal Media

Abstract: We show that impurity quantum states and Anderson localized states exhibit "superlocalization" in fractal media, that is their wave function decays faster than exponentially with distance More precisely, the wave function decays at large distances like exp [- |x|a] with a > 1 In the specific case of the quantum percolation problem at the percolation concentration pc, we argue that a ≈ 19 for d = 3 Analogous results hold for waves Applications are suggested to disordered and amorphous materials and to porous materials

Squeezing in Correlated Quantum Systems

Abstract: We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.

Dissipation and quantum fluctuations in granular superconductivity

Abstract: The effects of dissipation and quantum fluctuations on the onset of superconductivity are discussed. A model for a granular superconductor is considered which consists of a d-dimensional array of resistively shunted Josephson junctions with charging energy incorporating the long-ranged Coulomb interaction. In one dimension the model exhibits a T = 0 dynamical transition into a state with vanishing resistivity at a critical value of the shunt resistance, R/sub S/. Most surprisingly the system is always statically disordered even in the superconducting state. For dgreater than or equal to2 both the dynamical response and static ordering depend sensitively on R/sub S/. Specifically, for R/sub S/ less than a critical value of order the quantum of resistance, h/4e/sup 2/, the dissipation suppresses quantum fluctuations enabling the array to order at T = 0 for arbitrarily weak Josephson coupling. Above this critical resistance and for weak coupling, the order parameter suffers phase slips due to quantum tunneling driving the system normal.

Quantum kinetic equation for electronic transport in nondegenerate semiconductors

Abstract: We give a concise first-principles derivation of a quantum kinetic equation valid for a nondegenerate semiconductor. The general equations for the full correlation function are reduced to a non-Markovian quantum kinetic equation governing the Wigner distribution function. For the case of completed collisions we transform the kinetic equation to a form directly applicable to Monte Carlo methodology. The interacting spectral densities, which are a central feature of our theory, allow a systematic treatment of effects like collisional broadening and the intracollisional field effect. Results for a simple model semiconductor show that collision broadening is responsible for a significant increase of carriers in both the low- and high-energy regions of the hot-electron distribution function.

Disentanglement of quantum wave functions: Answer to ‘‘Comment on ‘Unified dynamics for microscopic and macroscopic systems’ ’’

Abstract: It is shown that the assumption of a stochastic localization process for the quantum wave function is essentially different from the suppression of coherence over macroscopic distances arising from the interaction with the environment and allows for a conceptually complete derivation of the classical behavior of macroscopic bodies.