Showing papers on "Quantum published in 1992"

Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise.

Abstract: We use the influence functional path-integral method to derive an exact master equation for the quantum Brownian motion of a particle linearly coupled to a general environment (ohmic, subohmic, or supraohmic) at arbitrary temperature and apply it to study certain aspects of the loss of quantum coherence.

The Transition to Chaos: Conservative Classical Systems and Quantum Manifestations

Abstract: 1. Overview / 2. Fundamental Concepts / 3. Area Preserving Maps / 4. Global Properties / 5. Random Matrix Theory / 6. Bounded Quantum Systems / 7. Manifestations of Chaos in Quantum Scattering Processes / 8. Semi-Classical Theory -- Path Integrals / 9. Time-Periodic Systems / 10. Stochastic Manifestations of Chaos / Appendices.

Weaving a classical metric with quantum threads

Abstract: Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that (i) while local operators such as the metric at a point may not be well defined, there do exist nonlocal operators, such as the area of a given two-surface, which can be regulated diffeomorphism invariantly and which are finite without renormalization; (ii) there exist quantum states which approximate a given metric at large scales, but such states exhibit a discrete structure at the Planck scale.

Classification of Abelian quantum Hall states and matrix formulation of topological fluids.

Abstract: We give a simple and unified treatment of quantum topological fluids such as the quantum Hall fluid. We show that the order in such fluids can be characterized by a symmetric matrix K, in terms of which various physical quantities can be determined. We construct K by a matrix iteration procedure which may be decomposed into two simple elementary steps. The hierarchy construction is shown to be contained in our matrix iteration construction. The relationship between the vortex basis and the dual electron basis is clarified. We also show that under certain mild assumptions the generalized hierarchy construction exhausts all possible Abelian fractional quantum Hall states. We identify and determine the topological quantity known as the shift. Our formalism may be relevant for recent experimental data on multilayered systems.

Wave-function quantum stochastic differential equations and quantum-jump simulation methods

Abstract: The quantum-stochastic-differential-equation formulation of driven quantum-optical systems is carried out in the interaction picture, and quantum stochastic differential equations for wave functions are derived on the basis of physical principles. The Ito form is shown to be the most practical, since it already contains all the radiation reaction terms. The connection between this formulation and the master equation is shown to be very straightforward. In particular, a direct connection is made to the theory of continuous measurements, which leads directly to the method of quantum-jump simulations of solutions of the master equation. It is also shown that all conceivable spectral and correlation-function information in output fields is accessible by means of an augmentation of the simulation process. Finally, the question of the reality of the jumps used in the simulations is posed.

Application of a multilevel Redfield theory to electron transfer in condensed phases

Abstract: A quantum mechanical theory of photoinduced electron transfer, based on the Redfield theory of relaxation, is developed and applied to the standard two state–one mode system interacting with a thermal bath. Quantum mechanical treatment of the reaction coordinate allows incorporation of both finite vibrational dephasing and energy flow rates into the description of electron transfer dynamics. The field–matter interaction is treated explicitly to properly incorporate the total energy and magnitude of the vibrational coherence present in the initially prepared state. Calculation of the reduced density matrix of the system is carried out in a vibronic basis that diagonalizes the electron exchange coupling so that the method is valid for arbitrarily large coupling strength. For weak electronic coupling, we demonstrate the equivalence between the results from Redfield theory and those obtained from the standard perturbative expression (golden rule) for nonadiabatic electron transfer. We then discuss quantitatively the breakdown of the Fermi golden rule with increasing electronic coupling strength. The failure of the golden rule is seen to result from either slow energy equilibration in the reactant or product well or from quantum interference effects resulting from finite dephasing rates. For cases where the reorganization energy is large compared to the frequency of reactive motion, such that we may ignore nuclear tunneling, results from the theory show good agreement with those from the semiclassical Landau–Zener theory when motion of the reaction coordinate through the surface crossing region can be considered to be ballistic. Finally results are shown in the weak damping (coherent) limit that demonstrate interference effects between phase coherences involving states in both wells.

Observation of quantum frequency conversion

Abstract: Quantum frequency conversion, a process with which an input beam of light can be converted into an output beam of a different frequency while preserving the quantum state, is experimentally demonstrated for the first time. Nonclassical intensity correlation (\ensuremath{\simeq}3 dB) between two beams at 1064 nm is used as the input quantum property. When the frequency of one of the beams is converted from 1064 to 532 nm, nonclassical intensity correlations (\ensuremath{\simeq}1.5 dB) appear between the up-converted beam and the remaining beam. Our measurements are in excellent agreement with the quantum theory of frequency conversion. The development of tunable sources of novel quantum light states seems possible.

Hydrogenic impurity states in quantum dots and quantum wires.

Abstract: The energies of hydrogenic impurity states with an impurity atom located at the center of a quantum dot and on the axis of a quantum-well wire are studied. These two systems are all assumed to have an infinite confining potential. In the case of the quantum dot, the impurity eigenfunctions are expressed in terms of Whittaker functions and Coulomb scattering functions. The calculated ground-state energy of the impurity approaches the correct limit of three-dimensional hydrogen atom as the radius of the quantum dot becomes very large. In the case of the quantum-well wire, analytical solutions can be obtained if we divide the space into a two-dimensional subspace (perpendicular to the axis of the quantum-well wire) and a one-dimensional subspace (parallel to the axis of the quantum-well wire). The calculated ground-state energy of the quantum-well wire approaches the ground-state energy of the shallow-impurity atom located on the surface as the radius of the wire becomes infinite. Variations of the state energies with the radius of the quantum dot and the quantum-well wire are obtained.

Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom.

Abstract: Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ``vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.

Schrödinger-cat states in the resonant Jaynes-Cummings model: Collapse and revival of oscillations of the photon-number distribution

Abstract: The Jaynes-Cummings model of optical resonance describes the simplest fully quantized interaction between two quantum systems of different nature: a two-level atom (fermionic system) and a quantized field mode (bosonic system). This interaction leads to extreme quantum entanglement of the atom and field. However, the model also predicts that, at precisely half of the revival time, the atom and field become asymptotically disentangled. This disentanglement becomes more exact as the coherent-state amplitude increases. In this paper we investigate the nature of the pure-field-state superposition generated at such times

Quantum continual measurements and a posteriori collapse on CCR

Abstract: A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one.

String Theory Modifies Quantum Mechanics

Abstract: We argue that the light particles in string theory obey an effective quantum mechanics modified by the inclusion of a quantum-gravitational friction term, induced by unavoidable couplings to unobserved massive string states in the space-time foam. This term is related to the $W$-symmetries that couple light particles to massive solitonic string states in black hole backgrounds, and has a formal similarity to simple models of environmental quantum friction. It increases apparent entropy, and may induce the wave functions of macroscopic systems to collapse.

Quantum Collapses and Revivals in a Quantized Trap

Abstract: A single two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field. When the atom's centre-of-mass motion is in a coherent state, we show that the atomic inversion exhibits collapses and revivals. Whereas in the Jaynes-Cummings model this behaviour occurs due to the discrete nature of the light field, in our case the behaviour is due to the discrete nature of the vibrational trap states. The Q-function for the external motion is also calculated and shown to break into two peaks in the collapse region. Finally the parameter ranges under which the collapses and revivals can be observed are discussed, as well as the possibility of an experiment.

Semiclassical quantization of chaotic billiards: a scattering theory approach

Abstract: The authors derive a semiclassical secular equation which applies to quantized (compact) billiards of any shape. Their approach is based on the fact that the billiard boundary defines two dual problems: the 'inside problem' of the bounded dynamics, and the 'outside problem' which can be looked upon as a scattering from the boundary as an obstacle. This duality exists both on the classical and quantum mechanical levels, and is therefore very useful in deriving a semiclassical quantization rule. They obtain a semiclassical secular equation which is based on classical input from a finite number of classical periodic orbits. They compare their result to secular equations which were derived by other means, and provide some numerical data which illustrate their method when applied to the quantization of the Sinai billiard.

Quantum transport in small disordered samples from the diffusive to the ballistic regime

Abstract: The authors review conductance effects in small samples at low temperatures where quantum confinement and quantum interference are significant perturbations on the classical Drude conductance. In disordered materials, the elastic scattering of the carriers from impurities leads to random conductance fluctuations or resistance fluctuations. The fluctuations arise because of interference among the scattered waves, and they are random and sample specific because the impurity potential is. The fluctuations appear in response to changes in many extrinsic parameters such as the carrier density, the applied measuring current, external electric fields and external fields. The interface fluctuations have consequences for much larger samples, particularly in flicker noise, even though quantum coherence is obtained only over regions much smaller than the sample size, in completely phase coherent conductors a number of purely quantum effects are observed, including non-local response and Aharonov-Bohm effects. Other 'applications' of the quantum fluctuations include studies of reciprocity (which is related to time-reversal symmetry) and of the effects of the measurement probes on a quantum system. Interestingly, these are two areas where disagreements remain with theoretical calculations. The size and correlation scale of the fluctuations, however, are mainly in agreement with theoretical calculations of the same quantities, although one or two other small disagreements of detail remain. In very clean semiconductor heterostructures, the mean free path length between scattering events is large enough to allow for studies of ballistic transport that reveal a variety of conductance anomalies that result from device shape (as opposed to fortuitous placement of impurities as in the metals). These ballistic effects are reviewed briefly and connection is made to the effects of disorder in ballistic systems, and experiments on disordered metal samples are reviewed in detail.

From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory

Abstract: The history of quantum theory is a maze of conceptual problems, through which Olivier Darrigol aims to provide a lucid and learned guide, tracking the role of formal analogies between classical and quantum theory. From Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. Rather than focusing on qualitative, global arguments, Darrigol's study follows the lines of mathematical reasoning and symbolizing and sets out to show the motivations of early quantum theorists more precisely - and provocatively. "From c-Numbers to q-Numbers" aims to be a philosophically perceptive and mathematically precise history of quantum mechanics.

Quantum Measurement: Quantum nondemolition measurements

Abstract: Some future gravitational-wave antennas will be cylinders of mass approximately 100 kilograms, whose end-to-end vibrations must be measured so accurately (10(-19) centimeter) that they behave quantum mechanically. Moreover, the vibration amplitude must be measured over and over again without perturbing it (quantum nondemolition measurement). This contrasts with quantum chemistry, quantum optics, or atomic, nuclear, and elementary particle physics, where one usually makes measurements on an ensemble of identical objects and does not care whether any single object is perturbed or destroyed by the measurement. This article describes the new electronic techniques required for quantum nondemolition measurements and the theory underlying them. Quantum nondemolition measurements may find application elsewhere in science and technology.

Thermo-electric properties of quantum point contacts

Abstract: The conductance, the thermal conductance, the thermopower and the Peltier coefficient of a quantum point contact all exhibit quantum size effects. The authors review and extend the theory of these effects. In addition, they review their experimental work on the quantum oscillations in the thermopower, observed using a current heating technique. New data are presented showing evidence for quantum steps in the thermal conductance, and (less unequivocally) for quantum oscillations in the Peltier coefficient. For these new experiments the authors have used a quantum point contact as a miniature thermometer.

Adiabatic quantum transport in multiply connected systems

Abstract: The adiabatic quantum transport in multiply connected systems is examined. The systems considered have several holes, usually three or more, threaded by independent flux tubes, the transport properties of which are described by matrix-valued functions of the fluxes. The main theme is the differential-geometric interpretation of Kubo's formulas as curvatures. Because of this interpretation, and because flux space can be identified with the multitorus, the adiabatic conductances have topological significance, related to the first Chern character. In particular, they have quantized averages. The authors describe various classes of quantum Hamiltonians that describe multiply connected systems and investigate their basic properties. They concentrate on models that reduce to the study of finite-dimensional matrices. In particular, the reduction of the "free-electron" Schr\"odinger operator, on a network of thin wires, to a matrix problem is described in detail. The authors define "loop currents" and investigate their properties and their dependence on the choice of flux tubes. They introduce a method of topological classification of networks according to their transport. This leads to the analysis of level crossings and to the association of "charges" with crossing points. Networks made with three equilateral triangles are investigated and classified, both numerically and analytically. Many of these networks turn out to have nontrivial topological transport properties for both the free-electron and the tight-binding models. The authors conclude with some open problems and questions.

Particle Labels and the Theory of Indistinguishable Particles in Quantum Mechanics

Abstract: We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description.

Molecular quantum similarity measures and N-dimensional representation of quantum objects. I. Theoretical foundations†

Abstract: A conceptual general definition of quantum similarity and similarity indices are given. The interpretation of molecular similarity from a quantum theoretical point of view is analyzed. Various approximations are also discussed.

Notes on quantum groups and quantum de Rham complexes

Abstract: De Rham complexes of quantum spaces and quantum groups are studied by means of extension of the “universal co-action” technique to the differential algebras.

Physical nonlinear aspects of classical and quantum q-oscillators

Abstract: The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat and second order correlation function of the q-oscillator which may serve for experimental checks for the non linearity.

Observation of quantum wire formation at intersecting quantum wells

Abstract: We report the first observation of a quantum bound state formed at the junction of two intersecting quantum wells in the shape of a T. The atomically precise T junctions are fabricated by a novel cleaved edge overgrowth process in the AlGaAs/GaAs system. The identification of bound states with energies in excess of 20 meV is made by optical emission and absorption spectroscopy. Such quantum wire states are caused by the unique confinement of the lowest state wave function to the region of the T junction.