Showing papers on "Open quantum system published in 1993"

Monte Carlo wave-function method in quantum optics

Abstract: We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.

The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics

Abstract: 1. Quantum mechanics and its interpretation 2. Hamilton-Jacobi theory 3. Elements of the quantum theory of motion 4. Simple applications 5. Interference and tunnelling 6. The classical limit 7. Many-body systems 8. Theory of experiments 9. Spin 1/2: The Pauli theory 10. Spin 1/2: The rigid rotator 11. The Einstein-Podolsky-Rosen experiment and nonlocality 12. Relativistic quantum theory References Index.

Quantum trajectory theory for cascaded open systems.

Abstract: The quantum trajectory theory of an open quantum system driven by a photoemissive source is formulated. The formalism is illustrated by applying it to photon scattering from an atom driven by strongly focused coherent light.

Semiconductor Quantum Dots

Abstract: "Semiconductor Quantum Dots" presents an overview of the background and recent developments in the rapidly growing field of ultrasmall semiconductor microscrystallites, in which the carrier confinement is sufficiently strong to allow only quantized states of the electrons and holes. The main emphasis of this book is the theoretical analysis of the confinement induced modifications of the optical and electronic properties of quantum dots in comparison to extended materials. The book develops the theoretical background material for the analysis of carrier quantum-confinement effects, it introduces different confinement regimes for absolute or center-of-mass motion quantization of the electron-hole-pairs, and it gives an overview of the best approximation schemes for each regime. A detailed discussion of the carrier states in quantum dots is presented, including variational calculations, a configuration interaction approach, and quantum Monte Carlo techniques. Surface polarization instabilities are analyzed which lead to the self-trapping of carriers near the surface of the dots and the influence of spin-orbit coupling on the quantum-confined carrier states is discussed. The linear and nonlinear optical properties of small and large quantum dots are analyzed in detail, including transient optical nonlinearities (photon echo) and two-photon transitions. The influence of the quantum-dot size distribution in many realistic samples is outlined, including the analysis of quantum dot growth laws and universal size distributions. Phonons in quantum dots, as well as the influence of external electric or magnetic fields are discussed. The recent developments dealing with regular systems of quantum dots are reviewed, including a lattice model of quantum dots and quantum dot superlattices.

Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere

Abstract: It is shown that the evolution of an open quantum system whose density operator obeys a Markovian master equation can in some cases be meaningfully described in terms of stochastic Schrodinger equations (SSE’s) for its state vector. A necessary condition for this is that the information carried away from the system by the bath (source of the irreversibility) be recoverable. The primary field of application is quantum optics, where the bath consists of the continuum of electromagnetic modes. The information lost from the system can be recovered using a perfect photodetector. The state of the system conditioned on the photodetections undergoes stochastic quantum jumps. Alternative measurement schemes on the outgoing light (homodyne and heterodyne detection) are shown to give rise to SSE’s with diffusive terms. These three detection schemes are illustrated on a simple quantum system, the two-level atom, giving new perspectives on the interpretation of measurement results. The reality of these and other stochastic processes for state vectors is discussed.

The quantum state diffusion picture of physical processes

Abstract: In earlier papers the authors introduced a quantum state diffusion model for the evolution of an individual open quantum system and proved localization theorems based on this model. This paper shows in more detail how the diffusion leads to localization in position and phase space, and to symmetry breaking for chiral molecules. The theory of radioactive decay of absorbers and detectors is described in the state diffusion picture. The Mott and Gurney theory of latent image formation in photography is presented in its state diffusion version. It is an example of quantum detection without significant amplification.

Quantum state diffusion, localization and quantum dispersion entropy

Abstract: The quantum state diffusion model introduced in an earlier paper represents the evolution of an individual open quantum system by an Ito diffusion equation for its quantum state. The diffusion and drift terms in this equation are derived from interaction with the environment. In this paper two localization theorems are proved. The dispersion entropy theorem shows that under special conditions, which are commonly satisfied to a good approximation, the mean quantum dispersion entropy, which measures the mean dispersion or delocalization of the quantum states, decreases at a rate equal to a weighted sum of effective interaction rates, so that the localization always increases in the mean, except when the effective interaction with the environment is zero. The general localization theorem provides a formula for more general conditions.

Fundamental Systems in Quantum Optics

Abstract: (1993). Fundamental Systems in Quantum Optics. Journal of Modern Optics: Vol. 40, No. 10, pp. 2057-2057.

Consistent interpretation of quantum mechanics using quantum trajectories.

Abstract: The probabilistic element of quantum theory can be combined with the unitary time evolution of Schr\"odinger's equation in a natural and consistent way using the idea of a quantum trajectory, the quantum analog of the trajectory traced out in phase space as a function of time by a point representing the state of a closed classical system. A family of quantum trajectories can be defined using bases for the quantum Hilbert space at different times chosen so that an appropriate noninterference condition, related to the Gell-Mann and Hartle notion of medium decoherence, is satisfied. The result is a generalization of the consistent histories approach to quantum mechanics.

Quantum dynamical model for wave-function reduction in classical and macroscopic limits

Abstract: In this paper, a quantum dynamical model describing the quantum-measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and the macroscopic limit with very large particle number in the measuring instrument, this model generally realizes the wave-packet collapse in quantum measurement as a consequence of the Schrodinger time evolution in either the exactly solvable case or the non-exactly-solvable case. For the latter, the quasiadiabatic case is explicitly analyzed by making use of the high-order adiabatic-approximation method, which manifests the wave-packet collapse as well as in the exactly solvable case

Quantum phase and phase dependent measurements

Abstract: The correct description of the phase variable in quantum mechanics is a question rooted in its earliest formulations. The atom mechanics [1] of Bohr and Sommerfeld—the precursor of modern quantum mechanics—ascribes a central role to action-angle variables. However, Heisenberg's matrix mechanics and Schrodinger's wave mechanics are formulated [2] in terms of the canonical variables representing cartesian coordinates and momenta. Stimulated by this work London [3] attempted a reformulation of these theories in the previously favored action-angle variables. However, this attempt failed due to the difficulty in ascribing quantum operators to the angle variables of classical theory. Despite these difficulties London found [4] an operator representation of the complex exponential of these angle variables. The quantum phase of light made its first appearance in Dirac's classic paper [5] on the quantization of the radiation field. In contrast to modern methods, he constructed the annihilation and creation operators for each field mode from the corresponding amplitude and phase operators. Phase and its quantum nature acquired new significance with the development of lasers in the early sixties: theoretical investigations highlighted significant problems with Dirac's original proposal for the phase operator. A particularly elegant illustration of the difficulty was given by Louisell [6] in 1963. The advent of phase sensitive quantum noise as demonstrated experimentally in the production and detection of squeezed light [7] has created a new wave of interest in the nature of quantum optical phase leading to the discovery of the hermitian optical phase operator [8]. There has followed an explosion of theoretical activity in this area stimulating fresh experimental investigations. In preparing this special issue we have attempted to present the current state of this active and rapidly moving field. We have arranged the papers into what we hope is a coherent representation of the field. The first papers give a historical perspective and overview of current thinking. The two recent experimental investigations which follow are intimately connected to the phase space description of quantum mechanics based on quasi-probability distributions. The representa tion of phase via phase space and its connection with phase-dependent measurements and the phase operator are addressed in the next section. Some more formal considerations pertinent to phase are presented in the following section. Gravitational wave detection and optical communication have motivated the study of the limits of phase noise. Some recent investigations on such optimal phase states are presented. The issue concludes with two papers discussing the significance of phase in light-matter interactions. In concluding we express our gratitude to the authors of the papers in this volume for their efforts in preparing their high quality presentations.

Exact description of spectral correlators by a quantum one-dimensional model with inverse-square interaction.

Abstract: The universal correlations which describe the response of energy levels of a disordered metallic grain to an arbitrary perturbation are shown to be equivalent to time-dependent correlations of a one-dimensional quantum Hamiltonian with inverse-square interaction. These resutls establish a direct connection between a strongly interacting quantum Hamiltonian, the nonlinear \ensuremath{\sigma} model of disordered electronic systems, and quantum chaotic spectra. As a consequence we have an expression for the correlation function of the quantum Hamiltonian which we believe to be exact for all space and time.

Quantum simulation of reaction dynamics by density-matrix evolution

Abstract: A density matrix evolution(DME) method to simulate the dynamics of quantum systems embedded in a classical environment is presented. The method is applicable when the quantum dynamical degrees of freedom can be described in a Hilbert space of limited dimensionality. The method is applied to the case of proton-transfer reactions in a fluctuating double-well potential [details are given in the following paper in this issue] and compared to other analytical and numerical solutions. The embedding of the quantum system within the classical system by using consistent equations of motion for the classical system with-proper conservation properties is discussed and applied to the one-dimensional collision of a classical particle with a quantum oscillator.

Impossible Measurements on Quantum Fields

Abstract: It is shown that the attempt to extend the notion of ideal measurement to quantum field theory leads to a conflict with locality, because (for most observables) the state vector reduction associated with an ideal measurement acts to transmit information faster than light. Two examples of such information-transfer are given, first in the quantum mechanics of a pair of coupled subsystems, and then for the free scalar field in flat spacetime. It is argued that this problem leaves the Hilbert space formulation of quantum field theory with no definite measurement theory, removing whatever advantages it may have seemed to possess vis a vis the sum-over-histories approach, and reinforcing the view that a sum-over-histories framework is the most promising one for quantum gravity.

Quantum phase and quantum phase operators: some physics and some history

Abstract: After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.

Solvable dynamical model for a quantum measurement process

Abstract: A model Hamiltonian describing an energy-exchange process between an ultrarelativistic particle and a one-dimensional spin array is proposed and solved exactly. Interesting relations with the quantum measurement problem are discussed

Quantum Structures Due to Fluctuations of the Measurement Situation

Abstract: We analyze the meaning of the nonclassical aspects of quantum structures. We proceed by introducing a simple mechanistic macroscopic experimental situation that gives rise to quantum-like structures. We use this situation as a guiding example for our attempts to explain the origin of the nonclassical aspects of quantum structures. We see that the quantum probabilities can be introduced as a consequence of the presence of fluctuations on the experimental apparatuses, and show that the full quantum structure can be obtained in this way. We define the classical limit as the physical situation that arises when the fluctuations on the experiment apparatuses disappear. In the limit case we come to a classical structure, but in between we find structures that are neither quantum nor classical. In this sense, our approach not only gives an explanation for the nonclassical structure of quantum theory, but also makes it possible to define and study the structure describing the intermediate new situations. By investigating how the nonlocal quantum behavior disappears during the limiting process, we can explain the“apparent”locality of the classical macroscopic world. We come to the conclusion that quantum structures are the ordinary structures of reality, and that our difficulties of becoming aware of this fact are due to prescientific prejudices, some of which we point out.

Decoherence of Correlation Histories

Abstract: We use a $\lambda\Phi^4$ scalar quantum field theory to illustrate a new approach to the study of quantum to classical transition. In this approach, the decoherence functional is employed to assign probabilities to consistent histories defined in terms of correlations among the fields at separate points, rather than the field itself. We present expressions for the quantum amplitudes associated with such histories, as well as for the decoherence functional between two of them. The dynamics of an individual consistent history may be described by a Langevin-type equation, which we derive. oindent {\it Dedicated to Professor Brill on the occasion of his sixtieth birthday, August 1993}

Quantum bouncer with chaos.

Abstract: We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.