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We study the role of continuous measurement in the quantum to classical transition for a particle in a harmonic well whose motion in the well is coupled to the internal spin. This system provides a rich illustration of the quantum to classical transition in weakly measured coupled systems. We demonstrate the emergence of classically regular as well as chaotic dynamics from the measured quantum trajectories when the external and internal actions are large relative to ℏ. We also show the breakdown of the conditions for the quantum‐classical transition in a mixed quantum‐classical regime where the spin is treated quantum mechanically but the motion in the well can be treated classically. The conditions for the transition can be quantified by examining the covariance matrix. We explore the behavior of entanglement between spin and motion in the (classical) limit of large actions and find that whereas the measured quantum trajectories recover classical dynamics, the conditioned evolution can lead to highly non‐classical entangled states. This is due to the finite resolution of the measurement.

A many-body density-matrix theory is derived by including quasiparticle renormalization of kinetic energy and dipole coupling to an external electromagnetic field, as well as the screening and quantum-interference effects. This theory is applied to a three-level resonant asymmetric double-quantum-well system in which the ground subband is coupled to the upper tunneling-split doublet by a strong external electromagnetic field. By using this theory, the quasiparticle energy-level separations and off-diagonal radiative-decay coupling rates, absorption coefficient, refractive-index function, and scaled subband electron density are calculated as functions of incident photon energy. The effects of quasiparticle renormalization on the quantum interference between a pair of optically induced polarizations are analyzed. The quantum interference is shown to be robust against the Coulomb-interaction effect in the mean-field approximation. The roles played by the dephasing rate and electron density are explained.

In this work, we give a description of the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Unruh radiation in Rob's frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in non inertial frames., 7 pages with 4 figures (in revtex4)

In this work, we describe the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Rob's frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in non-inertial frames. We discuss this reduction in fidelity for both bosonic and fermionic resources., Comment: Recalculates quant-ph/0302179 in the more physical dual rail basis, utilizing cavities and extends the results to include accelerated spin 1/2 particles. Submitted to J. Opt. B: Q.& Semi. Class. Opt, Special Issue on Fluctuations & Noise in Photonics & Quantum Optics, in memory of Herman Haus

Experimental measurements and a single‐mode analysis of a quantum‐well laser diode subject to strong optical injection are combined to demonstrate that the diode follows a period‐doubling route to chaos. All laser parameters used in this model, including the influence of spontaneous emission noise, were experimentally determined based on the four‐wave mixing technique. The transition to chaos can be used to reduce the uncertainty in the value of the linewidth enhancement factor.

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4)m−1.

In most encounters, chaotic behavior is considered a nuisance, if not a down right detriment to system performance, especially in laser devices. Often, much time and effort is spent in search of finding ways to eliminate or suppress the sources of chaos. However, within the last couple of years it has been recognized that chaos in a system can serve as a rich source of complex frequencies which one can access and easily switch between. The algorithm for locking the system into one of these frequencies was put forth in the pioneering paper by Ott, Grebogi, and Yorke in 1990. Since then there has been a flurry of both theoretical activity to refine the techniques used for controlling chaos and experimental efforts demonstrating control of chaos in various systems. Although, there now appears in the literature several algorithms for controlling chaos, they are essentially minor variants of the original ideas of the Ott, Gregobi and Yorke, or the OGY scheme as it has come to be known. At the Nonlinear Optics Center we are interested in the practical applications of controlling chaos to laser systems, in particular semiconductor diode lasers. By using the ideas of controlling chaos, we hope to be able to stabilize large arrays of coupled semiconductor diode lasers in regimes in which they would ordinarily be chaotic. A discussion of problems related to implementing the controlling algorithm in an experiment currently being conducted at the Phillips Laboratory is presented. >

The concept of controlling chaos has become part of the lexicon of physicists and engineers dealing with chaotic nonlinear dynamical systems. The authors showed that by using small, judiciously applied perturbations the unstable periodic orbits, which are dense in a chaotic attractor, could be stabilized. >

We have experimentally synchronized chaotic diode laser resonators using occasionally applied feedback. We have also synchronized and controlled a unidirectionally coupled array of diode resonators.

By including the effect of local fluctuations in the electron kinetic energies, the kinetic Fokker-Planck-type equation for excited conduction electrons in bulk semiconductors (such as GaAs, Si, etc.) is systematically derived in the presence of a pulsed laser beyond the classical limit. A new contribution from an antidiffusion process is found as a correction to the spontaneous-phonon emission from drifting electrons in addition to contributions from joule heating and a field-dependent diffusion of electrons. The stimulated interband optical transitions of electrons from single-photon absorption are included as one of the source terms of the equation. Some possible types of damage in semiconductors including optical, electrical, and structural damage are explored. The calculated results demonstrate the existence of a kinklike feature in the electron distribution function around the edge of the conduction band due to antidiffusion. The energy spectra of the electron distribution function are studied at different times and used to analyze the transient behavior of both the conduction electron density and the hot-electron temperature.

By using a first-order time-dependent perturbation theory and including the effect of energy drift from electron transport on the intraband transitions of electrons due to phonons, the kinetic Fokker-Planck equation for conduction electrons in semiconductors is systematically derived in the presence of a laser pulse. A contribution from the anti- diffusion current in the equation is found as a result of the coupling between the spontaneous-phonon emission and the energy drift of electrons due to joule heating by absorbing power from a laser. Analytical expressions for source terms of the equation are given simultaneously up to second-order in perturbation theory, including the stimulated interband optical transitions of electrons from single-photon laser- field absorption, impact ionization due to the Coulomb interaction between electrons and holes, and nonradiative recombination due to the phonon-mediated interaction. Some possible damage mechanisms in semiconductors including optical, electrical, and structural damage are explored. The energy spectra of the electron distribution function are studied and used to analyze the transient behavior of both the conduction electron density and the average kinetic energy of electrons (proportional to the electron temperature). The dynamical effects of anti-diffusion recombination, thermal diffusion and lattice temperature are all shown and explained. A new kink-like feature is observed around the edge of the conduction band in the electron distribution function due to anti-diffusion.

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed., 31 pages, 3 figures, submitted to Phys. Rev. A

The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from the coupling between the atomic spin and its center-of- mass motion. Experiments, performed deep in the quantum regime, correspond to dynamic quantum tunneling. This nonclassical behavior is contrasted with the predictions for an initial phase space distribution produced in the experiment, but undergoing classical Hamiltonian flow. We study conditions under which the trapped atoms can be made to exhibit classical dynamics through the process of continuous measurement, which localizes the probability distribution to phase space trajectories, consistent with the uncertainty principle and quantum back-action noise. This method allows us to analytically and numerically identify the quantum-classical boundary., Comment: Contribution to the Proceedings of the 7th Experimental Chaos Conference describing recent experimental and theoretical results

We study the role of continuous measurement in the quantum to classical transition for a system with coupled internal (spin) and external (motional) degrees of freedom. Even when the measured motional degree of freedom can be treated classically, entanglement between spin and motion causes strong measurement backaction on the quantum spin subsystem so that classical trajectories are not recovered in this mixed quantum-classical regime. The measurement can extract localized quantum trajectories that behave classically only when the internal action also becomes large relative to h-bar., Comment: Published version

We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from nonseparable couplings between the atomic spin and its center of mass motion. The main features of the chaotic dynamics are analyzed using action-angle variables and Poincare surfaces of section. We show that for the initial state prepared in current experiments [D. J. Haycock et al., Phys. Rev. Lett. 85, 3365 (2000)], the classical and quantum dynamics diverge, and the observed experimental dynamics are best described by quantum mechanics. Furthermore, the motion corresponds to tunneling through a dynamical potential barrier. The coupling between the spin and the motional subsystems, which are very different in nature from one another, leads to new questions regarding the transition from regular quantum dynamics to chaotic classical motion., 36 pages including 6 pages of figures. To be published in PRE Nov. 1st, 2001. Revised version contains a discussion and extra figure (Fig 5) related to gauge potentials, plus added refernces

We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in $\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations., Comment: 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 00

We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic $\delta-$function ``kicks''. We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potenital arises from overdamping of the phase of oscillation and not from any cooperative effect between the noise and the driving field. The model is investigated with a square wave drive, which has qualitatively similar features to the widely studied cosinusoidal drive, but has the additional advantage of allowing one to derive exact analytic expressions., Comment: 17 pages, 4 figures, submitted to Phys. Rev. E

We observe the quantum coherent dynamics of atomic spinor wavepackets in the double well potentials of a far-off-resonance optical lattice. With appropriate initial conditions the system Rabi oscillates between the left and right localized states of the ground doublet, and at certain times the wavepacket corresponds to a coherent superposition of these mesoscopically distinguishable quantum states. The atom/optical double well potential is a flexible and powerful system for further study of mesoscopic quantum coherence, quantum control and the quantum/classical transition., 12 pages, 4 figures, submitted to Physical Review Letters

An asymptotic theory of Lang and Kobayashi (LK) equations describing a semiconductor laser subject to optical feedback is investigated in detail. We obtain a simple third order, nonlinear, delay-differential equation for the phase of the laser field which admits multiple branches of time-periodic intensity solutions. The theory is based on typical values of LK dimensionless parameters and assumes that the pump parameter is not too small. In this paper, we examine the validity of this assumption by considering the small pump limit. We find the same phase equation as the leading problem of our asymptotic analysis but now with a stronger damping coefficient. This phase equation fails as a correct asymptotic approximation only for very low pump, close to the lasing threshold. The approximation for this case is more complicated and reveals a stronger influence of the laser intensity.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We characterize the nonlinear dynamics of a semiconductor laser subject to optical injection. The key characteristics of measured optical spectra are reproduced in calculations based on a single-mode model that includes spontaneous-emission noise. The laser exhibits chaos over a bounded range of injection levels. As the chaotic regime is approached from both lower and higher injection levels, a period-doubling route to chaos is followed, although the route is obscured by spontaneous-emission noise. A new, bounded regime of period-doubling occurs for injection levels well above the region of chaotic dynamics. Optical injection strongly modifies the carrier-field resonance coupling frequency.

Understanding the observer-dependent nature of quantum entanglement has been a central question in relativistic quantum information. In this paper we will review key results on relativistic entanglement in flat and curved spacetime and discuss recent work which shows that motion and gravity have observable effects on entanglement between localized systems., Ivette Fuentes previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schuller

A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott Grebogi and Yorke, including variants that utilize previous perturbations and/or delayedtime series data. 1. Introduction Chaotic systems are characterized by their sensitive dependence to small perturbations.In recent years. an abundance of theoretical and experimental research has been developedto capitalize on this fact and utilize it to control chaotic systems by applying very small,appropriately timed perturbations. Researchers have demonstrated the control of chaos in a host of physical systems ranging from lasers and electronic circuits to chemical and biological systems. For an excellent. recent review article see [1] and references therein.Neural networks are useful for a vast array of applications involving pattern and sym-hol recognition as well as for numerical computations. Recently. neural networks have beenemployed in the arena of dynamical systems as a tool for recognizing chaos in noisy experi

We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension., Comment: 19 pages, 2 figures

We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In most encounters, chaos is considered a nuisance, ifnot a down right detriment to system performance. especially in laser devices. However, the presence of chaos in a system can act as a rich source of complex frequencies if one only had a way of accessing them. In this workwe present a discussion of the recent work of Ott, Grebogi and Yorke on controlling chaos as applied to a semiconductor diode laser subject to optical feedback via an external mirror. In the regime in which the laser is chaotic, stabilization can be achieved by sampling the output intensity and feeding back minuscule amounts of a correcting signal on the pumping currentat the appropriate time interval. We present the results of our numerical investigations. 1. Introduction Semiconductor lasers diodes exposed to optical feedback undergo a dramatic spectral broadening for a large range of the feedback levels. The laser linewidth broadens from a few MHz to several GHz. The phenomenon is known as coherence collapse [1]. Its origin hasbeen interpreted as a manifestation of deterministic chaotic dynamics. This system deservesattention from the fundamental physics point, since it represents an example of an activetype of delayed feedback optical system with a behavior different from that of the well

We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of a radiation field prepared in a Glauber-Lachs state is investigated to study the development of seemingly chaotic oscillations of the atomic inversion from a regular collapse-and-revival phenomenon, as the field statistics is changed from the coherent state to the thermal state. The effect of thermal photons on the coherent light is shown to be striking: Both the photon distribution as well as the atomic inversion are highly sensitive to even a very small addition of thermal photons to an initially coherent radiation field. We also compare the collapse and revival occurring in the micromaser case with the Glauber-Lachs version of the Jaynes-Cummings model. ? 1992 The American Physical Society.

A unique structure composed of a half-space of air and a semi-infinite doped bulk GaAs covered by an InAs conducting interface sheet is proposed, from which the physics behind the interplay between the effects of transverse sheet current and the longitudinal three-dimensional plasma waves, as well as the effect of evanescent modes, can be explored. The in-plane and perpendicular components of a transverse field are modified by the inclusion of the InAs conducting sheet and a longitudinal field, and the coupling between transverse and longitudinal oscillations of an electromagnetic field parallel and perpendicular to the conducting sheet is made possible by the doped GaAs bulk. Based on this structure, a spatially nonlocal dynamic theory is derived, including the coupling between the transverse and longitudinal oscillations, the image-potential and retardation effects, and the effects of evanescent modes. The existence of the InAs conducting sheet is found to reduce the transmitted field by reflection from...

An approach for carrier cooling in undoped and contactless semiconductors is proposed by using thermal-drag effects in comparison with other methods, such as direct resonant tunneling, nonresonant thermionic, and junction-tunneling cooling, as well as indirect optothermionic and thermoelectric cooling, of carriers in doped and contacted semiconductors. A four-step microscopic model is proposed for this thermal-drag carrier cooling in undoped semiconductors. Wide-band-gap semiconductors with small lattice specific heat and small exchange specific heat between carriers and phonons are found to achieve the best thermal-drag carrier cooling under near-band-edge interband pumping by a weak field. This indirect carrier cooling is accompanied by the lattice cooling. The carrier temperature is pinned to the lattice temperature due to ultrafast carrier-phonon scattering, and it is dragged down by the reduction of the lattice temperature, i.e., the thermal-drag effects.

We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.

The two-photon absorption process is studied by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. The equations of motion of the coupled atom–field probability amplitudes for the effective two-level atom are obtained after adiabatically eliminating the intermediate states. These equations are then solved in the rotating-wave approximation. The time constants associated with the Rabi oscillation, collapse, and revival of the atomic inversion are derived, and the photon statistics are discussed with special reference to photon antibunching.