Experimental study of the quantum driven pendulum and its classical analog in atom optics

We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck’s constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Classical and quantum noise in electronic systems

We review the description of noise in electronic circuits in terms of electron transport. The Poisson process is used as a unifying principle. In recent years, much attention has been given to current noise in light-emitting diodes and laser diodes. In these devices, random events associated with electron transport are correlated with photon emission times, thus modifying both the current statistics and the statistics of the emitted light. We give a review of experiments in this area with special emphasis on the ability of such devices to produce subshot-noise currents and light beams. Finally we consider the noise properties of a class of mesoscopic devices based on the quantum tunnelling of an electron into and out of a bound state. We present a simple quantum model of this process which confirms that the current noise in such a device should be subshot-noise.

The contribution of classical (beta(1/2)-) and atypical beta-adrenoceptors to the stimulation of human white adipocyte lipolysis and right atrial appendage contraction by novel beta(3)-adrenoceptor agonists of differing selectivities

The role of beta(3)- and other putative atypical beta-adrenaceptors in human white adipocytes and right atrial appendage has been investigated using CGP 12177 and novel phenylethanolamine and aryloxypropanolamine beta(3)-adrenoceptor (beta(3)AR) agonists with varying intrinsic activities and selectivities for human cloned PAR subtypes. The ability to demonstrate beta(1/2)AR antagonist-insensitive (beta(3) or other atypical beta AR-mediated) responses to CGP 12177 was critically dependent on the albumin batch used to prepare and incubate the adipocytes. Four aryloxypropanolamine selective beta(3)AR agonists (SB-226552, SB-229432, SB-236923, SB-246982) consistently elicited beta(1/2)AR antagonist-insensitive lipolysis. However, a phenylethanolamine (SB-220646) that was a selective full beta(3)AR agonist elicited full lipolytic and inotropic responses that were sensitive to beta(1/2)AR antagonism, despite it having very low efficacies at cloned beta(1)- and beta(2)ARs. A component of the response to another phenylethanolamine selective beta(3)AR agonist (SB-215691) was insensitive to beta(1/2)AR antagonism in some experiments. Because novel aryloxypropanolamine had a beta(1/2)AR antagonist-insensitive inotropic effect, these results establish more firmly that beta(3)ARs mediate lipolysis in human white adipocytes, and suggest that putative 'beta(4)ARs' mediate inotropic responses to CGP 12177. The results also illustrate the difficulty of predicting from studies on cloned beta ARs which beta ARs will mediate responses to agonists in tissues that have a high number of beta(1)- and beta(2)ARs or a low number of beta(3)ARs.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Classical and quantum signatures of competing chi((2)) nonlinearities

We report the observation of the quantum effects of competing chi((2)) nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various chi((2)) up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

Quantum and classical fidelities for Gaussian states

We examine the physical significance of fidelity as a measure of similarity for Gaussian states by drawing a comparison with its classical counterpart. We find that the relationship between these classical and quantum fidelities is not straightforward, and in general does not seem to provide insight into the physical significance of quantum fidelity. To avoid this ambiguity we propose that the efficacy of quantum information protocols be characterized by determining their transfer function and then calculating the fidelity achievable for a hypothetical pure reference input state. (c) 2007 Optical Society of America.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

ROM-based computation: Quantum versus classical

We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.

Classical approach to interpretation of the charge-dependence of peptide mobilities obtained by capillary zone electrophoresis

Published mobility measurements obtained by capillary zone electrophoresis of human growth hormone peptides are described reasonably well by the classical theoretical relationships for electrophoretic migration. This conformity between theory and experiment has rendered possible a more critical assessment of a commonly employed empirical relationship between mobility (u), net charge (z) and molecular mass (M) of peptides in capillary electrophoresis. The assumed linear dependence between u and z/M-2/3 is shown to be an approximate description of a shallow curvilinear dependence convex to the abscissa. An improved procedure for the calculation of peptide charge (valence) is also described. (C) 2003 Elsevier B.V. All rights reserved.

Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Traffic control: p120-catenin acts as a gatekeeper to control the fate of classical cadherins in mammalian cells

Proteins of the p120 family have been implicated in the regulation of cadherin-based cell adhesion, but their relative importance in this process and their mechanism of action have remained less clear. Three papers in this issue suggest that p120 plays a key role in maintaining normal levels of cadherin in mammalian cells, and that it may do so by regulating cadherin trafficking.