Quantum phase-space analysis of the pendular cavity

We perform a quantum mechanical analysis of the pendular cavity, using the positive-P representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady-state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearised fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at 2 mK.Comment: 25 pages, 6 figures To be published in Phys. Rev.

Quantum correlations in pumped and damped Bose-Hubbard dimers

We propose and analyze two-well Bose-Hubbard models with pumping and losses, finding that these models, with damping and loss able to be added independently to each well, offer a flexibility not found in optical coupled cavity systems. With one well pumped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. Both the systems we analyze remain far from equilibrium, preserving good coherence between the wells in the steady state. We find a degree of quadrature squeezing and mode entanglement in these systems. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict

Invasions across secondary forest successional stages: effects of local plant community, soil, litter, and herbivory on Hovenia dulcis seed germination and seedling establishment

Species abilities for seed germination and seedling survival under different situations are good predictors of their capacity to colonize a broad range of habitats. Biotic conditions related to understory cover, and abiotic factors such as litter thickness and soil moisture can be determinants of plant establishment. We evaluated seed germination, seedling survival, and growth of the invasive tree Hovenia dulcis under experimental field conditions in three successional stages (open, semi-open, and closed vegetation) of a fragmented seasonal deciduous forest in southern Brazil. Our hypotheses were that H. dulcis seed germination, seedling survival, and seedling growth decrease along the successional gradient, that these factors are positively affected by soil moisture and percentage of bare soil, and negatively affected by understory cover and litter thickness. We also tested the hypothesis that herbivory on H. dulcis would decrease along the successional gradient. Our main finding was that H. dulcis can germinate and establish along all forest successional stages because it is shadetolerant. Abiotic factors were more important than biotic factors for seed germination. Soil moisture positively affected seed germination while litter thickness negatively influenced seed germination. Percentage of bare soil negatively influenced seedling survival. Germination rates were higher in closed vegetation, whereas seedling survival was higher in semi-open vegetation, and growth rates were higher in open vegetation. There was no difference in herbivory among successional stages. The results of our study show that intermediate forest succession stages congregate the most favorable conditions for H. dulcis establishment, likely making them more susceptible to invasion.Fil: Dechoum, Michele. Universidade Federal de Santa Catarina; BrasilFil: Zenni, Rafael D.. Universidade do Brasília; BrasilFil: Castellani, Tania. Universidade Federal de Santa Catarina; BrasilFil: Zalba, Sergio Martín. Universidad Nacional del Sur. Departamento de Biología, Bioquímica y Farmacia; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rejmánek, M.. University of California at Davis; Estados Unido

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a non-equilibrium quantum system with a critical point phase-transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P-representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing and EPR correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator

Cauchy-Schwarz characterization of tripartite quantum correlations in an optical parametric oscillator

We analyze the three-mode correlation properties of the electromagnetic field in a optical parametric oscillator below threshold. We employ a perturbative expansion of the It\^o equations derived from the positive-P representation of the density matrix. Using the generalized Cauchy-Schwarz inequality, we investigate the genuine quantum nature of the triple correlations between the interacting fields, since in this case continuous variable entanglement is not detected by the van Loock-Furusawa criterion [Phys. Rev. A {\bf 67}, 052315 (2003)]. Although not being a necessary condition, these triple correlations are a sufficient evidence of tripartite entanglement. Of course, our characterization of the quantum correlations is applicable to non-Gaussian states, which we show to be the case of the optical parametric oscillator below threshold, provided nonlinear quantum fluctuations are properly taken into account.Comment: 4 pages, 2 figure

Spin Path Integrals and Generations

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman \emph{position} path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question "what happens when \emph{spin} path integrals are computed over products of MUBs?" Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons.Comment: 20 pages, 2 figures, accepted at Foundations of Physic

Semiclassical Wigner distribution for two-mode entangled state

We derive the steady state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. We assume that the pump mode is strongly damped, which permits its adiabatic elimination. When the elimination is correctly executed, the resulting stochastic equations contain multiplicative noise terms, and do not admit a potential solution. However, we develop an heuristic scheme leading to a satisfactory steady-state solution. This provides a clear view of the intracavity two-mode entangled state valid in all operating regimes of the OPO. A nongaussian distribution is obtained for the above threshold solution.Comment: 9 pages, 5 figures. arXiv admin note: this contains the content of arXiv:0906.531

Casimir interaction between a microscopic dipole oscillator and a macroscopic solenoid

We discuss the interaction between a microscopic electric dipole oscillator and a long solenoid which are separated by a small distance. The solenoid belongs to a simple RLC circuit and the zero point and thermal current fluctuations within the solenoid coils are taken into account. We describe how they affect the equilibrium state and the excited states of the oscillator, thus providing a description of the Casimir interaction of the system. We calculate the modification in the lifetime of the oscillator excited states as a function of the parameters of the circuit, the dipole orientation, and the distance between the dipole and the solenoid. The Casimir force between the solenoid and the electric dipole is calculated, and it is shown that this Casimir interaction always exists, that is, it occurs even when the macroscopic current in the solenoid is zero. We suggest experiments which can exhibit these effects related to the electromagnetic interactions between atoms or molecules and simple circuits