Optical realization of the two-site Bose-Hubbard model in waveguide lattices

A classical realization of the two-site Bose-Hubbard Hamiltonian, based on light transport in engineered optical waveguide lattices, is theoretically proposed. The optical lattice enables a direct visualization of the Bose-Hubbard dynamics in Fock space.Comment: to be published, J Phys. B (Fast Track Communication

Wave packet evolution in non-Hermitian quantum systems

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase space metric---a phenomenon having no analog in Hermitian theories.Comment: Example added, references updated, 4 pages, 2 figure

Breakdown of adiabatic transfer of light in waveguides in the presence of absorption

In atomic physics, adiabatic evolution is often used to achieve a robust and efficient population transfer. Many adiabatic schemes have also been implemented in optical waveguide structures. Recently there has been increasing interests in the influence of decay and absorption, and their engineering applications. Here it is shown that even a small decay can significantly influence the dynamical behaviour of a system, above and beyond a mere change of the overall norm. In particular, a small decay can lead to a breakdown of adiabatic transfer schemes, even when both the spectrum and the eigenfunctions are only sightly modified. This is demonstrated for the generalization of a STIRAP scheme that has recently been implemented in optical waveguide structures. Here the question how an additional absorption in either the initial or the target waveguide influences the transfer property of the scheme is addressed. It is found that the scheme breaks down for small values of the absorption at a relatively sharp threshold, which can be estimated by simple analytical arguments.Comment: 8 pages, 7 figures, revised and extende

Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates

We study the dynamical stability of the macroscopic quantum oscillations characterizing a system of three coupled Bose-Einstein condensates arranged into an open-chain geometry. The boson interaction, the hopping amplitude and the central-well relative depth are regarded as adjustable parameters. After deriving the stability diagrams of the system, we identify three mechanisms to realize the transition from an unstable to stable behavior and analyze specific configurations that, by suitably tuning the model parameters, give rise to macroscopic effects which are expected to be accessible to experimental observation. Also, we pinpoint a system regime that realizes a Josephson-junction-like effect. In this regime the system configuration do not depend on the model interaction parameters, and the population oscillation amplitude is related to the condensate-phase difference. This fact makes possible estimating the latter quantity, since the measure of the oscillating amplitudes is experimentally accessible.Comment: 25 pages, 12 figure

Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well

The time-independent nonlinear Schr\"odinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the other. We show that for vanishing nonlinearity the model captures all the features known from studies of PT symmetric optical wave guides, e.g., the coalescence of modes in an exceptional point at a critical value of the loss/gain parameter, and the breaking of PT symmetry beyond. With the nonlinearity present, the equation is a model for a Bose-Einstein condensate with loss and gain in a double well potential. We find that the nonlinear Hamiltonian picks as stationary eigenstates exactly such solutions which render the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and bifurcation scenarios different from those known from linear PT symmetric Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics

Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approximation it provides a rich mixed phase space dynamics with regular and chaotic regions. By increasing the kick-strength a bifurcation leads to the appearance of self-trapping states localized on regular islands. This self-trapping is also found for the many particle system, however in general suppressed by coherent many particle tunneling oscillations. The tunneling time can be calculated from the quasi-energy splitting of the corresponding Floquet states. By varying the kick-strength these quasi-energy levels undergo both avoided and even actual crossings. Therefore stimulation or complete destruction of tunneling can be observed for this many particle system

From Cooperative Scans to Predictive Buffer Management

In analytical applications, database systems often need to sustain workloads with multiple concurrent scans hitting the same table. The Cooperative Scans (CScans) framework, which introduces an Active Buffer Manager (ABM) component into the database architecture, has been the most effective and elaborate response to this problem, and was initially developed in the X100 research prototype. We now report on the the experiences of integrating Cooperative Scans into its industrial-strength successor, the Vectorwise database product. During this implementation we invented a simpler optimization of concurrent scan buffer management, called Predictive Buffer Management (PBM). PBM is based on the observation that in a workload with long-running scans, the buffer manager has quite a bit of information on the workload in the immediate future, such that an approximation of the ideal OPT algorithm becomes feasible. In the evaluation on both synthetic benchmarks as well as a TPC-H throughput run we compare the benefits of naive buffer management (LRU) versus CScans, PBM and OPT; showing that PBM achieves benefits close to Cooperative Scans, while incurring much lower architectural impact.Comment: VLDB201

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd