Dissipation induced coherence of a two-mode Bose-Einstein condensate

We discuss the dynamics of a Bose-Einstein condensate in a double-well trap subject to phase noise and particle loss. The phase coherence of a weakly-interacting condensate as well as the response to an external driving show a pronounced stochastic resonance effect: Both quantities become maximal for a finite value of the dissipation rate matching the intrinsic time scales of the system. Even stronger effects are observed when dissipation acts in concurrence with strong inter-particle interactions, restoring the purity of the condensate almost completely and increasing the phase coherence significantly.Comment: 10 pages, 5 figure

Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems. We show that this description clearly goes beyond the common mean-field limit. In particular it resolves well-known problems where the common mean-field approach fails, like the description of dynamical instabilities and chaotic dynamics. Moreover, it provides a valuable tool for a semi-classical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach. As a prominent example, we analyse the depletion and heating of the condensate. A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples.Comment: Significantly enhanced and revised version (20 pages, 20 figures

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

Quantum dynamics of Bose-Einstein condensates in tilted and driven bichromatic optical lattices

We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band split up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling and allow for a variety of applications in matter wave interferometry and quantum metrology. In the present paper we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.Comment: 9 pages, 9 figures, to appear in Phys. Rev.

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

COMPETITION AMONG HOSPITALS AND ITS MEASUREMENT: THEORY AND A CASE STUDY

Our paper provides several insights on the characteristics of the concept of “Poles d’Excellence Rurale” (PER) through bilateral comparisons with that of Competitive Pole (CP) and cluster. The concept of PER is a French government’ initiative designed for the development of rural areas similar to that of the Competitive Pole. We emphasize important particularities of these concepts by analyzing some of their similarities and major differences.Pole d’Excellence Rurale, Competitive Pole, cluster, rural development

Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure

Gas phase formation of extremely oxidized pinene reaction products in chamber and ambient air

High molecular weight (300–650 Da) naturally charged negative ions have previously been observed at a boreal forest site in Hyytiälä, Finland. The long-term measurements conducted in this work showed that these ions are observed practically every night between spring and autumn in Hyytiälä. The ambient mass spectral patterns could be reproduced in striking detail during additional measurements of α-pinene (C<sub>10</sub>H<sub>16</sub>) oxidation at low-OH conditions in the Jülich Plant Atmosphere Chamber (JPAC). The ions were identified as clusters of the nitrate ion (NO<sub>3</sub><sup>−</sup>) and α-pinene oxidation products reaching oxygen to carbon ratios of 0.7–1.3, while retaining most of the initial ten carbon atoms. Attributing the ions to clusters instead of single molecules was based on additional observations of the same extremely oxidized organics in clusters with HSO<sub>4</sub><sup>−</sup> (Hyytiälä) and C<sub>3</sub>F<sub>5</sub>O<sub>2</sub><sup>−</sup> (JPAC). The most abundant products in the ion spectra were identified as C<sub>10</sub>H<sub>14</sub>O<sub>7</sub>, C<sub>10</sub>H<sub>14</sub>O<sub>9</sub>, C<sub>10</sub>H<sub>16</sub>O<sub>9</sub>, and C<sub>10</sub>H<sub>14</sub>O<sub>11</sub>. The mechanism responsible for forming these molecules is still not clear, but the initial reaction is most likely ozone attack at the double bond, as the ions are mainly observed under dark conditions. β-pinene also formed highly oxidized products under the same conditions, but less efficiently, and mainly C<sub>9</sub> compounds which were not observed in Hyytiälä, where β-pinene on average is 4–5 times less abundant than α-pinene. Further, to explain the high O/C together with the relatively high H/C, we propose that geminal diols and/or hydroperoxide groups may be important. We estimate that the night-time concentration of the sum of the neutral extremely oxidized products is on the order of 0.1–1 ppt (~10<sup>6</sup>–10<sup>7</sup> molec cm<sup>−3</sup>). This is in a similar range as the amount of gaseous H<sub>2</sub>SO<sub>4</sub> in Hyytiälä during day-time. As these highly oxidized organics are roughly 3 times heavier, likely with extremely low vapor pressures, their role in the initial steps of new aerosol particle formation and growth may be important and needs to be explored in more detail in the future