Decoherence and dephasing in strongly driven colliding Bose-Einstein condensates

We report on a series of measurements of decoherence and wavepacket dephasing between two colliding, strongly coupled, identical Bose-Einstein condensates. We measure, in the strong excitation regime, a suppression of the mean-field shift, compared to the shift which is observed for a weak excitation. This suppression is explained by applying the Gross-Pitaevskii energy functional. By selectively counting only the non-decohered fraction in a time of flight image we observe oscillations for which both inhomogeneous and Doppler broadening are suppressed, in quantitative agreement with a full Gross-Pitaevskii equation simulation. If no post selection is used, the decoherence rate due to collisions can be extracted, and is in agreement with the local density average calculated rate.Comment: 4 pages, 5 figure

Toward a dynamical systems analysis of neuromodulation

This work presents some first steps toward a more thorough understanding of the control systems employed in evolutionary robotics. In order to choose an appropriate architecture or to construct an effective novel control system we need insights into what makes control systems successful, robust, evolvable, etc. Here we present analysis intended to shed light on this type of question as it applies to a novel class of artificial neural networks that include a neuromodulatory mechanism: GasNets. We begin by instantiating a particular GasNet subcircuit responsible for tuneable pattern generation and thought to underpin the attractive property of “temporal adaptivity”. Rather than work within the GasNet formalism, we develop an extension of the well-known FitzHugh-Nagumo equations. The continuous nature of our model allows us to conduct a thorough dynamical systems analysis and to draw parallels between this subcircuit and beating/bursting phenomena reported in the neuroscience literature. We then proceed to explore the effects of different types of parameter modulation on the system dynamics. We conclude that while there are key differences between the gain modulation used in the GasNet and alternative schemes (including threshold modulation of more traditional synaptic input), both approaches are able to produce tuneable pattern generation. While it appears, at least in this study, that the GasNet’s gain modulation may not be crucial to pattern generation , we go on to suggest some possible advantages it could confer

On a nonlinear theory of elastic shells

Nonlinear theory of elastic shells with deformation gradient

Bose-Einstein condensate in a rapidly rotating non-symmetric trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function psi(x,y) is a Gaussian exp(-r^2/2), multiplied by an analytic function f(z) of the complex variable z= x+ i y. The criterion for a quantum phase transition to a non-superfluid correlated many-body state is usually expressed in terms of the ratio of the number of particles to the number of vortices. Here, a similar description applies to a rapidly rotating non-symmetric two-dimensional trap with arbitrary quadratic anisotropy (omega_x^2 < omega_y^2). The corresponding condensate wave function psi(x,y) is a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function f(z), where z = x + i \beta_- y is a stretched complex variable and 0< \beta_- <1 is a real parameter that depends on the trap anisotropy and the rotation frequency. Both in the mean-field Thomas-Fermi approximation and in the mean-field lowest Landau level approximation with many visible vortices, an anisotropic parabolic density profile minimizes the energy. An elongated condensate grows along the soft trap direction yet ultimately shrinks along the tight trap direction. The criterion for the quantum phase transition to a correlated state is generalized (1) in terms of N/L_z, which suggests that a non-symmetric trap should make it easier to observe this transition or (2) in terms of a "fragmented" correlated state, which suggests that a non-symmetric trap should make it harder to observe this transition. An alternative scenario involves a crossover to a quasi one-dimensional condensate without visible vortices, as suggested by Aftalion et al., Phys. Rev. A 79, 011603(R) (2009).Comment: 20 page

ac Stark shift and multiphoton-like resonances in low-frequency driven optical lattices

We suggest that Bose-Einstein condensates in optical lattices subjected to ac forcing with a smooth envelope may provide detailed experimental access to multiphoton-like transitions between ac-Stark-shifted Bloch bands. Such transitions correspond to resonances described theoretically by avoided quasienergy crossings. We show that the width of such anticrossings can be inferred from measurements involving asymmetric pulses. We also introduce a pulse tracking strategy for locating the particular driving amplitudes for which resonances occur. Our numerical calculations refer to a currently existing experimental set-up [Haller et al., PRL 104, 200403 (2010)].Comment: 5 pages, 6 figure

Regions of beta 2 and beta 4 responsible for differences between the steady state dose-response relationships of the alpha 3 beta 2 and alpha 3 beta 4 neuronal nicotinic receptors

We constructed chimeras of the rat beta 2 and beta 4 neuronal nicotinic subunits to locate the regions that contribute to differences between the acetylcholine (ACh) dose-response relationships of the alpha 3 beta 2 and alpha 3 beta 4 receptors. Expressed in Xenopus oocytes, the alpha 3 beta 2 receptor displays an EC50 for ACh approximately 20-fold less than the EC50 of the alpha 3 beta 4 receptor. The apparent Hill slope (n(app)) of alpha 3 beta 2 is near one whereas the alpha 3 beta 4 receptor displays an n(app) near two. Substitutions within the first 120 residues convert the EC50 for ACh from one wild-type value to the other. Exchanging just beta 2:104-120 for the corresponding region of beta 4 shifts the EC50 of ACh dose-response relationship in the expected direction but does not completely convert the EC50 of the dose- response relationship from one wild-type value to the other. However, substitutions in the beta 2:104-120 region do account for the relative sensitivity of the alpha 3 beta 2 receptor to cytisine, tetramethylammonium, and ACh. The expression of beta 4-like (strong) cooperativity requires an extensive region of beta 4 (beta 4:1-301). Relatively short beta 2 substitutions (beta 2:104-120) can reduce cooperativity to beta 2-like values. The results suggest that amino acids within the first 120 residues of beta 2 and the corresponding region of beta 4 contribute to an agonist binding site that bridges the alpha and beta subunits in neuronal nicotinic receptors

Harmonic oscillators coupled by springs: discrete solutions as a Wigner Quantum System

We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In this paper, we approach the system as a Wigner Quantum System, not imposing the canonical commutation relations, but using instead weaker relations following from the compatibility of Hamilton's equations and the Heisenberg equations. In such a setting, the quantum system allows solutions in a finite-dimensional Hilbert space, with a discrete spectrum for all physical operators. We show that a class of solutions can be obtained using generators of the Lie superalgebra gl(1|M). Then we study the properties and spectra of the physical operators in a class of unitary representations of gl(1|M). These properties are both interesting and intriguing. In particular, we can give a complete analysis of the eigenvalues of the Hamiltonian and of the position and momentum operators (including multiplicities). We also study probability distributions of position operators when the quantum system is in a stationary state, and the effect of the position of one oscillator on the positions of the remaining oscillators in the chain

Splitting in the Excitation Spectrum of A Bose-Einstein Condensate Undergoing Strong Rabi Oscillations

We report on a measurement of splitting in the excitation spectrum of a condensate driven by an optical travelling wave. Experimental results are compared to a numerical solution of the Gross Pitaevskii equation, and analyzed by a simple two level model and by the more complete band theory, treating the driving beams as an optical lattice. In this picture, the splitting is a manifestation of the energy gap between neighboring bands that opens on the boundary of the Brillouin zone.Comment: 5 pages, 5 figure

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs