Exact c-number Representation of Non-Markovian Quantum Dissipation

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr{\"o}dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born--Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.Comment: 4 pages, 2 figures. To be published in Phys. Rev. Let

Topological phases and circulating states of Bose-Einstein condensates

We show that the quantum topological effect predicted by Aharonov and Casher (AC effect) [Phys. Rev. Lett. 53, 319 (1984)] may be used to create circulating states of magnetically trapped atomic Bose-Einstein condensates (BEC). A simple experimental setup is suggested based on a multiply connected geometry such as a toroidal trap or a magnetic trap pinched by a blue-detuned laser. We give numerical estimates of such effects within the current atomic BEC experiments, and point out some interesting properties of the associated quantized circulating states.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Phase dynamics in a binary-collisions atom laser scheme

Various aspects of the phase dynamics of an atom laser scheme based on binary collisions are investigated. Analytical estimates of the influence of elastic atom-atom collisions on the laser linewidth are given, and linewidths achievable in a recently proposed atom laser scheme [Phys. Rev. A 56, 2989 (1997)] are evaluated explicitly. The extent to which a relative phase can be established between two interfering atom lasers, as well as the properties of that phase, are also investigated.Comment: Revtex, 10 pages, 6 figure

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization. This is consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.Comment: 5 pages, two embedded figures. To appear in Phys. Rev. A (RC

Laser cooling of trapped atoms to the ground state : a dark state in position space

We propose a scheme that allows us to laser cool trapped atoms to the ground state of a one-dimensional confining potential. The scheme is based on the creation of a dark state by designing the laser profile, so that the hottest atoms are coherently pumped to another internal level, and then repumped back. The scheme works beyond the Lamb-Dicke limit. We present results of a full quantum treatment for a one-dimensional model

Out-of-equilibrium physics in driven dissipative coupled resonator arrays

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by D.G.Angelakis, Quantum Science and Technology Series, Springer 201

Impairment of Auditory-Motor Timing and Compensatory Reorganization after Ventral Premotor Cortex Stimulation

Integrating auditory and motor information often requires precise timing as in speech and music. In humans, the position of the ventral premotor cortex (PMv) in the dorsal auditory stream renders this area a node for auditory-motor integration. Yet, it remains unknown whether the PMv is critical for auditory-motor timing and which activity increases help to preserve task performance following its disruption. 16 healthy volunteers participated in two sessions with fMRI measured at baseline and following rTMS (rTMS) of either the left PMv or a control region. Subjects synchronized left or right finger tapping to sub-second beat rates of auditory rhythms in the experimental task, and produced self-paced tapping during spectrally matched auditory stimuli in the control task. Left PMv rTMS impaired auditory-motor synchronization accuracy in the first sub-block following stimulation (p<0.01, Bonferroni corrected), but spared motor timing and attention to task. Task-related activity increased in the homologue right PMv, but did not predict the behavioral effect of rTMS. In contrast, anterior midline cerebellum revealed most pronounced activity increase in less impaired subjects. The present findings suggest a critical role of the left PMv in feed-forward computations enabling accurate auditory-motor timing, which can be compensated by activity modulations in the cerebellum, but not in the homologue region contralateral to stimulation

Bose-Einstein condensates in atomic gases: simple theoretical results

These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic interaction potential - finite temperature Hartree-Fock approximation - Gross-Pitaevskii equation for the condensate wavefunction - what we learn from a linearization of the Gross-Pitaevskii equation - Bogoliubov approach and thermodynamical stability - phase coherence properties of Bose-Einstein condensates - symmetry breaking description of condensatesComment: 146 pages, 17 figures, Lecture Notes of Les Houches Summer School 199

The role of the cerebellum in adaptation: ALE meta‐analyses on sensory feedback error

It is widely accepted that unexpected sensory consequences of self‐action engage the cerebellum. However, we currently lack consensus on where in the cerebellum, we find fine‐grained differentiation to unexpected sensory feedback. This may result from methodological diversity in task‐based human neuroimaging studies that experimentally alter the quality of self‐generated sensory feedback. We gathered existing studies that manipulated sensory feedback using a variety of methodological approaches and performed activation likelihood estimation (ALE) meta‐analyses. Only half of these studies reported cerebellar activation with considerable variation in spatial location. Consequently, ALE analyses did not reveal significantly increased likelihood of activation in the cerebellum despite the broad scientific consensus of the cerebellum's involvement. In light of the high degree of methodological variability in published studies, we tested for statistical dependence between methodological factors that varied across the published studies. Experiments that elicited an adaptive response to continuously altered sensory feedback more frequently reported activation in the cerebellum than those experiments that did not induce adaptation. These findings may explain the surprisingly low rate of significant cerebellar activation across brain imaging studies investigating unexpected sensory feedback. Furthermore, limitations of functional magnetic resonance imaging to probe the cerebellum could play a role as climbing fiber activity associated with feedback error processing may not be captured by it. We provide methodological recommendations that may guide future studies