Second Josephson excitations beyond mean field as a toy model for thermal pressure: exact quantum dynamics and the quantum phase model

A simple four-mode Bose-Hubbard model with intrinsic time scale separation can be considered as a paradigm for mesoscopic quantum systems in thermal contact. In our previous work we showed that in addition to coherent particle exchange, a novel slow collective excitation can be identified by a series of Holstein-Primakoff transformations. This resonant energy exchange mode is not predicted by linear Bogoliubov theory, and its frequency is sensitive to interactions among Bogoliubov quasi-particles; it may be referred to as a second Josephson oscillation, in analogy to the second sound mode of liquid Helium II. In this paper we will explore this system beyond the Gross-Pitaevskii mean field regime. We directly compare the classical mean field dynamics to the exact full quantum many-particle dynamics and show good agreement over a large range of the system parameters. The second Josephson frequency becomes imaginary for stronger interactions, however, indicating dynamical instability of the symmetric state. By means of a generalized quantum phase model for the full four-mode system, we then show that, in this regime, high-energy Bogoliubov quasiparticles tend to accumulate in one pair of sites, while the actual particles preferentially occupy the opposite pair. We interpret this as a simple model for thermal pressure

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with short-range interaction and dipole-dipole interaction is given

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

Eye position signal modulates a human parietal pointing region during memory-guided movements.

Using functional magnetic resonance imaging, we examined the signal in parietal regions that were selectively activated during delayed pointing to flashed visual targets and determined whether this signal was dependent on the fixation position of the eyes. Delayed pointing activated a bilateral parietal area in the intraparietal sulcus (rIPS), rostral/anterior to areas activated by saccades. During right-hand pointing to centrally located targets, the left rIPS region showed a significant increase in activation when the eye position was rightward compared with leftward. As expected, activation in motor cortex showed no modulation when only eye position changed. During pointing to retinotopically identical targets, the left rIPS region again showed a significant increased signal when the eye position was rightward compared with leftward. Conversely, when pointing with the left arm, the right rIPS showed an increase in signal when eye position was leftward compared with rightward. The results suggest that the human parietal hand/arm movement region (rIPS), like monkey parietal areas (Andersen et al., 1985), exhibits an eye position modulation of its activity; modulation that may be used to transform the coordinates of the retinotopically coded target position into a motor error command appropriate for the wrist

Intrinsic functional boundaries of lateral frontal cortex in the common marmoset monkey

© 2019 the authors. The common marmoset (Callithrix jacchus) is a small New World primate species that has been recently targeted as a potentially powerful preclinical model of human prefrontal cortex dysfunction. Although the structural boundaries of frontal cortex were described in marmosets at the start of the 20th century (Brodmann, 1909) and refined more recently (Paxinos et al., 2012), the broad functional boundaries of marmoset frontal cortex have yet to be established. In this study, we sought to functionally derive boundaries of the marmoset lateral frontal cortex (LFC) using ultra-high field (9.4 T) resting-state functional magnetic resonance imaging (RS-fMRI). We collectedRS-fMRIdatainseven(fourfemales,threemales)lightlyanesthetizedmarmosetsandusedadata-drivenhierarchicalclustering approach to derive subdivisions of the LFC based on intrinsic functional connectivity. We then conducted seed-based analyses to assess the functional connectivity between these clusters and the rest of the brain. The results demonstrated seven distinct functional clusters withintheLFC.Thefunctionalconnectivitypatternsoftheseclusterswiththerestofthebrainwerealsofoundtobedistinctandorganized along a rostrocaudal gradient, consonant with those found in humans and macaques. Overall, these results support the view that marmosets are a promising preclinical modeling species for studying LFC dysfunction related to neuropsychiatric or neurodegenerative human brain diseases

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

Classical versus quantum dynamics of the atomic Josephson junction

We compare the classical (mean-field) dynamics with the quantum dynamics of atomic Bose-Einstein condensates in double-well potentials. The quantum dynamics are computed using a simple scheme based upon the Raman-Nath equations. Two different methods for exciting a non-equilbrium state are considered: an asymmetry between the wells which is suddenly removed, and a periodic time oscillating asymmetry. The first method generates wave packets that lead to collapses and revivals of the expectation values of the macroscopic variables, and we calculate the time scale for these revivals. The second method permits the excitation of a single energy eigenstate of the many-particle system, including Schroedinger cat states. We also discuss a band theory interpretation of the energy level structure of an asymmetric double-well, thereby identifying analogies to Bloch oscillations and Bragg resonances. Both the Bloch and Bragg dynamics are purely quantum and are not contained in the mean-field treatment.Comment: 31 pages, 14 figure

Bose-Einstein condensates in a double well: mean-field chaos and multi-particle entanglement

A recent publication [Phys. Rev. Lett. 100, 140408 (2008)] shows that there is a relation between mean-field chaos and multi-particle entanglement for BECs in a periodically shaken double well. 'Schrodinger-cat' like mesoscopic superpositions in phase-space occur for conditions for which the system displays mean-field chaos. In the present manuscript, more general highly-entangled states are investigated. Mean-field chaos accelerates the emergence of multi-particle entanglement; the boundaries of stable regions are particularly suited for entanglement generation.Comment: 5 Pages, 5 jpg-figures, to be published in the proceedings of the LPHYS0

Cortico-subcortical functional connectivity profiles of resting-state networks in marmosets and humans

Copyright © 2020 the authors Understanding the similarity of cortico-subcortical networks topologies between humans and nonhuman primate species is critical to study the origin of network alternations underlying human neurologic and neuropsychiatric diseases. The New World common marmoset (Callithrix jacchus) has become popular as a nonhuman primate model for human brain function. Most marmoset connectomic research, however, has exclusively focused on cortical areas, with connectivity to subcortical networks less extensively explored. Here, we aimed to first isolate patterns of subcortical connectivity with cortical resting-state networks in awake marmosets using resting-state fMRI, then to compare these networks with those in humans using connectivity fingerprinting. In this study, we used 5 marmosets (4 males, 1 female). While we could match several marmoset and human resting-state networks based on their functional fingerprints, we also found a few striking differences, for example, strong functional connectivity of the default mode network with the superior colliculus in marmosets that was much weaker in humans. Together, these findings demonstrate that many of the core cortico-subcortical networks in humans are also present in marmosets, but that small, potentially functionally relevant differences exist

Dynamics of Dipolar Spinor Condensates

We study the semiclassical dynamics of a spinor condensate with the magnetic dipole-dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depends greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin exchange and dipole-dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and Macroscopic Quantum Self Trapping. Simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.Comment: 13 pages,3 figure