Nonlinear dynamics of a Bose-Einstein condensate in a magnetic waveguide

We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.     

Observation of topologically stable 2D Skyrmions in an antiferromagnetic spinor Bose-Einstein condensate

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.     

Coupling between Collective Excitations of a Bose--Einstein Condensate and Modulated Interactions

We investigate collective excitations of a Bose Einstein repulsive interactions, and analytically demonstrate that condensate in the presence of temporal modulation of the modulated interaction can drive the condensate to oscillate with the external modulation frequency, and that the interaction couples with the eigen modes of the condensate collective excitations, which was previously considered to be independent of interaction. When the external modulation frequency approaches or is far away from the eigen frequency of the density monopole mode, the condensate shows resonant or beating behaviour.     

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram,self-similar solutions,and dispersive shock waves

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.     

AdS/CFT Correspondence and Dark Soliton

In this paper we use the AdS/CFT correspondence to study dark soliton solutions in a holographic model of a relativistic superfluid. We calculate the length scales corresponding to the condensate and the charge density depletion, and find relation with the chemical potential. We compare our solutions with the quasiparticle excitations above the holographic superfluid and find that the scale of the excitations is comparable to the soliton coherence length scales.     

The high temperature superconductivity in cuprates: physics of the pseudogap region

We discuss the physics of the high temperature superconductivity in hole doped copperoxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonianrelevant to the dynamics of holes injected into the copper oxide layers proposed in aprevious paper, we determine the superconductive condensate wavefunction. We show that thelow-lying elementary condensate excitations are analogous to the rotons in superfluid⁴He. We arguethat the rotons-like excitations account for the specific heat anomaly at the criticaltemperature. We discuss and compare with experimental observations the London penetrationlength, the Abrikosov vortices, the upper and lower critical magnetic fields, and thecritical current density. We give arguments to explain the origin of the Fermi arcs andFermi pockets. We investigate the nodal gap in the cuprate superconductors and discussboth the doping and temperature dependence of the nodal gap. We suggest that the nodal gapis responsible for the doping dependence of the so-called nodal Fermi velocity detected inangle resolved photoemission spectroscopy studies. We discuss the thermodynamics of thenodal quasielectron liquid and their role in the low temperature specific heat. We proposethat the ubiquitous presence of charge density wave in hole doped cuprate superconductorsin the pseudogap region originates from instabilities of the nodal quasielectrons drivenby the interaction with the planar CuO₂ lattice. We investigate the doping dependence of thecharge density wave gap and the competition between charge order and superconductivity. Wediscuss the effects of external magnetic fields on the charge density wave gap andelucidate the interplay between charge density wave and Abrikosov vortices. Finally, weexamine the physics underlying quantum oscillations in the pseudogap region.     

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.     

Analysis of a Bose-Einstein condensate double-well atom interferometer

Motivated by an open theoretical question in Bose-Einstein condensate atom interferometry, we introduce a novel computational method to describe the condensate order parameter in the presence of a central barrier. We are able to follow the full dynamics of the system during the raising of a barrier, from a single macroscopically occupied ground state to a state where imaging shows a split density and, finally, to the observation of a phase-controlled interference pattern. We are able to discriminate between a mean-field and a two-mode state via the Penrose-Onsager criterion. By simulating the first such experiment, where in spite of the observed splitting of the condensate density there is never more than a single macroscopically occupied state, we provide a definitive interpretation of these systems as a novel many-body form of Young's double-slit experiment.     

Soliton excitations in a polariton condensate with defects

To study soliton excitations in a polariton condensate with defects, we use the Gross-Pitaevskii equation and its hydrodynamic form. An extra term is added to take into account the non-equilibrium nature of the polariton condensate and the presence of defects. The reductive perturbation method transforms these hydrodynamic equations into a modified Korteweg-de Vries equation in the long wavelength limit. We linearize this equation and study the soliton linear excitations.We give an analytic expression of traveling excitations using the variation of constants method. In the more general form,we show numerically that the excitations are oscillations, i.e., the amplitude and the width of the dark soliton oscillate simultaneously but in an opposite way.     

Broken Gauge Symmetry in Macroscopic Quantum Circuits

In this paper, we discuss the macroscopic quantum behavior of simple superconducting circuits. Starting from a Lagrangian for electromagnetic field with broken gauge symmetry, we construct a quantum circuit model for a superconducting weak link (SQUID) ring, together with the appropriate canonical commutation relations. We demonstrate that this model can be used to describe macroscopic excitations of the superconducting condensate and the localized charge states found in some ultrasmall-capacitance weak-link devices.     

Bose glass and superfluid phases of cavity polaritons

We report the calculation of cavity exciton-polariton phase diagram including realistic structural disorder. With increasing density polaritons first undergo a quasiphase transition toward a Bose glass: the condensate is localized in at least one minimum of the disorder potential. A further increase of the density leads to a percolation process of the polariton fluid giving rise to a Kosterlitz-Thouless phase transition toward superfluidity. The spatial representation of the condensate wave function as well as the spectrum of elementary excitations are obtained from the Gross-Pitaevskii equation for all the phases.     

Quantum chaos of bogoliubov waves for a bose-einstein condensate in stadium billiards

We investigate the possibility of quantum (or wave) chaos for the Bogoliubov excitations of a Bose-Einstein condensate in billiards. Because of the mean field interaction in the condensate, the Bogoliubov excitations are very different from the single particle excitations in a noninteracting system. Nevertheless, we predict that the statistical distribution of level spacings is unchanged by mapping the non-Hermitian Bogoliubov operator to a real symmetric matrix. We numerically test our prediction by using a phase shift method for calculating the excitation energies.     

Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are, respectively, responsible for a conical wave front and a fan-shaped series of precursors.     

Quantum enhancement of higher-order phononlike excitations of a Bose-Einstein condensate

In a Bose-Einstein condensate, the excitation of a Bogoliubov phonon with low momentum (e.g., by a two-photon Bragg process) is strongly suppressed due to destructive interference between two indistinguishable excitation pathways. Here we show that scattering of this sound excitation into a double-momentum mode is strongly enhanced due to constructive interference. This enhancement yields an inherent amplification of second-order sound excitations of the condensate, as we confirm experimentally. We further show that due to parity considerations, this effect is extended to higher-order excitations.     

Possibility of a phase transition to a pion condensate in neutron stars

We consider the possibility that a pion condensate may arise in an infinite nuclear medium as a consequence of the modification of the pion propagator due to isobar-hole and nucleon-hole excitations, This does not seem likely in a system with N = Z at densities of less than 0.17 fm^?3, but does seem likely to occur at the densities encountered in the interior of neutron stars. We estimate a necessary neutron density of ? 0.38 fm^?3 and a condensate energy density of ? ? 0.25 MeV fm^?3.     

Beliaev damping of quasiparticles in a Bose-Einstein condensate

We report a measurement of the suppression of collisions of quasiparticles with ground state atoms within a Bose-Einstein condensate at low momentum. These collisions correspond to Beliaev damping of the excitations, in the previously unexplored regime of the continuous quasiparticle energy spectrum. We use a hydrodynamic simulation of the expansion dynamics, with the Beliaev damping cross section, in order to confirm the assumptions of our analysis.     

Two types of quasiparticles excited in a Bose gas

We present a novel approach for investigating the superfluid liquid 4He based on the proper use of the nonideal Bose gas model for dilute hard spheres. The results show that the presence of a macroscopic number of condensate atoms leads to the existence of a nonphysical branch, corresponding to density excitations, in addition to the continuous branch of the phonon-maxon-roton excitation spectrum.     

Pair Excitations and the Mean Field Approximation of Interacting Bosons, I

In our previous work (Grillakis et al. in Commun Math Phys 294:273–301, 2010; Adv Math 228:1788–1815, 2011) we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In Grillakis et al. (Adv Math 228:1788–1815, 2011) we carried out the analysis assuming that the interactions are independent of the number of particles N. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain a priori estimates independent of the number of particles and use these to compare the exact with the approximate dynamics.