Excitations of a Binary Dipolar Supersolid.

We predict a rich excitation spectrum of a binary dipolar supersolid in a linear crystal geometry, where the ground state consists of two partially immiscible components with alternating, interlocking domains. We identify three Goldstone branches, each with first-sound, second-sound, or spin-sound character. In analogy with a diatomic crystal, the resulting lattice has a two-domain primitive basis and we find that the crystal (first-sound-like) branch is split into optical and acoustic phonons.

Measurement of the Excitation Spectrum of a Dipolar Gas in the Macrodroplet Regime.

The excitation spectrum of a cigar-shaped strongly dipolar quantum gas at the crossover from a Bose-Einstein condensate to a trapped macrodroplet is predicted to exhibit peculiar features-a strong upward shift of low momentum excitation energies together with a strong multiband response for high momenta. By performing Bragg spectroscopy over a wide range of momenta, we observe both key elements and also confirm the predicted stiffening of excitation modes when approaching the macrodroplet regime. Our measurements are in good agreement with numerical calculations taking into account finite size effects.

Propagating Ferrodark Solitons in a Superfluid: Exact Solutions and Anomalous Dynamics.

Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher energy branch with negative inertial mass.

Quantum Droplet States of a Binary Magnetic Gas.

Quantum droplets can emerge in bosonic binary magnetic gases (BMGs) from the interplay of short- and long-ranged interactions, and quantum fluctuations. We develop an extended mean field theory for this system and use it to predict equilibrium and dynamical properties of BMG droplets. We present a phase diagram and characterize miscible and immiscible droplet states.

Droplet Crystal Ground States of a Dipolar Bose Gas.

We show that the ground state of a dipolar Bose gas in a cylindrically symmetric harmonic trap has a rich phase diagram, including droplet crystal states in which a set of droplets arrange into a lattice pattern that breaks the rotational symmetry. An analytic model for small droplet crystals is developed and used to obtain a zero temperature phase diagram that is numerically validated. We show that in certain regimes a coherent low-density halo surrounds the droplet crystal, giving rise to a novel phase with localized and extended features.

Collective Excitations of Self-Bound Droplets of a Dipolar Quantum Fluid.

We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low-angular-momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number N is reduced to the critical value N_{c} is associated with a monopolelike excitation going soft as ε_{0}∼(N-N_{c})^{1/4}.

Coarsening Dynamics of an Isotropic Ferromagnetic Superfluid.

In zero magnetic field the ground-state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits Z_{2} vortices as topological defects. We investigate the phase-ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero-temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains.

Solving the spin-2 Gross-Pitaevskii equation using exact nonlinear dynamics and symplectic composition.

We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates.

Multiple scattering dynamics of fermions at an isolated p-wave resonance.

The wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions, this requirement strictly prohibits scattering into 90° angles. Here we experimentally investigate the collisions of ultracold clouds fermionic (40)K atoms by directly measuring scattering distributions.

Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation.

We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exactly solvable flows. We use this to implement a second-order and a fourth-order symplectic integration method.

Universal Coarsening Dynamics of a Quenched Ferromagnetic Spin-1 Condensate.

We demonstrate that a quasi-two-dimensional spin-1 condensate quenched to a ferromagnetic phase undergoes universal coarsening in its late time dynamics. The quench can be implemented by a sudden change in the applied magnetic field and, depending on the final value, the ferromagnetic phase has easy-axis (Ising) or easy-plane (XY) symmetry, with different dynamical critical exponents. Our results for the easy-plane phase reveal a fractal domain structure and the crucial role of polar-core spin vortices in the coarsening dynamics.

Number fluctuations of a dipolar condensate: anisotropy and slow approach to the thermodynamic regime.

We present a theory for the number fluctuations of a quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate measured with finite resolution cells. We show that when the dipoles are tilted to have a component parallel to the plane of the trap, the number fluctuations become anisotropic, i.e.

Numerical method for the stochastic projected Gross-Pitaevskii equation.

We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction.

Fingerprinting rotons in a dipolar condensate: super-Poissonian peak in the atom-number fluctuations.

We demonstrate that measurements of atom-number fluctuations in a trapped dipolar condensate can reveal the presence of the elusive roton excitation. The key signature is a super-Poissonian peak in the fluctuations as the size of the measurement cell is varied, with the maximum occurring when the size is comparable to the roton wavelength. The magnitude of this roton feature is enhanced with temperature.

Numerical method for evolving the dipolar projected Gross-Pitaevskii equation.

We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic-oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low-energy c -field region of the system. We present a scheme, using a Hermite-polynomial-based spectral representation, which precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE.

Numerical method for evolving the projected Gross-Pitaevskii equation.

In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE.

Critical temperature of a trapped Bose gas: comparison of theory and experiment.

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature Tc of a harmonically confined Bose gas as reported in Gerbier et al., Phys. Rev.

Thermal activation of vortex-antivortex pairs in quasi-two-dimensional Bose-Einstein condensates.

Here we show, by performing ab initio classical field simulations that two distinct superfluid phases, separated by thermal vortex-antivortex pair creation, exist in experimentally producible quasi-2D Bose gas. These results resolve the debate on the nature of the low temperature phase(s) of a trapped interacting 2D Bose gas.

Spatially selective bragg scattering: a signature for vortices in Bose-Einstein condensates.

We demonstrate that Bragg scattering from a condensate can be sensitive to the spatial phase distribution of the initial state. This allows preferential scattering from a selected spatial region, and provides a robust signature for a vortex state. We develop an analytic model which accurately describes this phenomenon, and we give quantitative predictions for current experimental conditions.