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We study the nonequilibrium dynamics of an ultracold, non-degenerate dipolar gas of $^{164}$Dy atoms in a cylindrically symmetric harmonic trap. To do so, we investigate the normal modes and linear response of the gas when driven by means of periodic modulations to the trap axial-frequency. We find that the resonant response of the gas depends strongly on the dipole alignment axis, owing to anisotropies in the differential cross section of the atoms. We employ the use of the method of averages as well as numerical Monte Carlo methods for our analysis. A striking result is that certain normal modes, termed "melting modes", initiated in an anisotropic out-of-equilibrium configuration, relax to equilibrium without oscillating., Comment: 14 pages, 11 figures

We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations., Comment: 10 pages, 5 figures

We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the post-expansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases, reducing error in expansion thermometry from tens of percent to only a few percent. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion., Comment: main text and supplement, 11 pages total, 4 figures

We report the measurement of the triplet s-partial-wave scattering length $a$ of two bosonic isotopes of the highly magnetic element, dysprosium: $a=122(10)a_0$ for $^{162}$Dy and $a=92(8)a_0$ for $^{164}$Dy, where $a_0$ is the Bohr radius. The scattering lengths are determined by the cross-dimensional relaxation of ultracold gases of these Dy isotopes at temperatures above quantum degeneracy. In this temperature regime, the measured rethermalization dynamics can be compared to simulations of the Boltzmann equation using a direct-simulation Monte Carlo (DSMC) method employing the anisotropic differential scattering cross section of dipolar particles., Comment: corrected a typo in the value of the 162Dy scattering length

We study the relaxation and damping dynamics of an ultracold, but not quantum degenerate, gas consisting of dipolar particles. These simulations are performed using a direct simulation Monte Carlo method and employing the highly anisotropic differential cross section of dipoles in the Wigner threshold regime. We find that both cross-dimensional relaxation and damping of breathing modes occur at rates that are strongly dependent on the orientation of the dipole moments relative to the trap axis. The relaxation simulations are in excellent agreement with recent experimental results in erbium. The results direct our interest toward a less explored regime in dipolar gases where interactions are dominated by collision processes rather than mean-field interactions.

We use the Bogoliubov theory of Bose-Einstein condensation to study the properties of dipolar particles (atoms or molecules) confined in a uniform two-dimensional geometry at zero temperature. We find equilibrium solutions to the dipolar Gross-Pitaevskii equation and the Bogoliubov-de Gennes equations. Using these solutions we study the effects of quantum fluctuations in the system, particularly focussing on the instability point, where the roton feature in the excitation spectrum touches zero. Specifically, we look at the behaviour of the noncondensate density, the phase fluctuations, and the density fluctuations in the system. Near the instability, the density-density correlation function shows a particularly intriguing oscillatory behaviour. Higher order correlation functions display a distinct hexagonal lattice pattern formation, demonstrating how an observation of broken symmetry can emerge from a translationally symmetric quantum state., Comment: 9 pages, 7 figures

We study magnetic fluctuations in a system of interacting spins on a lattice at high temperatures and in the presence of a spatially varying magnetic field. Starting from a microscopic Hamiltonian we derive effective equations of motion for the spins and solve these equations self-consistently. We find that the spin fluctuations can be described by an effective diffusion equation with a diffusion coefficient which strongly depends on the ratio of the magnetic field gradient to the strength of spin-spin interactions. We also extend our studies to account for external noise and find that the relaxation times and the diffusion coefficient are mutually dependent.

This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as Goldstone modes) to the linearised problem. These solutions are then used to construct a Greens matrix which gives the first-order spatial response due to some perturbation. Finally we apply this Greens matrix to find the correction to the dark-soliton wavefunction of a Bose-Einstein condensate in the presence of fluctuations., Comment: 14 pages, 3 figures, submitted to Journal of Physics A

The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytical solutions to the Bogoliubov-de Gennes equations for a gray soliton. Our results raise questions regarding the quantum dynamics in the formation of persistent currents in superfluids., Comment: 7 pages (including supplementary material)

The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring., Comment: 13 pages, 12 figures