Particle creation in Bose--Einstein condensates: Theoretical formulation based on conserving gapless mean field theory

We formulate particle creation phenomena in Bose--Einstein condensates in terms of conserving gapless mean field theory for weakly interacting Bose gases. The particle creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean field theory. The conservation implies that quasiparticle creation is accompanied by quantum backreaction to the condensates. Particle creation in this mean field theory is found to be equivalent to that in quantum field theory (QFT) in curved spacetime. An expression is obtained for an effective metric affected by quantum backreaction. The formula for the particle creation spectrum obtained in terms of QFT in curved spacetime is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.Comment: 9 pages, typos correcte

Transition to superfluid turbulence governed by an intrinsic parameter

Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hydrodynamics of the B phase of superfluid 3He, we discovered a sharp transition at 0.60Tc between two regimes, with regular behaviour at high-temperatures and turbulence at low-temperatures. Unlike in classical fluids, this transition is insensitive to velocity and occurs at a temperature where the dissipative vortex damping drops below a critical limit. This discovery resolves the conflict between existing high- and low-temperature measurements in 3He-B: At high temperatures in rotating flow a vortex loop injected into superflow has been observed to expand monotonically to a single rectilinear vortex line, while at very low temperatures a tangled network of quantized vortex lines can be generated in a quiescent bath with a vibrating wire. The solution of this conflict reveals a new intrinsic criterion for the existence of superfluid turbulence.Comment: Revtex file; 5 pages, 2 figure

Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling

In $2048^3$ simulation of quantum turbulence within the Gross-Pitaevskii equation we demonstrate that the large scale motions have a classical Kolmogorov-1941 energy spectrum E(k) ~ k^{-5/3}, followed by an energy accumulation with E(k) ~ const at k about the reciprocal mean intervortex distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck model of gradual eddy-wave crossover [J. Low Temp. Phys. 153, 140-161 (2008)], further developed in the paper.Comment: (re)submitted to PRB: 5.5 pages, 4 figure

Quantum Turbulence in a Trapped Bose-Einstein Condensate

We study quantum turbulence in trapped Bose-Einstein condensates by numerically solving the Gross-Pitaevskii equation. Combining rotations around two axes, we successfully induce quantum turbulent state in which quantized vortices are not crystallized but tangled. The obtained spectrum of the incompressible kinetic energy is consistent with the Kolmogorov law, the most important statistical law in turbulence.Comment: 4 pages, 4 figures, Physical Review A 76, 045603 (2007

Numerical simulation of stochastic vortex tangles

We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the interaction with the normal component, or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, e.i. we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-disspation relation, which implies that thermodynamic equilibrium should be reached. In the paper we describe the numerical methods for integration of stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of calculation of some characteristics of a vortex tangle such as the total length, distribution of loops in the space of their length, and the energy spectrum.Comment: 8 pages, 5 figure

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence has been numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtained the mutual friction coefficients of the vortex dynamics as functions of temperature, which can be applied to the vortex dynamics in dilute Bose-Einstein condensates.Comment: 4 pages, 6 figures, submitted to AP

Optical response of ferromagnetic YTiO_3 studied by spectral ellipsometry

We have studied the temperature dependence of spectroscopic ellipsometry spectra of an electrically insulating, nearly stoichiometric YTiO_3 single crystal with ferromagnetic Curie temperature T_C = 30 K. The optical response exhibits a weak but noticeable anisotropy. Using a classical dispersion analysis, we identify three low-energy optical bands at 2.0, 2.9, and 3.7 eV. Although the optical conductivity spectra are only weakly temperature dependent below 300 K, we are able to distinguish high- and low-temperature regimes with a distinct crossover point around 100 K. The low-temperature regime in the optical response coincides with the temperature range in which significant deviations from Curie-Weiss mean field behavior are observed in the magnetization. Using an analysis based on a simple superexchange model, the spectral weight rearrangement can be attributed to intersite d_i^1d_j^1 \longrightarrow d_i^2d_j^0 optical transitions. In particular, Kramers-Kronig consistent changes in optical spectra around 2.9 eV can be associated with the high-spin-state (^3T_1) optical transition. This indicates that other mechanisms, such as weakly dipole-allowed p-d transitions and/or exciton-polaron excitations, can contribute significantly to the optical band at 2 eV. The recorded optical spectral weight gain of 2.9 eV optical band is significantly suppressed and anisotropic, which we associate with complex spin-orbit-lattice phenomena near ferromagnetic ordering temperature in YTiO_3

Shape oscillation of a rotating Bose-Einstein condensate

We present a theoretical and experimental analysis of the transverse monopole mode of a fast rotating Bose-Einstein condensate. The condensate's rotation frequency is similar to the trapping frequency and the effective confinement is only ensured by a weak quartic potential. We show that the non-harmonic character of the potential has a clear influence on the mode frequency, thus making the monopole mode a precise tool for the investigation of the fast rotation regime

Turbulence in Boundary Flow of Superfluid 4^4He Triggered by Free Vortex Rings

The transition to turbulence in the boundary flow of superfluid $^4$He is investigated using a vortex--free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.Comment: 4 pages, 4 figures, submitted to AP

Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential

We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, intensity, and lattice constant of the rotating lattice potential.Comment: 6 pages, 8 figures, submitted to Quantum Fluids and Solids Conference (QFS 2006