Phonon background versus analogue Hawking radiation in Bose-Einstein condensates

We determine the feasibility of detecting analogue Hawking radiation in a Bose-Einstein condensate in the presence of atom loss induced heating. We find that phonons created by three-body losses overshadow those due to analogue Hawking radiation. To overcome this problem, three-body losses may have to be suppressed, for example as proposed by Search et al. [Phys. Rev. Lett. 92 140401 (2004)]. The reduction of losses to a few percent of their normal rate is typically sufficient to suppress the creation of loss phonons on the time scale of a fast analogue Hawking phonon detection.Comment: 4 pages, no figures, revised versio

Dark matter axions

The hypothesis of an `invisible' axion was made by Misha Shifman and others, approximately thirty years ago. It has turned out to be an unusually fruitful idea, crossing boundaries between particle physics, astrophysics and cosmology. An axion with mass of order $10^{-5}$ eV (with large uncertainties) is one of the leading candidates for the dark matter of the universe. It was found recently that dark matter axions thermalize and form a Bose-Einstein condensate (BEC). Because they form a BEC, axions differ from ordinary cold dark matter (CDM) in the non-linear regime of structure formation and upon entering the horizon. Axion BEC provides a mechanism for the production of net overall rotation in dark matter halos, and for the alignment of cosmic microwave anisotropy multipoles. Because there is evidence for these phenomena, unexplained with ordinary CDM, an argument can be made that the dark matter is axions.Comment: 12 pages, invited talk at the Workshop `Crossing the Boundaries: Gauge Dynamics at Strong Coupling' in honor of Misha Shifman's 60th birthday, March 14-17, 2009, in Minneapolis, M

Limits to the analogue Hawking temperature in a Bose-Einstein condensate

Quasi-one dimensional outflow from a dilute gas Bose-Einstein condensate reservoir is a promising system for the creation of analogue Hawking radiation. We use numerical modeling to show that stable sonic horizons exist in such a system under realistic conditions, taking into account the transverse dimensions and three-body loss. We find that loss limits the analogue Hawking temperatures achievable in the hydrodynamic regime, with sodium condensates allowing the highest temperatures. A condensate of 30,000 atoms, with transverse confinement frequency omega_perp=6800*2*pi Hz, yields horizon temperatures of about 20 nK over a period of 50 ms. This is at least four times higher than for other atoms commonly used for Bose-Einstein condensates.Comment: 9 pages, 4 figures, replaced with published versio

Potential Harmonics Expansion Method for Trapped Interacting Bosons : Inclusion of Two-Body Correlation

We study a system of $A$ identical interacting bosons trapped by an external field by solving ab initio the many-body Schroedinger equation. A complete solution by using, for example, the traditional hyperspherical harmonics (HH) basis develops serious problems due to the large degeneracy of HH basis, symmetrization of the wave function, calculation of the matrix elements, etc. for large $A$. Instead of the HH basis, here we use the "potential harmonics" (PH) basis, which is a subset of HH basis. We assume that the contribution to the orbital and grand orbital [in $3(A-1)$-dimensional space of the reduced motion] quantum numbers comes only from the interacting pair. This implies inclusion of two-body correlations only and disregard of all higher-body correlations. Such an assumption is ideally suited for the Bose-Einstein condensate (BEC), which is extremely dilute. Unlike the $(3A-4)$ hyperspherical variables in HH basis, the PH basis involves only three {\it{active}} variables. It drastically reduces the number of coupled equations and calculation of the potential matrix becomes tremendously simplified, as it involves integrals over only three variables for any $A$. One can easily incorporate realistic atom-atom interactions in a straight forward manner. We study the ground and excited state properties of the condensate for both attractive and repulsive interactions for various particle number.Comment: 36 pages, 7 included figures, plain late

Gap solitons in quasiperiodic optical lattices

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three bandgaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.Comment: 8 pages, 11 figure

Dipole Oscillations in Bose - Fermi Mixture in the Time-Dependent Grosspitaevskii and Vlasov equations

We study the dipole collective oscillations in the bose-fermi mixture using a dynamical time-dependent approach, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. We find big difference in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the random-phase approximation and the sum-rule approach. While the bose gas oscillates monotonously, the fermion oscillation shows a beat and a damping. When the amplitude is not minimal, the dipole oscillation of the fermi gas cannot be described with a simple center-of-mass motion.Comment: 17 pages text, and 15 figure

Collapsing Bose-Einstein condensates beyond the Gross-Pitaevskii approximation

We analyse quantum field models of the bosenova experiment, in which $^{85}$Rb Bose-Einstein condensates were made to collapse by switching their atomic interactions from repulsive to attractive. Specifically, we couple the lowest order quantum field correlation functions to the Gross-Pitaevskii function, and solve the resulting dynamical system numerically. Comparing the computed collapse times with the experimental measurements, we find that the calculated times are much larger than the measured values. The addition of quantum field corrections does not noticeably improve the agreement compared to a pure Gross-Pitaevskii theory.Comment: 8 pages, 4 figure

Cosmic axion thermalization

Axions differ from the other cold dark matter candidates in that they form a degenerate Bose gas. It is shown that their huge quantum degeneracy and large correlation length cause cold dark matter axions to thermalize through gravitational self-interactions when the photon temperature reaches approximately 500 eV. When they thermalize, the axions form a Bose-Einstein condensate. Their thermalization occurs in a regime, herein called the `condensed regime', where the Boltzmann equation is not valid because the energy dispersion of the particles is smaller than their interaction rate. We derive analytical expressions for the thermalization rate of particles in the condensed regime, and check the validity of these expressions by numerical simulation of a toy model. We revisit axion cosmology in light of axion Bose-Einstein condensation. It is shown that axions are indistinguishable from ordinary cold dark matter on all scales of observational interest, except when they thermalize or rethermalize. The rethermalization of axions that are about to fall in a galactic potential well causes them to acquire net overall rotation as they go to the lowest energy state consistent with the total angular momentum they acquired by tidal torquing. This phenomenon explains the occurrence of caustic rings of dark matter in galactic halos. We find that photons may reach thermal contact with axions and investigate the implications of this possibility for the measurements of cosmological parameters.Comment: 38 pages, 1 figur

Monopole Oscillations and Dampings in Boson and Fermion Mixture in the Time-Dependent Gross-Pitaevskii and Vlasov Equations

We construct a dynamical model for the time evolution of the boson-fermion coexistence system. The dynamics of bosons and fermions are formulated with the time-dependent Gross-Pitaevsky equation and the Vlasov equation. We thus study the monopole oscillation in the bose-fermi mixture. We find that large damping exists for fermion oscillations in the mixed system even at zero temperature.Comment: 16 pages text and 12 figure

Sinusoidal Excitations in Two Component Bose-Einstein Condensates

The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit pure sinusoidal, propagating wave solutions in quasi one dimensional geometry. These solutions, which exist for a wide parameter range, are then investigated in the presence of a harmonic oscillator trap with time dependent scattering length. This illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. We subsequently analyzed this system in an optical lattice, where the occurrence of an irreversible phase transition from superfluid to insulator phase is seen.Comment: 6 pages, 1 figur