Two-component Bose gas in an optical lattice at single-particle filling

The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose.Comment: 11 page

Decoupling Dark Energy from Matter

We examine the embedding of dark energy in high energy models based upon supergravity and extend the usual phenomenological setting comprising an observable sector and a hidden supersymmetry breaking sector by including a third sector leading to the acceleration of the expansion of the universe. We find that gravitational constraints on the non-existence of a fifth force naturally imply that the dark energy sector must possess an approximate shift symmetry. When exact, the shift symmetry provides an example of a dark energy sector with a runaway potential and a nearly massless dark energy field whose coupling to matter is very weak, contrary to the usual lore that dark energy fields must couple strongly to matter and lead to gravitational inconsistencies. Moreover, the shape of the potential is stable under one-loop radiative corrections. When the shift symmetry is slightly broken by higher order terms in the Kähler potential, the coupling to matter remains small. However, the cosmological dynamics are largely affected by the shift symmetry breaking operators leading to the appearance of a minimum of the scalar potential such that dark energy behaves like an effective cosmological constant from very early on in the history of the universe

Dynamics of Fermionic Four-Wave Mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the novel technique of ``atom echoes''.Comment: 8 pages, 7 figure

Can a matter-dominated model with constant bulk viscosity drive the accelerated expansion of the universe?

We test a cosmological model which the only component is a pressureless fluid with a constant bulk viscosity as an explanation for the present accelerated expansion of the universe. We classify all the possible scenarios for the universe predicted by the model according to their past, present and future evolution and we test its viability performing a Bayesian statistical analysis using the SCP ``Union'' data set (307 SNe Ia), imposing the second law of thermodynamics on the dimensionless constant bulk viscous coefficient \zeta and comparing the predicted age of the universe by the model with the constraints coming from the oldest globular clusters. The best estimated values found for \zeta and the Hubble constant Ho are: \zeta=1.922 \pm 0.089 and Ho=69.62 \pm 0.59 km/s/Mpc with a \chi^2=314. The age of the universe is found to be 14.95 \pm 0.42 Gyr. We see that the estimated value of Ho as well as of \chi^2 are very similar to those obtained from LCDM model using the same SNe Ia data set. The estimated age of the universe is in agreement with the constraints coming from the oldest globular clusters. Moreover, the estimated value of \zeta is positive in agreement with the second law of thermodynamics (SLT). On the other hand, we perform different forms of marginalization over the parameter Ho in order to study the sensibility of the results to the way how Ho is marginalized. We found that it is almost negligible the dependence between the best estimated values of the free parameters of this model and the way how Ho is marginalized in the present work. Therefore, this simple model might be a viable candidate to explain the present acceleration in the expansion of the universe.Comment: 31 pages, 12 figures and 2 tables. Accepted to be published in the Journal of Cosmology and Astroparticle Physics. Analysis using the new SCP "Union" SNe Ia dataset instead of the Gold 2006 and ESSENCE datasets and without changes in the conclusions. Added references. Related works: arXiv:0801.1686 and arXiv:0810.030

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde

Laser-induced collective excitations in a two-component Fermi gas

We consider the linear density response of a two-component (superfluid) Fermi gas of atoms when the perturbation is caused by laser light. We show that various types of laser excitation schemes can be transformed into linear density perturbations, however, a Bragg spectroscopy scheme is needed for transferring energy and momentum into a collective mode. This makes other types of laser probing schemes insensitive for collective excitations and therefore well suited for the detection of the superfluid order parameter. We show that for the special case when laser light is coupled between the two components of the Fermi gas, density response is always absent in a homogeneous system.Comment: 6 pages, no figure

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex

Casimir Energies for 6D Supergravities Compactified on T_2/Z_N with Wilson Lines

We compute (as functions of the shape and Wilson-line moduli) the one-loop Casimir energy induced by higher-dimensional supergravities compactified from 6D to 4D on 2-tori, and on some of their Z_N orbifolds. Detailed calculations are given for a 6D scalar field having an arbitrary 6D mass m, and we show how to extend these results to higher-spin fields for supersymmetric 6D theories. Particular attention is paid to regularization issues and to the identification of the divergences of the potential, as well as the dependence of the result on m, including limits for which m^2 A> 1 where A is the volume of the internal 2 dimensions. Our calculation extends those in the literature to very general boundary conditions for fields about the various cycles of these geometries. The results have potential applications towards Supersymmetric Large Extra Dimensions (SLED) as a theory of the Dark Energy. First, they provide an explicit calculation within which to follow the dependence of the result on the mass of the bulk states which travel within the loop, and for heavy masses these results bear out the more general analysis of the UV-sensitivity obtained using heat-kernel methods. Second, because the potentials we find describe the dynamics of the classical flat directions of these compactifications, within SLED they would describe the present-day dynamics of the Dark Energy.Comment: 40 pages, 7 figure

Theory of output coupling for trapped fermionic atoms

We develop a dynamic theory of output coupling, for fermionic atoms initially confined in a magnetic trap. We consider an exactly soluble one-dimensional model, with a spatially localized delta-type coupling between the atoms in the trap and a continuum of free-particle external modes. Two important special cases are considered for the confinement potential: the infinite box and the harmonic oscillator. We establish that in both cases a bound state of the coupled system appears for any value of the coupling constant, implying that the trap population does not vanish in the infinite-time limit. For weak coupling, the energy spectrum of the outgoing beam exhibits peaks corresponding to the initially occupied energy levels in the trap; the height of these peaks increases with the energy. As the coupling gets stronger, the energy spectrum is displaced towards dressed energies of the fermions in the trap. The corresponding dressed states result from the coupling between the unperturbed fermionic states in the trap, mediated by the coupling between these states and the continuum. In the strong-coupling limit, there is a reinforcement of the lowest-energy dressed mode, which contributes to the energy spectrum of the outgoing beam more strongly than the other modes. This effect is especially pronounced for the one-dimensional box, which indicates that the efficiency of the mode-reinforcement mechanism depends on the steepness of the confinement potential. In this case, a quasi-monochromatic anti-bunched atomic beam is obtained. Results for a bosonic sample are also shown for comparison.Comment: 16 pages, 7 figures, added discussion on time-dependent spectral distribution and corresponding figur

Pairing in two-dimensional boson-fermion mixtures

The possibilities of pairing in two-dimensional boson-fermion mixtures are carefully analyzed. It is shown that the boson-induced attraction between two identical fermions dominates the p-wave pairing at low density. For a given fermion density, the pairing gap becomes maximal at a certain optimal boson concentration. The conditions for observing pairing in current experiments are discussedComment: 10 pages, 5 figs, revtex