Phase Coherence in a Driven Double-Well System

We analyze the dynamics of the molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunnelling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunnelling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.Comment: 5 pages, 2 figure

General Non-minimal Kinetic coupling to gravity

We study a new model of scalar field with a general non-minimal kinetic coupling to itself and to the curvature, as a source of dark energy, and analyze the cosmological dynamics of this model and the issue of accelerated expansion. A wide variety of scalar fields and potentials giving rise to power-law expansion have been found. The dynamical equation of state is studied for the two cases, without and with free kinetic term . In the first case, a behavior very close to that of the cosmological constant was found. In the second case, a solution was found, which match the current phenomenology of the dark energy. The model shows a rich variety of dynamical scenarios.Comment: 25 pages, 3 figures; figure added, references adde

Regularizing cosmological singularities by varying physical constants

Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $\Lambda$-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.Comment: 9 pages, 6 figures, Revtex4-1, an improved version to appear in JCA

Phase Conjugation of a Quantum-Degenerate Atomic Fermi Beam

We discuss the possibility of phase-conjugation of an atomic Fermi field via nonlinear wave mixing in an ultracold gas. It is shown that for a beam of fermions incident on an atomic phase-conjugate mirror, a time reversed backward propagating fermionic beam is generated similar to the case in nonlinear optics. By adopting an operational definition of the phase, we show that it is possible to infer the presence of the phase-conjugate field by the loss of the interference pattern in an atomic interferometer

Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.Comment: revtex, 15 pages,8 figure

A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints

We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and positive propagation speeds, and free of separatrices). Models that satisfy these physical and observational constraints are found in this analysis and do provide fits to the data that are very close to those of the LCDM concordance model. However, we find that the limitation of the models considered here comes from the presence of superluminal mode propagations for the constrained parameter space of the models.Comment: 12 pages, 6 figure

Measuring dark energy spatial inhomogeneity with supernova data

The gravitational lensing distortion of distant sources by the large-scale distribution of matter in the Universe has been extensively studied. In contrast, very little is known about the effects due to the large-scale distribution of dark energy. We discuss the use of Type Ia supernovae as probes of the spatial inhomogeneity and anisotropy of dark energy. We show that a shallow, almost all-sky survey can limit rms dark energy fluctuations at the horizon scale down to a fractional energy density of ~10^-4Comment: 4 pages; PRL submitte

Direct Measurement of the Positive Acceleration of the Universe and Testing Inhomogeneous Models under Gravitational Wave Cosmology

One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $\Lambda$CDM and these inhomogeneous models, direct measurement of the acceleration of the universe can be a powerful tool in probing them. We have shown that, if $\Lambda$CDM is the correct model, DECIGO/BBO would be able to detect the positive redshift drift (which is the time evolution of the source redshift $z$) in 3--5 year gravitational wave (GW) observations from neutron-star binaries, which enables us to rule out any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. We may even be able to rule out any LTB model unless we allow unrealistically steep density profile at $z\sim 0$. This test can be performed with GW observations alone, without any reference to electromagnetic observations, and is more powerful than the redshift drift measurement using Lyman $\alpha$ forest.Comment: 5 pages, 2 figure

Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $\Lambda CDM$ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for $\Omega_{\Lambda}>1/3$ as implied by previous proofs that $q^{app}_0$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $\Lambda CDM$ models not only because it is not possible to reproduce a negative apparent central deceleration $q^{app}_0$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.Comment: 18 pages, corrected a typo in the definition of the energy density which doesn't change the conclusion, references adde

Comparison of Recent SnIa datasets

We rank the six latest Type Ia supernova (SnIa) datasets (Constitution (C), Union (U), ESSENCE (Davis) (E), Gold06 (G), SNLS 1yr (S) and SDSS-II (D)) in the context of the Chevalier-Polarski-Linder (CPL) parametrization $w(a)=w_0+w_1 (1-a)$, according to their Figure of Merit (FoM), their consistency with the cosmological constant ($\Lambda$CDM), their consistency with standard rulers (Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO)) and their mutual consistency. We find a significant improvement of the FoM (defined as the inverse area of the 95.4% parameter contour) with the number of SnIa of these datasets ((C) highest FoM, (U), (G), (D), (E), (S) lowest FoM). Standard rulers (CMB+BAO) have a better FoM by about a factor of 3, compared to the highest FoM SnIa dataset (C). We also find that the ranking sequence based on consistency with $\Lambda$CDM is identical with the corresponding ranking based on consistency with standard rulers ((S) most consistent, (D), (C), (E), (U), (G) least consistent). The ranking sequence of the datasets however changes when we consider the consistency with an expansion history corresponding to evolving dark energy $(w_0,w_1)=(-1.4,2)$ crossing the phantom divide line $w=-1$ (it is practically reversed to (G), (U), (E), (S), (D), (C)). The SALT2 and MLCS2k2 fitters are also compared and some peculiar features of the SDSS-II dataset when standardized with the MLCS2k2 fitter are pointed out. Finally, we construct a statistic to estimate the internal consistency of a collection of SnIa datasets. We find that even though there is good consistency among most samples taken from the above datasets, this consistency decreases significantly when the Gold06 (G) dataset is included in the sample.Comment: 13 pages, 9 figures. Included recently released SDSS-II dataset. Improved presentation. Main results unchanged. The mathematica files and datasets used for the production of the figures may be downloaded from http://leandros.physics.uoi.gr/datacomp