Bogoliubov space of a Bose--Einstein condensate and quantum spacetime fluctuations

In the present work we consider the role that metric fluctuations could have upon the properties of a Bose--Einstein condensate. In particular we consider the Bogoliubov space associated to it and show that there are, at least, two independent ways in which the average size of these metric fluctuations could be, experimentally, determined. Indeed, we prove that the pressure and the speed of sound of the ground state define an expression allowing us to determine the average size of these fluctuations. Afterwards, an interferometric experiment involving Bogoliubov excitations of the condensate and the pressure (or the speed of sound of the ground state) provides a second and independent way in which this average size could be determined, experimentally

Space--time fluctuations and the spreading of wavepackets

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation we derive a Schr\"odinger equation with an additive gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow to study the dynamics of wavepackets in a fluctuating space-time, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.Comment: 11 page

Test of constancy of speed of light with rotating cryogenic optical resonators

A test of Lorentz invariance for electromagnetic waves was performed by comparing the resonance frequencies of two optical resonators as a function of orientation in space. In terms of the Robertson-Mansouri-Sexl theory, we obtain $\beta-\delta-1/2=(+0.5\pm 3\pm 0.7) E-10$, a ten-fold improvement compared to the previous best results. We also set a first upper limit for a so far unknown parameter of the Standard Model Extension test theory, $|(\tilde{\kappa}_{e-})^{ZZ}| < 2\cdot E-14$.Comment: 4 pages, 2 figures, accepted for publication Phys. Rev. A (2005

Metric fluctuations and decoherence

Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization of the inertial mass tensor results from a local space average over the fluctuations of the metric over a fixed background metric. Here, we demonstrate that the metric fluctuations of this model lead to a further physical effect, namely to an effective decoherence of the quantum particle. We derive a quantum master equation for the particle's density matrix, discuss in detail its dissipation and decoherence properties, and estimate the corresponding decoherence time scales. By contrast to other models discussed in the literature, in the present approach the metric fluctuations give rise to a decay of the coherences in the energy representation, i. e., to a localization in energy space.Comment: 7 page

Quantum spacetime fluctuations: Lamb Shift and hyperfine structure of the hydrogen atom

We consider the consequences of the presence of metric fluctuations upon the properties of a hydrogen atom. Particularly, we introduce these metric fluctuations in the corresponding effective Schroedinger equation and deduce the modifications that they entail upon the hyperfine structure related to a hydrogen atom. We will find the change that these effects imply for the ground state energy of the system and obtain a bound for its size comparing our theoretical predictions against the experimental uncertainty reported in the literature. In addition, we analyze the corresponding Lamb shift effect emerging from these fluctuations of spacetime. Once again, we will set a bound to these oscillations resorting to the current experimental outcomesComment: 26 page

Dephasing of a non-relativistic quantum particle due to a conformally fluctuating spacetime

We investigate the dephasing suffered by a nonrelativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein-Gordon field, the low velocity limit yields an effective Schrodinger equation where the wave function couples to gravity through an effective nonlinear potential induced by the conformal fluctuations. The quantum evolution is studied through a Dyson expansion scheme up to second order. We show that only the nonlinear part of the potential can induce dephasing. This happens through an exponential decay of the off diagonal terms of the particle density matrix. The bath of conformal radiation is modeled in 3-dimensions and its statistical properties are described in general in terms of a power spectral density. The case of a Lorentz invariant spectral density, allowing to model vacuum fluctuations at a low energy domain, is investigated and a general formula describing the loss of coherence derived. This depends quadratically on the particle mass and on the inverse cube of a typical particle dependent cutoff scale. Finally, the possibilities for experimental verification are discussed. It is shown that current interferometry experiments cannot detect such an effect. However this conclusion may improve by using high mass entangled quantum states.Comment: 30 pages, 4 figures; to appear in Class. Quantum Grav. (2009

STE-QUEST - Test of the Universality of Free Fall Using Cold Atom Interferometry

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the Universality of Free Fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of Rb85 and Rb87. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the E\"otv\"os parameter of at least 2x10E-15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources