Sagnac Effect of Goedel's Universe

We present exact expressions for the Sagnac effect of Goedel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Goedel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.Comment: 26 pages, including 4 figures, corrected typos, changed reference

Quantum reservoirs with ion chains

Ion chains are promising platforms for studying and simulating quantum reservoirs. One interesting feature is that their vibrational modes can mediate entanglement between two objects which are coupled through the vibrational modes of the chain. In this work we analyse entanglement between the transverse vibrations of two heavy impurity defects embedded in an ion chain, which is generated by the coupling with the chain vibrations. We verify general scaling properties of the defects dynamics and demonstrate that entanglement between the defects can be a stationary feature of these dynamics. We then analyse entanglement in chains composed of tens of ions and propose a measurement scheme which allows one to verify the existence of the predicted entangled state.Comment: 14 pages, 12 figure

Phase-dependent light propagation in atomic vapors

Light propagation in an atomic medium whose coupled electronic levels form a diamond-configuration exhibits a critical dependence on the input conditions. In particular, the relative phase of the input fields gives rise to interference phenomena in the electronic excitation whose interplay with relaxation processes determines the stationary state. We integrate numerically the Maxwell-Bloch equations and observe two metastable behaviors for the relative phase of the propagating fields corresponding to two possible interference phenomena. These phenomena are associated to separate types of response along propagation, minimize dissipation, and are due to atomic coherence. These behaviors could be studied in gases of isotopes of alkali-earth atoms with zero nuclear spin, and offer new perspectives in control techniques in quantum electronics.Comment: 16 pages, 11 figures, v2: typos corrected, v3: final version, to appear in Phys. Rev.

New frontiers at the interface of general relativity and quantum optics

In the present paper we follow three major themes: (i) concepts of rotation in general relativity, (ii) effects induced by these generalized rotations, and (iii) their measurement using interferometry. Our journey takes us from the Foucault pendulum via the Sagnac interferometer to manifestations of gravito-magnetism in double binary pulsars and in Gödel\u27s Universe. Throughout our article we emphasize the emerging role of matter wave interferometry based on cold atoms or Bose-Einstein condensates leading to superior inertial sensors. In particular, we advertise recent activities directed towards the operation of a coherent matter wave interferometer in an extended free fall. © 2009 Springer Science+Business Media B.V

Enhanced frequency up-conversion in Rb vapor

We demonstrate highly efficient generation of coherent 420nm light via up-conversion of near-infrared lasers in a hot rubidium vapor cell. By optimizing pump polarizations and frequencies we achieve a single-pass conversion efficiency of 260% per Watt, significantly higher than in previous experiments. A full exploration of the coherent light generation and fluorescence as a function of both pump frequencies reveals that coherent blue light is generated close to 85Rb two-photon resonances, as predicted by theory, but at high vapor pressure is suppressed in spectral regions that do not support phase matching or exhibit single-photon Kerr refraction. Favorable scaling of our current 1mW blue beam power with additional pump power is predicted.Comment: 6 pages, 4 figures. Modified to include referees' improvement

Dropping cold quantum gases on Earth over long times and large distances

We describe the non-relativistic time evolution of an ultra-cold degenerate quantum gas (bosons/fermions) falling in Earth's gravity during long times (10 sec) and over large distances (100 m). This models a drop tower experiment that is currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany). Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop the quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate non-inertial forces, provided all external potentials (trap, gravity) can be approximated with a second order Taylor expansion around the instantaneous trap center. This is an excellent assumption and the harmonic potential theorem applies. As an application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest-frame of the superfluid wave packet, the long-distance drop (100m) can be studied easily on a numerical grid.Comment: 18 pages latex, 5 eps figures, submitte

General relativistic Sagnac formula revised

The Sagnac effect is a time or phase shift observed between two beams of light traveling in opposite directions in a rotating interferometer. We show that the standard description of this effect within the framework of general relativity misses the effect of deflection of light due to rotational inertial forces. We derive the necessary modification and demonstrate it through a detailed analysis of the square Sagnac interferometer rotating about its symmetry axis in Minkowski space-time. The role of the time shift in a Sagnac interferometer in the synchronization procedure of remote clocks as well as its analogy with the Aharanov-Bohm effect are revised.Comment: 11 pages, 3 figure