On a generalized gravitational Aharonov-Bohm effect

A massless spinor particle is considered in the background gravitational field due to a rotating body. In the weak field approximation it is shown that the solution of the Weyl equations depend on the angular momentum of the rotating body, which does not affect the curvature in this approximation. This result may be looked upon as a generalization of the gravitational Aharonov-Bohm effect.Comment: 10 pages, LATEX fil

Sagnac interferometry based on ultra-slow polaritons in cold atomic vapors

The advantages of light and matter-wave Sagnac interferometers -- large area on one hand and high rotational sensitivity per unit area on the other -- can be combined utilizing ultra-slow light in cold atomic gases. While a group-velocity reduction alone does not affect the Sagnac phase shift, the associated momentum transfer from light to atoms generates a coherent matter-wave component which gives rise to a substantially enhanced rotational signal. It is shown that matter-wave sensitivity in a large-area interferometer can be achieved if an optically dense vapor at sub-recoil temperatures is used. Already a noticeable enhancement of the Sagnac phase shift is possible however with much less cooling requirements.Comment: 4 pages, 3 figure

A large magnetic storage ring for Bose-Einstein condensates

Cold atomic clouds and Bose-Einstein condensates have been stored in a 10cm diameter vertically-oriented magnetic ring. An azimuthal magnetic field enables low-loss propagation of atomic clouds over a total distance of 2m, with a heating rate of less than 50nK/s. The vertical geometry was used to split an atomic cloud into two counter-rotating clouds which were recombined after one revolution. The system will be ideal for studying condensate collisions and ultimately Sagnac interferometry.Comment: 4 pages, 5 figure

Gravitomagnetism, clocks and geometry

New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The effect of the angular momentum of the source is manifested in the fact that inertial observers must be replaced by local non rotating observers. Starting from this an exact formula for circular trajectories is found. Numerical estimates for the Earth environment show that light would be a better probe than actual clocks to evidence the angular momentum influence. The advantages of light in connection with some principle experiments are shortly reviewed.Comment: TCI Latex, 12 pages, 2 figures. To appear in European Journal of Physic

Quantum sensitivity limit of a Sagnac hybrid interferometer based on slow-light propagation in ultra-cold gases

The light--matter-wave Sagnac interferometer based on ultra-slow light proposed recently in (Phys. Rev. Lett. 92, 253201 (2004)) is analyzed in detail. In particular the effect of confining potentials is examined and it is shown that the ultra-slow light attains a rotational phase shift equivalent to that of a matter wave, if and only if the coherence transfer from light to atoms associated with slow light is associated with a momentum transfer and if an ultra-cold gas in a ring trap is used. The quantum sensitivity limit of the Sagnac interferometer is determined and the minimum detectable rotation rate calculated. It is shown that the slow-light interferometer allows for a significantly higher signal-to-noise ratio as possible in current matter-wave gyroscopes.Comment: 12 pages, 6 figure

Versatile compact atomic source for high resolution dual atom interferometry

We present a compact $^{87}$Rb atomic source for high precision dual atom interferometers. The source is based on a double-stage magneto-optical trap (MOT) design, consisting of a 2-dimensional (2D)-MOT for efficient loading of a 3D-MOT. The accumulated atoms are precisely launched in a horizontal moving molasses. Our setup generates a high atomic flux ($>10^{10}$ atoms/s) with precise and flexibly tunable atomic trajectories as required for high resolution Sagnac atom interferometry. We characterize the performance of the source with respect to the relevant parameters of the launched atoms, i.e. temperature, absolute velocity and pointing, by utilizing time-of-flight techniques and velocity selective Raman transitions.Comment: uses revtex4, 9 pages, 12 figures, submitted to Phys. Rev.

The Relative Space: Space Measurements on a Rotating Platform

We introduce here the concept of relative space, an extended 3-space which is recognized as the only space having an operational meaning in the study of the space geometry of a rotating disk. Accordingly, we illustrate how space measurements are performed in the relative space, and we show that an old-aged puzzling problem, that is the Ehrenfest's paradox, is explained in this purely relativistic context. Furthermore, we illustrate the kinematical origin of the tangential dilation which is responsible for the solution of the Ehrenfest's paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of Physic

Adjustable microchip ring trap for cold atoms and molecules

We describe the design and function of a circular magnetic waveguide produced from wires on a microchip for atom interferometry using deBroglie waves. The guide is a two-dimensional magnetic minimum for trapping weak-field seeking states of atoms or molecules with a magnetic dipole moment. The design consists of seven circular wires sharing a common radius. We describe the design, the time-dependent currents of the wires and show that it is possible to form a circular waveguide with adjustable height and gradient while minimizing perturbation resulting from leads or wire crossings. This maximal area geometry is suited for rotation sensing with atom interferometry via the Sagnac effect using either cold atoms, molecules and Bose-condensed systems

Detection of the gravitomagnetic clock effect

The essence of the gravitomagnetic clock effect is properly defined showing that its origin is in the topology of world lines with closed space projections. It is shown that, in weak field approximation and for a spherically symmetric central body, the loss of synchrony between two clocks counter-rotating along a circular geodesic is proportional to the angular momentum of the source of the gravitational field. Numerical estimates are presented for objects within the solar system. The less unfavorable situation is found around Jupiter.Comment: 14 pages; Latex. To be published on Classical and Quantum Gravit

Long Phase Coherence Time and Number Squeezing of two Bose-Einstein Condensates on an Atom Chip

We measured the relative phase of two Bose-Einstein condensates confined in an radio frequency induced double well potential on an atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 beyond the phase diffusion limit expected for a coherent state in our experimental conditions (20 ms). The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrated a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.Comment: 5 pages, 5 figure