Navigation in Curved Space-Time

A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered

Sagnac interference in Carbon nanotube loops

In this paper we study electron interference in nanotube loops. The conductance as a function of the applied voltage is shown to oscillate due to interference between electron beams traversing the loop in two opposite directions, with slightly different velocities. The period of these oscillations with respect to the gate voltage, as well as the temperatures required for the effect to appear, are shown to be much larger than those of the related Fabry-Perot interference. This effect is analogous to the Sagnac effect in light interferometers. We calculate the effect of interactions on the period of the oscillations, and show that even though interactions destroy much of the near-degeneracy of velocities in the symmetric spin channel, the slow interference effects survive.Comment: 5 pages, 4 figure

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

Triangular Ring Resonator: Direct measurement of the parity-odd parameters of the photon sector of SME

We introduce the the Triangular Ring (TR) resonator. We show that the difference between the clockwise and anti-clockwise resonant frequencies of a vacuum TR resonator is sensitive to the birefringence parity-odd parameters of the photon's sector of the minimal Standard Model Extension (mSME): the Standard Model plus all the perturbative parameters encoding the break the Lorentz symmetry. We report that utilizing the current technology allows for direct measurement of these parameters with a sensitivity of the parity even ones and improves the best current resonator bounds by couple of orders of magnitudes. We note that designing an optical table that rotates perpendicular to the gravitational equipotential surface (geoid) allows for direct measurement of the constancy of the light speed at the vicinity of the earth in all directions in particular perpendicular to the geoid. If this table could achieve the precision of the ordinary tables, then it would improve the GPS bounds on the constancy of the light speed perpendicular to geoid by about eight orders of magnitude.Comment: ref. added, minor corrections, matches the published versio

Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber

A fiber optic conveyor has been developed for investigating the travel-time difference between two counter-propagating light beams in uniformly moving fiber. Our finding is that there is a travel-time difference Deltat=2vDeltal/c^2 in a fiber segment of length Deltal moving with the source and detector at a speed v, whether the segment is moving uniformly or circularly.Comment: 4 pages, including 4 figure

Entanglement enhanced atomic gyroscope

The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fibre-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on the interference of unentangled photons to measure mechanical rotation. The sensitivity of these devices scales with the number of particles used as $1/ \sqrt{N}$. Here we demonstrate how, by using sources of entangled particles, it is possible to do better and even achieve the ultimate limit allowed by quantum mechanics where the precision scales as 1/N. We propose a gyroscope scheme that uses ultra-cold atoms trapped in an optical ring potential.Comment: 19 pages, 2 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