Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

Measurement of the Gravity-Field Curvature by Atom Interferometry

We present the first direct measurement of the gravity-field curvature based on three conjugated atom interferometers. Three atomic clouds launched in the vertical direction are simultaneously interrogated by the same atom interferometry sequence and used to probe the gravity field at three equally spaced positions. The vertical component of the gravity-field curvature generated by nearby source masses is measured from the difference between adjacent gravity gradient values. Curvature measurements are of interest in geodesy studies and for the validation of gravitational models of the surrounding environment. The possibility of using such a scheme for a new determination of the Newtonian constant of gravity is also discussed.Comment: 5 pages, 3 figure

Determination of the Newtonian Gravitational Constant Using Atom Interferometry

We present a new measurement of the Newtonian gravitational constant G based on cold atom interferometry. Freely falling samples of laser-cooled rubidium atoms are used in a gravity gradiometer to probe the field generated by nearby source masses. In addition to its potential sensitivity, this method is intriguing as gravity is explored by a quantum system. We report a value of G=6.667 10^{-11} m^{3} kg^{-1} s^{-2}, estimating a statistical uncertainty of $\pm$ 0.011 10^{-11} m^{3} kg^{-1} s^{-2} and a systematic uncertainty of $\pm$ 0.003 10^{-11} m^{3} kg^{-1} s^{-2}. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement accuracy below the 100 ppm level.Comment: 4 figure

Quantum test of the equivalence principle for atoms in superpositions of internal energy eigenstates

The Einstein Equivalence Principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or Weak Equivalence Principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms. A Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eotvos ratio of atoms in two hyperfine levels with relative uncertainty in the low $10^{-9}$, improving previous results by almost two orders of magnitude.Comment: Accepted for publication in Nature Communicatio

Sensitivity limits of a Raman atom interferometer as a gravity gradiometer

We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long-term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short term sensitivity of 3*10^(-9) g/Hz^(-1/2) to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows to reach a resolution of 5*10^(-11) g after 8000 s on the measurement of differential gravity acceleration. The long term stability is compatible with a measurement of the gravitational constant G at the level of 10^(-4) after an integration time of about 100 hours.Comment: 19 pages, 20 figure

New apparatus design for high-precision measurement ofG with atom interferometry

We propose a new scheme for an improved determination of the Newtonian gravitational constant G and evaluate it by numerical simulations. Cold atoms in free fall are probed by atom interferometry measurements to characterize the gravitational field generated by external source masses. Two source mass configurations having different geometry and using different materials are compared to identify an optimized experimental setup for the G measurement. The effects of the magnetic fields used to manipulate the atoms and to control the interferometer phase are also characterized

Atom Interferometry with the Rb Blue Transitions

We demonstrate a novel scheme for Raman-pulse and Bragg-pulse atom interferometry based on the $5\mathrm{S} - 6\mathrm{P}$ blue transitions of $^{87}$Rb that provides an increase by a factor $\sim 2$ of the interferometer phase due to accelerations with respect to the commonly used infrared transition at 780 nm. A narrow-linewidth laser system generating more than 1 W of light in the 420-422 nm range was developed for this purpose. Used as a cold-atom gravity gradiometer, our Raman interferometer attains a stability to differential acceleration measurements of $1\times10^{-8}$ $g$ at 1 s and $2\times 10^{-10}$ $g$ after 2000 s of integration time. When operated on first-order Bragg transitions, the interferometer shows a stability of $6\times10^{-8}$ g at 1 s, averaging to $1\times10^{-9}$ g after 2000 s of integration time. The instrument sensitivity, currently limited by the noise due to spontaneous emission, can be further improved by increasing the laser power and the detuning from the atomic resonance. The present scheme is attractive for high-precision experiments as, in particular, for the determination of the Newtonian gravitational constant

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant \textit{G}. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and show that the sensor is able to detect the gravitational field induced by source masses. A discussion of projected accuracy for \textit{G} measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.Comment: 9 pages,9 figures, Submitte

A slow and dark atomic beam

We demonstrate a method to produce a very slow atomic beam from a vapour cell magneto-optical trap. Atoms are extracted from the trap using the radiation pressure imbalance caused by a push beam. An additional transfer beam placed near the center of the trap transfers the atomic beam into an off-resonant state. The velocity of the atomic beam has been varied by changing the intensity of the push beam or the position of the transfer beam. The method can be used to generate a continuous, magnetically guided atomic beam in a dark state.Comment: 14 page