![]() ![]() We can drive, at every launch, the transition choosing if the atomic recoil will be in the + z or − z direction. The associated recoil velocity for an atom is v r≃12 mm s −1. Note that between the Raman beams and the atoms there is a small energy exchange of the order, where ω ab≃2 π×6.8 GHz is the frequency separation between | a〉 and | b〉, but a large momentum exchange, where k≃16×10 6 m −1, corresponding to twice the momentum of an optical photon at 780 nm. The blow-away pulses use radiation pressure to remove from the cloud atoms that remain in the initial state after a Raman pulse. The state | b〉 is also in the fundamental electronic level. The Raman pulses are induced by two counter-propagating laser beams (Raman beams) directed along the vertical z-axis that transfer atoms between the states | a〉 and | F=2, m F=0〉=| b〉. State preparation uses a combination of stimulated Raman transitions and blow-away optical pulses. Finally, we will present the short-term perspectives for future high precision G measurements based on cold atoms.įollowing the seminal work presented in, in our experiment a cloud of cold 87Rb atoms can be launched along the vertical z-direction and prepared in the non-magnetic | F=1, m F=0〉=| a〉 hyperfine state of the fundamental electronic level. A detailed description of the sources of instability and uncertainty that should limit our experimental apparatus below the 100 ppm level has already been published. In this article, after a schematic description of the operating principle of an atomic gradiometer we would like to discuss the evaluation of type A and type B uncertainties with emphasis on data analysis. Since atomic interferometry is a newcomer in the field of precision G measurements, special care must be taken in describing the process that leads from raw data to a value for G. After proof-of-principle measurements at 1% in Florence, 0.5% in Stanford and finally 0.2% again in Florence, we have reported an uncertainty of 150 ppm which is for the first time comparable with that of the current CODATA value. In this spirit, more than 10 years ago an experiment aiming at a measurement of G based on an atomic gradiometer with an uncertainty in the 100 ppm range was started in Florence. Measurements based on different techniques can then be useful in an attempt to detect systematic errors, even if their uncertainties are quite higher than the best reported ones. In the last three versions of the CODATA database, the standard relative uncertainties moved from 150 ppm in 2002, to 100 ppm in 2006 and finally to 120 ppm in 2010 . Most measurements however are mutually incompatible according to the standard statistical tests and are scattered over a range of about 460 ppm.Ĭlearly, sources of systematic error must be present and this is acknowledged in the recommended value for G. ![]() In the past 15 years, at least five independent groups reported measurements with a total uncertainly below 30 ppm. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period.This monographic issue clearly shows that measuring the Newtonian constant of gravitation G with a total uncertainty below 100 ppm is a formidable task. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 1. For small displacements, a pendulum is a simple harmonic oscillator. Some have crucial uses, such as in clocks some are for fun, such as a child’s swing and some are just there, such as the sinker on a fishing line. Also shown are the forces on the bob, which result in a net force of − mg sin θ toward the equilibrium position-that is, a restoring force. The linear displacement from equilibrium is s, the length of the arc. A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably.
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