Here we just want to stress that ϕ and a are linked by a conveniently large factor kT 2 that is very easy to measure with high accuracy. To get a taste of all the subtleties actually involved in a high accuracy measurement of the local gravity acceleration, see. Since P a can be measured accurately by state selective fluorescence detection, a very sensitive acceleration sensor is available. If a constant acceleration a in the z-direction is present, the probability of finding an atom in the state | a〉 at the end of the sequence can be written as where ϕ= kaT 2. Starting from a pure state | a〉 we can apply a π/2-pulse that creates a superposition of | a〉 and | b〉 with equal amplitudes, or a π-pulse that creates a pure state | b〉.Īn ‘interferometric sequence’ here is a series of three pulses, π/2− π− π/2, separated by a time interval T. We will distinguish between these two cases, when necessary, by using the ↑ and ↓ subscripts respectively.Īfter preparation there are about 10 5 atoms in the cloud which has a spatial Gaussian distribution with standard deviation σ s≃3 mm.ĭuring the parabolic flight the cloud is illuminated again by the Raman beams to create coherent superpositions of | a〉 and | b〉. 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. This monographic issue clearly shows that measuring the Newtonian constant of gravitation G with a total uncertainty below 100 ppm is a formidable task.
0 Comments
Leave a Reply. |