Abstract
The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where such quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.
Highlights
Since its birth about 30 years ago [1], the field of atom interferometry (AI) has matured significantly
Atom interferometry has been used to probe the gravitational field produced by a heavy test mass [4,5,12,20,21]
Using a double-difference technique [4], one can extract that part of the phase of the AI signal caused by the gravitational field of the test mass
Summary
Since its birth about 30 years ago [1], the field of atom interferometry (AI) has matured significantly. The accumulated phase produced by the test mass’ gravitational field, δg (x,t), increases with decreasing distance ymin between the test mass and the trajectories of the atoms in the interferometer and increases with increasing delay times T between the Raman pulses. Where k is an effective wave vector of the Raman field and T is the time delay between Raman pulses This phase change arises owing to the acceleration of the atoms produced by the field of the test mass. It was shown that, with a proper choice of field polarization, Raman standing waves in the Raman–Nath regime can be used to create a 4hk beam splitter without increasing the number of separated Raman pulses [45,50] To account for such enhancements, our calculations of the AI’s phase are carried out for an effective k-vector that is scaled by an integer factor nk. The calculations enable us to establish the regions of validity of the approximate expressions for the phases
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