Techniques for measuring the atomic recoil frequency using a grating-echo atom interferometer

I have developed three types of time-domain echo atom interferometer (AIs) that use either two or three standing-wave pulses in different configurations. Experiments approaching the transit time limit are achieved using samples of laser-cooled rubidium atoms with temperatures < 5 μK contained within a glass vacuum chamber—an environment that is largely free of both magnetic fields and field gradients. The principles of the atom-interferometric measurement of Eq can be understood based on a description of the "two-pulse" AI. This interferometer uses two standing-wave pulses applied at times t = 0 and t = T 21 to create a superposition of atomic momentum states differing by multiples of the two-photon momentum, ħq = 2 ħk where k is the optical wave number, that interfere in the vicinity of t = 2T 21. This interference or "echo" manifests itself as a density grating in the atomic sample, and is probed by applying a near-resonant traveling-wave "read-out" pulse and measuring the intensity of the coherent light Bragg-scattered in the backward direction. The scattered light from the grating is associated with a λ/2-periodic modulation produced by the interference of momentum states differing by ħq. Interfering states that differ by more than ħq—which produce higher-frequency spatial modulation within the sample—cannot be detected due to the nature of the Bragg scattering detection technique employed in the experiment. The intensity of the scattered light varies in a periodic manner as a function of the standing-wave pulse separation, T21. The fundamental frequency of this modulation is the two-photon atomic recoil frequency, ω q = ħq2/2M, where q = 2k and M is the mass of the atom (a rubidium isotope in this case). The recoil frequency, ω q, is related to the recoil energy, Eq = ħωq, which is the kinetic energy associated with the recoil of the atom after a coherent two-photon scattering process. By performing the experiment on a suitably long time scale ( T21 >> τq = π/ω q ∼32 μs), ωq can be measured precisely. Since ωq contains the ratio of Planck's constant to the mass of the atom, h/M, a precise measurement of ωq can be used as a strict test of quantum theories of the electromagnetic force.;This two-pulse technique has a number of disadvantages for a precision measurement of ωq, such as a complicated functional dependence on T21 (due to the nature of Kapitza-Dirac diffraction, the level structure of the atom, and spontaneous emission). However, many of these difficulties can be avoided by using a three-pulse "perturbative" echo technique, where a third standing-wave pulse is applied at t = T21 + δT , with δT < T21. The function of the third pulse is to convert the difference between interfering momentum states from nħq (n > 1) to ħq. In this manner, interference between high-order momentum states contributes more significantly to the three-pulse echo than to the two-pulse echo. By fixing T21 and varying δT between the second standing-wave pulse and the echo time, the signal exhibits a simple shape with narrow fringes that revive periodically at the recoil period, τq. Using this technique, I have achieved a single measurement of ωq with a relative statistical uncertainty of ∼ 180 parts per 109 (ppb) on a time scale of 2T21 ∼ 72 ms in ∼ 15 minutes of data acquisition. Further improvements are anticipated by extending the experimental time scale and narrowing the signal fringe width. To demonstrate the final statistical uncertainty using the current configuration of the experiment, I acquired 82 individual measurements of ω q under the same experimental conditions. This resulted in a final measurement with a statistical precision of 37 ppb. However, this measurement is currently overwhelmed by systematic errors at the level of ∼ 5.7 parts per 106 (ppm). The first survey of systematic effects on the measurement of ωq with this technique has also been carried out, where individual measurements had relative statistical uncertainties of ≲ 1 ppm. These experimental studies, along with theoretical calculations, can be used to reduce and eliminate such effects in future rounds of experimentation. (Abstract shortened by UMI.).