Atom interferometric studies of light scattering - A new technique for measuring atomic recoil

This dissertation presents two techniques for measuring the atomic recoil frequency, oq, using a single-state atom interferometer that utilizes a dilute cloud of laser-cooled 85Rb atoms. An important motivation for these measurements is that o q, which is related to the ratio of Planck's constant and the atomic mass of rubidium hmRb , can be used to infer the atomic fine structure constant, alpha. The two techniques presented here involve time domain measurements carried out with standing-wave laser fields that manipulate atoms in the same atomic ground state and exploit the wave nature of cold atoms. The first technique uses two off-resonant standing-wave pulses to interfere momentum states so that the recoil frequency can be determined. However, to model the signal shape it is necessary to include effects of spontaneous emission during the interaction with light and the spatial profile of the laser beam. The second technique provides a robust alternative approach for measuring the recoil frequency because the signal shape is considerably simpler and can be modeled easily. We report measurements of atomic recoil using both techniques that are precise to ∼ 1 part per million. The precision was limited mainly by the time scale of the experiment (∼ 20 ms) due to the presence of magnetic field gradients. The dissertation also discusses recent improvements that have extended the time scale to the transit time limit for cold atoms. This is the time of travel of cold atoms through the region of interaction defined by the laser beams.;To carry out the measurement of oq using the first technique, it is necessary to understand the effects of spontaneous emission and the spatial profile of the laser beam. We find that spontaneous emission influences both the shape of the echo signal and its periodic T dependent amplitude in a manner consistent with theoretical predictions. The results show that the T dependent signal is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation, such as the variation in momentum transfer due to the change in the angle between the traveling-wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. We have also demonstrated a considerable improvement in the signal-to-noise ratio of the echo signal by using intensity detection with a photomultiplier tube in place of heterodyne detection.;We have also used this interferometer to investigate the effect of light scattering due to an additional standing wave pulse applied at t = 2T -- deltaT. In this case, the grating contrast can be fully recovered if deltaT is an integral multiple of the recoil period Tr = pi/o q. Measuring the revival in contrast over the time scale of the experiment has resulted in the development of the second technique to measure oq. The contrast is accurately described by a coherence function which is the Fourier transform of the momentum distribution produced by the additional standing wave pulse. The effects of spontaneous emission and spatial profile of the laser beam are only to modify the Fourier coefficients used to fit the data and, therefore, no prior knowledge of these parameters is required, ensuring that the technique is both simple and robust.;We also show that coherence functions can be used to make a direct measurement of the probabilities of momentum states associated with the ground state. This measurement is interesting as it is performed under the conditions where the velocity distribution of the sample is much larger than the recoil velocity upsilon r = ℏkm . These measurements are consistent with Monte Carlo wave function simulations.;The interferometer uses two standing-wave pulses separated by time T to put the atoms in a superposition of momentum states. Interference between momentum states produce a density grating echo signal at time 2 T. The echo time, 2T, corresponds to the time at which the Doppler phases of the momentum states associated with all atoms in the sample cancel. The echo technique is, therefore, a general method to overcome the effect of the velocity distribution of the sample. The amplitude of the echo signal is related to the contrast of the density grating and is periodic in T. The first technique exploits this dependence to measure oq.;The signal shape obtained in the second technique is also described by a much simpler analytical function than the fitting function used in the first technique. We present an analytical calculation of this signal shape using the theory of echo formation. This theory enables us to understand the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. We show that the results for the signal shape match the predictions obtained using coherence functions. The theory of echo formation also predicts scaling laws for the grating contrast as a function of pulse area and number of additional standing wave pulses that are investigated experimentally. These studies are important for realizing improvements in precision measurements of oq.;If the additional pulse at t = 2T -- delta T is a traveling wave, we observe an overall loss in contrast due to decoherence associated with spontaneous emission. The signal exhibits quasi-periodic revivals in contrast as a function of deltaT and this shape can be described by a suitable coherence function. This aspect of our work resembles previous studies in atomic beams. From the data, we accurately measure the probabilities of single and multiple photon scattering events and investigate the dependence of the photon scattering rate on detuning. The grating contrast is studied as a function of the intensity of continuous wave light and this data is used to extract the photon scattering rate as a function of detuning and light intensity as well as to infer the photon scattering cross section.;Finally, we have made significant progress in extending the precision of our measurements of atomic recoil since our previous measurement which is precise to 2.5 parts per million (ppm). These improvements are related to increases in signal lifetime and the signal-to-noise ratio. We will discuss the prospect of a 10 parts per billion measurement in the near future that relies on these improvements.