Measuring The Gravitational Field with an Atomic Ruler

This thesis presents the experimental and theoretical studies of the survival resonances in a dissipative atom-optics system, and their applications. We demonstrate this resonant phenomenon by using an alternative approach to the standard atom-optics $\delta$-kicked rotor (AODKR), where we add spatially periodic dissipation or loss to each pulse. The system evolution is therefore non-unitary. We first investigate the emergence of the survival resonances by exposing a cloud of laser-cooled Rubidium-85 atoms to standing-wave light pulses. The frequency of the light is tuned close to an open atomic transition. Scattering of the light from the standing wave leads the atoms to decay into a dark state that is far-off-resonance to both the standing-wave light and the subsequent detection light. Once the atoms go to the dark state, they are considered to be lost. The atom number is thereby {\it not} a conserved quantity. Consequently, a meaningful dynamic observable is the survival probability of the atoms. Varying the pulse interval reveals a series of resonant peaks at integer multiples of half the Talbot time. These peaks are deemed survival resonances and are a matter-wave interferometric phenomenon. The appearance of the peaks can be conceptually understood through the matter-wave Talbot-Lau effect. For a complete understanding, we build a model to simulate the system which captures the dynamics well. In addition to acting as an optical mask that modulates the wave functions' amplitude, the still present optical dipole force of the standing wave imprints a phase pattern to the atomic wave functions. This gives rise to a micro-lensing effect that increases the peak survival dramatically. Using such an effect can help to enhance the incisiveness of the resonances, which might find applications in precision measurements. The width of survival resonance peaks narrows faster than expected from the Fourier-limit when the pulse number is changed. The standard AODKR displays a similar sub-Fourier behavior. This thesis also demonstrates two applications of using survival resonances. The temporally pulsed spatially periodic dissipation is used for preparing well-defined initial conditions. Feeding back lost atoms gives a non-thermal atomic state that enhances subsequent survival resonance measurements. This can find its application in the state preparation in atom interferometry. To show the feasibility of using survival resonances in an atom interferometer, we construct a proof-of-concept atomic gravimeter. With a vertically arranged standing-wave light beam, we perform an interferometric measurement of the gravitational acceleration $g$ utilizing the survival resonances. Gravity removes the survival resonances, but they re-emerge when the standing wave co-moves with the free-falling atomic cloud. To study the performance of this technique and find a good parameter combination, we carry out a series of simulations and experiments. We measure $g$ with a precision of 5 ppm using a drop distance of less than 1 mm. The sensitivity improves with the square of the drop time, which indicates we can reach a precision of the $\mu$-Gal regime with a drop distance of 10 cm. The simple implementation makes this technique an attractive candidate for a low cost and compact atomic gravimeter