Bose-Einstein Condensate Based Atom-Optics Delta-Kicked Rotor For Precision Measurements

Abstract

This thesis presents the realization of a Bose-Einstein Condensate (BEC) based Atom-Optics $\delta$-Kicked Rotor experiment (AOKR) using 87Rb atoms and its utility in atom interferometry and precision measurements. The AOKR involves subjecting the BEC to a series of optical lattice pulses. The phase modulation of the BEC wavefunction due to the optical lattice potential splits it into discrete momentum states. When the pulse period is equal to an integer or half integer multiple of the ‘Talbot time’, the total energy imparted to the system per pulse either quadratically increases (resonance) or is completely suppressed (anti-resonance). Monitoring these resonances allows measurement of Talbot time which is connected to the atomic recoil frequency. The recoilfrequency along with other physical quantities constitutes the fine structure constant $\alpha$. Since the value of $\alpha$ governs the strength of interactions between elementary particles, its precision measurement via different techniques is important. In the AOKR pulse scheme that we follow, the optical lattice pulse phase modulation is negated by inverting its sign for the rest of the pulses. The measurement of the revival of the initial state or the fidelity then constitutes as the Talbot time measurement. The sign inversion of the phase modulation is brought about by shifting the phase of the optical lattice by $\pi$- radians. The pulse scheme can also be thought of as a multi-path atom interferometer. The BEC which is used as an input for this interferometer is obtained after laser cooling in a Magneto-Optical Trap (MOT) and subsequent evaporative cooling in an hybrid optical crossed dipole trap. Since the quasi-momentum dynamics are theoretically predicted to play an important role in the dynamics of the AOKR pulse scheme, the characterization of the BEC initial state and its evolution is done. The finite momentum spread of the BEC is theoretically proposed to affect the sensitivity of the AOKR pulse sequence. We measure this predicted deviation from ideal dispersion-less AOKR behavior and it agrees with the simulations. Ultimately, we measure the Talbot time with a relative uncertainty of 1.2$\times10^{−3}$. While execution of the phase-inversion pulse sequences, it is observed that the momentum distribution within a diffracted order and the population of the orders about zero momentum state shows an asymmetry when the phase differed from $\pi$ radians. This intra-order and inter-order asymmetry is characterized for the case of two pulses. The intra-order asymmetry has been previously unreported and is unique as it possess a net asymmetry without a net momentum current. The enhancement in sensitivity of inter-order asymmetry to resonance suggests that it can be used as a probe in future AOKR experiments.