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.
