Quantum Control of Cold Rydberg Ensembles and Non-Hermitian Systems

In this dissertation, mechanisms of dephasing in a cold dipole-dipole coupled Rydberg gas are discussed, and control sequences for suppressing dephasing are introduced and experimentally demonstrated. Additionally, population control in a two level non-Hermitian system facilitated by control loops in 2-dimensional parameter space is simulated and modeled analytically.

Detuning jump sequences inspired by quasi-phase matching in nonlinear optics are introduced and utilized to suppress dephasing in a cold Rydberg gas. Rabi flopping in random dipole-dipole coupled systems with more than a few atoms is demonstrated for the first time by actively suppressing dephasing with detuning jump sequences. The dephasing suppression mechanism is introduced
and experimental results at different detunings and different Rydberg atom densities are compared.

Dephasing in cold dipole-dipole coupled Rydberg gases due to (1) inhomogeneities in dipole-dipole interaction strengths between atoms and (2) Rydberg excitation hopping between different atoms, is considered. By comparing experimental Rabi oscillation spectra with the results of simulations with hopping effects turned on/off, it was found that excitation hopping plays a more important role when the system is far detuned from energy transfer resonance. Increased density results in proportional increases in the dephasing associated with the two mechanisms.

The second part of the dissertation focuses on a numerical study of population transfer in a two level non-Hermitian system subject to control loops along which the coupling and energy separation betwen the two levels are adiabatically varied. Contrary to previous studies, we found that population transfer can be achieved even when the control loop does not encircle an exceptional point (EP) of degeneracy in the chiral complex eigenvalue landscape.