We report that the Bloch-Siegert shift which appears in Nuclear Magnetic Resonance (NMR) spectroscopy can also be shown to originate as a part of a complex drive-induced second-order susceptibility term. The shift terms thus obtained are shown to have an absorptive Kramers-Kronig pair. The theoretical treatment involves a finite time-propagation of a nuclear spin-
1/2 system and the spin-bearing molecule under the action of thermal fluctuations acting on the latter. The finite propagator is constructed to account for many instances of thermal fluctuations occurring in a time-scale during which the spin density matrix changes infinitesimally. Following an ensemble average, the resulting quantum master equation directly yields a finite time-nonlocal complex susceptibility term from the external drive, which is extremely small but measurable in solution-state NMR spectroscopy. The dispersive part of this susceptibility term originating from the non-resonant component of the external drive results in the Bloch-Siegert shift. We have verified experimentally the existence of the absorptive Kramers-Kronig pair of the second-order shift term, by using a novel refocussed nutation experiment. Our method provides a single approach to explain both relaxation phenomena as well as Bloch-Siegert effect, which have been treated using non-concurrent techniques in the past.
Spin dynamics are investigated in several rare-earth-ion-doped crystals, both for so-called Kramers ions and non-Kramers ions. I have studied two illustrative examples of such systems, Neodymium (Kramers) and Europium (non-Kramers). The main motivation behind these studies is the search for long relaxation and coherence times in solid state atomic ensembles. To this end I employ spectroscopic techniques to probe different kinds of interactions and relaxation mechanisms taking place in the samples. I perform spectroscopy of Neodymium (Kramers) in two different crystal lattices, yttrium orthosilicate and yttrium orthovanadate. I propose new methods to improve the relaxation lifetimes, and make precise characterizations of the interactions taking place within the atomic ensemble. In particular we achieve the most precise measurement of a kind of interaction which has received considerable attention recently in other areas of physics, the Dzyaloshinskii-Moriya interaction. These spectroscopic studies are of course of fundamental interest, but they can also be applied to quantum communication and computation. In this context, we were able to increase the efficiency of a quantum memory based on a Kramers ion (Nd) to be on par with the best non-Kramers (Eu,Pr) memories. Using Neodymium ions, I have certified that multi-dimensional entanglement can be stored in a quantum memory. The second part of this thesis concerns the study of Europium (non-Kramers), starting with a characterization of the Zeeman and quadrupole interactions. I believe these studies will pave the way for long duration (100 ms or more) quantum storage in a rare-earth-ion-doped crystal.