Exploring nonlinear effects in spin-systems using NMR

Abstract

Nonlinear dynamics forms the core of classical complex systems. The varied degrees of interactions among multiple parameters characterizing a system give rise to a plethora of phenomena from cosmic dynamics, chemical kinetics, circadian rhythms, atmospheric dynamics to markets and social networks. In the domain of physics, nonlinear dynamics has been exhaustively investigated in classical systems. However, its extension to quantum mechanics is yet to completely understood. Research into the bridge connecting nonlinear dynamical behaviour in classical and quantum regimes started decades ago, and it continues to remain significant today, especially with the development of quantum technology. Quantum computing and information processing protocols that harness innate quantum properties, such as superpositions and entanglement, have gone beyond theoretical constructs to become experimentally realizable reality that have also demonstrated extremely important and useful applications in security, metrology, communication, etc. Quantum technology currently is still very much in its infancy, and it is hence of timely interest to explore implications of nonlinearity in quantum systems and their possible applications. To this end, in this thesis, we have experimentally studied some facets of nonlinear effects in nuclear spin systems using Nuclear Magnetic Resonance (NMR) architecture. NMR is an extremely versatile test bed with precise control and manipulation of spins, and long coherence times that allows emulation of a wide range of desired Hamiltonians. We simulate dynamics under nonlinear Hamiltonian evolution via interactions between spins to study phenomena such as quantum chaos, quantum dynamical tunneling, interaction-induced Rydberg blockade and freezing, and quantum phase-synchronization. Aside from fundamental interest, these phenomena also have practical applications in quantum technology including but not limited to quantum control, developing efficient quantum computers with multiple interacting qubits, quantum networks, entangled state creation, selective control of qubits in a multi-qubit system, spectroscopy, etc.