Hybrid quantum systems in cavity QED and optomechanics

Quantum mechanics has been demonstrated on many experimental platforms which include super conducting cavities, trapped ions and atomic systems. However, each of these platforms have attributes which make them suitable under certain conditions and applicable to only specific tasks. By combining these quantum systems it is possible to create hybrids which benefit from each of the individual advantages of the comprising subsystems. Such combined systems are referred to as hybrid quantum systems and can be used to reach regimes, observe behaviours and results which are otherwise impossible to achieve. In this thesis two hybrid quantum systems are studied with the intentions of both creating a practical quantum system for applications in quantum technologies and creating macroscopic quantum states for fundamental studies of quantum mechanics. The first hybrid quantum system which is studied focuses on light-matter interactions between spins and an optical resonator. Achieving strong light-matter interactions is one of the focal points of modern quantum mechanics as such strengths not only allow for the transportation of quantum information via photons but also for the generation of entangled quantum states. These are traits that are intensively sought after in almost every field of quantum science for both fundamental studies and the development of practical quantum technologies. Fabry-Pérot resonators have been most commonly used to study light-matter interactions due to their simplicity and compatibility with many experimental configurations.Here, however, an alternative type of resonator is considered, otherwise referred to as a Whispering Gallery resonator. Such hybrid resonators have more recently become popular due to their potentially more favourable scalability, in comparison with Fabry-Pérot resonators. In particular, this work focuses on the interaction between spins and the Whispering Gallery Modes (WGMs) of a fused silica microsphere with the intention of achieving effective interactions between distant spins. The spherical symmetry of the resonator is utilised to show that such resonators are capable of supporting an ensemble of degenerate optical modes which can result in a collective enhancement to the light-matter interaction strength. It is shown that enhanced interaction strengths on the order of GHz can be achieved, allowing for strong effective interactions to be attained between distant spins. These interaction strengths would allow for the construction of large arrays of coupled spherical resonators/spins which can be used to create quantum networks, perform quantum simulations of many-body systems and of course, as a platform for quantum computation. The second hybrid system focuses on the creation of macroscopic quantum states which are analogous to the Schrödinger cat state. The creation of such states is currently one of the most attractive goals in quantum mechanics as they can resemble states which reside at the borders of the classical and quantum worlds, allowing for the study of how quantum states become classical. Despite current technological advances, the largest Schrödinger cat states which have been observed to date still lie within atomic scales. With the intentions of achieving quantum superpositions of macroscopic objects many researchers have directed their attention to the field of optomechanics. Here interactions between light and mechanical oscillators are exploited to concoct schemes in which quantum superpositions of the mechanical oscillator's position can be created. While the creation of cat states can be somewhat guaranteed after entangling the position of the oscillator with a single photon or qubit, creating such states using larger systems requires measurement thus making the creation process probabilistic. In this work a novel, completely deterministic method of macroscopic cat state creation is proposed. Here cat states are created by exploiting properties in the optomechanical Membrane In The Middle model where a mechanical oscillator, or membrane, is placed within a Fabry-Pérot cavity. It is shown that by controlling the membrane's opacity its position can be driven to achieve large spatial displacements. This process is used to deterministically grow the spatial extent of a cat state of the membrane's position. It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatia separations of up to ~300 nm can be achieved. These cat states are significantly larger than any which have been observed to date and are created in a completely deterministic manner.