Geometric phases in polarization mixed states

Debido a la generalidad de su formulación, las fases geométricas han sido objeto de constantes investigaciones en áreas muy diversas y han llevado a muchos desarrollos, tanto en aplicaciones como en trabajo teórico. Esta tesis se incluye dentro de las investigaciones experimentales y se enfoca en las fases geométricas que aparecen al manipular el grado de libertad de polarización. Se divide en dos partes. La primera se centra en los aspectos teóricos esenciales que definen y relacionan los estados mixtos de polarización con la luz láser parcialmente polarizada, y en las propiedades de las fases geométricas que aparecen en los primeros. La segunda parte presenta dos arreglos experimentales, uno que genera estados polarización y uno que permite medir la fase geométrica adquirida por dichos estados después de alguna evolución unitaria. El primero otorga un control casi arbitrario del estado de polarización de la luz láser que deja el arreglo y, con una ligera modificación, puede utilizarse en fotones individuales con casi idéntica efectividad. El segundo utiliza al primero para generar estados mixtos de polarización y luego los somete a distintas evoluciones. Las fases geométricas adquiridas son entonces determinadas mediante su relación con las fases de Pancharatnam correspondientes, que son cantidades directamente observables. Si bien hubo casos en los que la fase no se pudo determinar debido a su sensibilidad a errores experimentales, en aquellas mediciones en las que se pudo obtener un valor experimental este se ajustó muy bien a la predicción teórica.Tesi

Spin squeezing in mixed-dimensional anisotropic lattice models

We describe a theoretical scheme for generating scalable spin squeezing with nearest-neighbour interactions between spin-1/2 particles in a 3D lattice, which are naturally present in state-of-the-art 3D optical lattice clocks. We propose to use strong isotropic Heisenberg interactions within individual planes of the lattice, forcing the constituent spin-1/2s to behave as large collective spins. These large spins are then coupled with XXZ anisotropic interactions along a third direction of the lattice. This system can be realized via superexchange interactions in a 3D optical lattice subject to an external linear potential, such as gravity, and in the presence of spin-orbit coupling (SOC) to generate spin anisotropic interactions. We show there is a wide range of parameters in this setting where the spin squeezing improves with increasing system size even in the presence of holes.Comment: 13+9 pages, 8+1 figure

Many-Body Dynamics and Quantum Metrology in Long-Range Interacting Arrays

The field of quantum technologies presents us with highly controllable experimental platforms in which to explore quantum many-body physics. In particular, systems exhibiting long-range (or even infinite-range) interactions have, in the past, shown a great potential for quantum-enhanced metrology, and provide some of the simplest circumstances in which to study interacting quantum dynamics. In this thesis we present theoretical work precisely on the subjects of quantum dynamics and metrology, in two iconic long-range interacting systems: neutral atoms inside an optical cavity and two dimensional trapped ion arrays. We first focus on the atom-cavity system, analyze its time development in the presence of an external driving laser, and encounter "dynamical phase transitions", which are sharp changes in long-time dynamical behaviour of easy-to-measure observables. We diagnose this using mean field theory methods and comparing them with exact numerics, when feasible. We then center our attention on the steady state behaviour of this same system and the driven-dissipative phase transition it displays. We use analytical techniques to assess accurately the metrological potential (in the form of spin squeezing) of these steady states near the phase transition point. We then pivot to quantum metrology and investigate the fundamental limits with which the driving light can be frequency locked to the transition frequency of the intracavity atoms. We investigate a few more metrological protocols. First we focus on performing precise measurements of electric fields and spatial displacements. We present theory work indicating how to implement this protocol in the atom-cavity system, and then show its realization in the trapped ion setup. We also analyze protocols, designed to measure spin rotations, that rely on creating entanglement as fast as possible to mitigate the effects of unwanted decoherence. These protocols are applicable to both trapped ions and atoms in a cavity.</p

Photon-mediated correlated hopping in a synthetic ladder

We propose a new direction in quantum simulation that uses multilevel atoms in an optical cavity as a toolbox to engineer new types of bosonic models featuring correlated hopping processes in a synthetic ladder spanned by atomic ground states. The underlying mechanisms responsible for correlated hopping are collective cavity-mediated interactions that dress a manifold of excited levels in the far detuned limit. By weakly coupling the ground state levels to these dressed states using two laser drives with appropriate detunings, one can engineer correlated hopping processes while suppressing undesired single-particle and collective shifts of the ground state levels. We discuss the rich many-body dynamics that can be realized in the synthetic ladder including pair production processes, chiral transport and light-cone correlation spreading. The latter illustrates that an effective notion of locality can be engineered in a system with fully collective interactions.Comment: 6+9 pages, 4+4 figure

Fast generation of spin squeezing via resonant spin-boson coupling

We propose protocols for the creation of useful entangled states in a system of spins collectively coupled to a bosonic mode, directly applicable to trapped-ion and cavity QED setups. The protocols use coherent manipulations of the spin-boson interactions naturally arising in these systems to prepare spin squeezed states exponentially fast in time. We demonstrate the robustness of the protocols by analyzing the effects of natural sources of decoherence in these systems and show their advantage compared to more standard slower approaches where entanglement is generated algebraically with time.Comment: 6 pages, 4 figures (18 pages, 8 figures with appendices