Open Quantum Systems Initially Correlated with their Environment

Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutors: Philipp Strasberg, Javier Cerrillo MorenoMost descriptions of open quantum system dynamics assume a product initial state between the system and its environment, as the presence of correlations causes both practical and conceptual difficulties in characterizing the evolution of the open system. In this thesis we study initially correlated states by employing an operational approach to open quantum dynamics, which resolves these problems by mapping initial preparations to future states. We apply this framework to study the dynamics of systems initially in global thermal equilibrium and we distinguish between classical and quantum correlations as classified by the notion of quantum discord. Regarding the former, we solve for the exact dynamics of the spin-boson pure dephasing model and study the effect that initial correlations have on the geometry of the decoherence in the Bloch-sphere, while also presenting an analytical treatment of a general class of pure dephasing models. We then move into the quantum domain and derive a family of weak-coupling master equations using second-order perturbation theory in the system-environment coupling. The obtained equation contains a non-negligible inhomogeneous correction term to the conventional Born-Markov master equation and is a general theoretical tool that can be applied to many physical models in the weak-coupling regime

Production of Fock Mixtures in Trapped Ions for Motional Metrology

J.C. acknowledges support from Ministerio de Ciencia, Innovación y Universidades (Spain) (“Beatriz Galindo” Fellowship BEAGAL18/00081). D.R. acknowledges support from Junta de Andalucía through the project P18-FR-3432.We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband, measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the red sideband pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyze the parametric regime where these states can be reliably reproduced.Ministerio de Ciencia, Innovación y Universidades (Spain) BEAGAL18/00081Junta de Andalucía P18-FR-343