Román Roche, Juan
Zueco Láinez, David
Teorías efectivas para el acoplo ultrafuerte entre luz y materia
2019
2019
This End-of-Degree Thesis is structured as follows: In Section 1, we briefly show how the linear cavity array with coupled qubits naturally leads to the spin-boson model, we also analyse the motivation behind the introduction of the Polaron Transform for the study of said model. In Section 2 we apply the PT to a single-qubit system in order to assert its superiority over the RWA in the USC regime. We benchmark it using exact diagonalisation in small-sized systems and characterise both the GS and spontaneous emission. In Section 3 we present a generalisation of the PT for the two-qubit model and apply it successfully, proving that it converges to the single qubit scenario for sufficiently distant qubits. We show that the two-qubit system presents a ferromagnetic Ising ground state, as well as bound excited states that can be described using a simple tight-binding model, and serve as the basis for a proposed lossless state-transfer protocol. Finally, we draw some conclusions from our results and outline possible continuations. Technical details are left for the Appendix, including a link to a public repository where all the code, originally developed for this project, can be found.<br />