Dynamical tunneling in time crystals

Abstract

Entanglement is a key concept in quantum information science and quantum metrology. NOON states represent an important class of these entangled states. Such states can be created through a process of collective tunneling of an ultracold bosonic gas between two wells of a symmetric double-well potential. Specifically, the NOON state is achieved at the halfway point of this collective tunneling process. Thus, the aim of this Master's thesis is to calculate the time of the collective tunneling of a Bose-Einstein condensate between the two sites of a time crystal. This is done using the two-site Bose-Hubbard model and the Floquet theory.