Exotic quantum matter generated from floquet engineering

Resum

The thesis investigates three time periodic quantum mechanical systems, all of which are of particular interest for research related to ultracold atoms in optical lattices. In the first system, a synthetic uniform magnetic field is created through the shaking of a two dimensional square optical lattice. In this way an effective magnetic field can be felt by ultra cold atoms trapped in the lattice. Simple continuous shaking, however, produces non-uniform effective masses (tunneling amplitudes) which lead to non-uniform flux configurations. This is addressed both analytically and numerically in this work. In addition, the limitations of continuous shaking schemes are discussed and several non-continuous shaking protocols are analyzed and compared. At the end of this investigation, the shaking schemes that yield a uniform effective mass and magnetic flux are identified. The second system under investigation in this work centers on the effect of a rapidly oscillating magnetic charge of a magnetic monopole. Floquet theory is used to derive a high-frequency limit of an electric charge coupled to such a Floquet magnetic monopole. A non-relativistic solution to the Schrödinger equation of this effective system is presented. This solution is then compared to a charge confined to a sphere and coupled to a static magnetic monopole. The third system under investigation is a one-dimensional Bose-Hubbard chain, whose tunneling amplitude is varied periodically (kinetic driving) with a zero time average. The system is investigated for both periodic and hard wall boundary conditions. With the help of Floquet theory, a time-independent effective Hamiltonian is calculated, in which nearest-neighbor single particle hopping is suppressed. The effective Hamiltonian consists of correlated hoppings and non-local interaction processes. For a critical value of the driving parameter, the system shows evidence of a Mott to superfluid transition. The superfluid consists of two fragmented condensates with opposite non-zero momenta. For large values of the driving parameter, the system shows similarities to Richardson-Gaudin models. This connection provides key insights into the problem of interacting bosons. A particular type of pairing interaction in momentum space explains the formation of the macroscopic superposition of bosons in non-zero and opposite momentum eigenstates. These interactions also give rise to a peculiar depletion cloud (reduction cloud) that is shared by both branches of the cat. The branches are identified precisely through symmetry considerations and studied with regard to several quality measures. In the ring (periodic boundary conditions), the system is sensitive to variations of the effective flux but only in such a way that the macroscopic superposition is preserved. The cat structure stays intact in the presence of a harmonic confinement, with a single impurity in the ring and a disorder potential, as long as it does not cause localization. The shared reduction cloud provides additional protection against premature decay due to particle losses. These and other considerations discussed in this work highlight a remarkable intrinsic protection against collapse.