Quantum systems engineering

Abstract:

We investigate the ground-state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction ν = 1/2. We find that our system supports topologically ordered states by calculating the topological entanglement entropy, and its value is in good agreement with the theoretical value for the ν = 1/2 Laughlin state. By exploring the behavior of the density profiles, edge currents, and singleparticle correlation functions, we find that the ground state on the cylinder shows all signatures of a fractional quantum Hall state even for large values of the magnetic flux density. Furthermore, we determine the dependence of the correlation functions and edge currents on the interaction strength. We find that depending on the magnetic flux density, the transition toward Laughlin-like behavior can be either smooth or it can happen abruptly for some critical interaction strength

Abstract:

We show that the macroscopic magnetic and electronic properties of strongly correlated electron systems can be manipulated by coupling them to a cavity mode. As a paradigmatic example we consider the Fermi-Hubbard model and find that the electron-cavity coupling enhances the magnetic interaction between the electron spins in the ground-state manifold. At half filling this effect can be observed by a change in the magnetic susceptibility. At less than half filling, the cavity introduces a next-nearest-neighbor hopping and mediates a long-range electron-electron interaction between distant sites. We study the ground-state properties with tensor network methods and find that the cavity coupling can induce a phase characterized by a momentum-space pairing effect for electrons.