Non-Equilibrium Quantum Phases In The Jaynes-Cummings Lattice

Abstract

Superconducting circuits provide a versatile platform for performing on-chip strongly correlated many-body experiments by strongly coupling microwave photons to superconducting qubits [9]. In this thesis we report experimental progress on fabricating a Jaynes-Cummings kagome lattice in which each site is constituted of a microwave resonator strongly coupled to a superconducting transmon qubit, allowing photon hopping between nearest neighbor sites. When driven with a constant power, the lattice allows the investigation of the non-equilibrium steady state regime characteristic of an open quantum system. The strong dispersive coupling between the resonator and the qubit gives rise to hybrid elementary excitations known as polaritons, which have been theoretically shown to exhibit distinct quantum phases determined by the competition between the on-site interaction energy and the nearest neighbor hopping energy [13] [17]. Theoretical calculations for a finite size lattice with an alternative geometry (linear chain) suggest that even in the presence of dissipation [1] one should observe the Mott insulator phase, in which each lattice site has a well defined polariton number, and the superfluid phase, in which polaritons are delocalized. This thesis presents a computationally tractable numerical simulation scheme based on the Gutzwiller wave function ansatz for modeling a finite size lattice in the presence of decay and dissipation. We further report experimental results on a novel local probe that, when integrated into the Jaynes-Cummings lattice, can distinguish between the Mott insulator phase and the superfluid phase by coupling an additional qubit to the central lattice site and thereby performing local photon statistics measurements.