quantum simulation with waveguide photons: theory and experiment

Abstract

Recently, waveguide photons have emerged as a versatile platform for the simulation quantum dynamics. So far, the majority of works in this field have been limited to the non-interacting regime, and intriguing nonlinear and interactive quantum many-body phenomena such as Bose-Hubbard or fractional quantum Hall (FQH) physics have remained elusive for this particular platform. In this thesis, we present both experimental work that demonstrates the versatility of the waveguide photonic platform as well as theory works that aim to introduce strong photon-photon interactions.For the experiment, we demonstrate a dynamically controllable non-Hermitian quantum walk using the waveguide photonic platform. For the first theory work, we introduce a two level atom beamsplitter and use this nonlinear beamsplitter to study a quantum walk with strong interaction. For the second ensemble of theory work, we first establish a general framework for bosonic quantum many-body Hamiltonian simulation using waveguide photons, and show that a tunable “on-site interaction” can be simulated using a photon number selective phase gate. Specifically, we proposed a concrete architecture for such a phase gate based on a three-level-atom-mediated photon subtraction and addition. We showcase the effectiveness of our Hamiltonian simulation framework with concrete examples including the Bose-Hubbard model and fractional quantum Hall model. Moreover, we present the probing and preparation scheme of the ground state of the FQH model by simulating certain Lindbladians under the same simulation framework. Our theoretical proposal opens a novel and scalable avenue to explore intriguing phenomena in strongly interacting many-body physics such as FQH states of light, non-Abelian braiding and statistics and beyond.