Site-wise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators

TL;DR

This paper proposes a superconducting circuit-based quantum simulator for the Bose Hubbard model, enabling the study of Mott insulator-superfluid transitions through site-wise manipulations and detailed theoretical analysis.

Contribution

It introduces a novel superconducting circuit design that simulates the Bose Hubbard model with single-site control and analyzes the MI-SF transition using mean-field and exact methods.

Findings

The simulator can induce MI-SF transitions via single-site manipulations.

Mean-field and exact diagonalization methods confirm the transition signatures.

Photon density variance and fidelity metrics clearly indicate the phase transition.

Abstract

The Bose Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator (MI)-superfluid (SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photon-like. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.