Experimental Quantum Nonlinear Optics in a Superconducting Circuit

Abstract

Superconducting circuits are an ideal platform for simulating many body physics with photons. Such simulations are greatly enhanced by the ability to engineer photon-photon interactions. Single photon-photon interactions are difficult to design because of the massive nonlinearities required to achieve a strong interaction between individual photons. Nonlinearities arising from single photons are present in the dispersive limit of Jaynes-Cummings Hamiltonian. In this limit, the interaction of two photons is mediated by a virtual qubit excitation. This system can exhibit behavior known as photon blockade, where the presence of a single photon in an optical cavity prevents other photons from entering the cavity. The light exiting the cavity is then antibunched, which serves both as evidence of the quantization of the electromagnetic field and as a signature of photon blockade. Experimentally, we explore the strong qubit-field coupling regime of the Jaynes-Cummings Hamiltonian with circuit quantum electrodynamics. Using conventional microfabrication techniques, we build a superconducting microwave resonator coupled to a transmon qubit based on the Josephson junction. We observe photon number splitting of the qubit energy, demonstrating that we are in the strong coupling qubit-field coupling regime, allowing us to perform quantum non-demolition measurements of the cavity photon number, and providing conclusive evidence of the quantization of the electromagnetic field into photons. Further, we observe nonlinear effects arising from a small photon number consistent with the nonlinear Kerr Hamiltonian approximation of the Jaynes-Cummings Hamiltonian. Because the cavity dissipation κ is larger than the single photon cavity frequency shift ζ, we are unable to observe photon blockade or measure photon antibunching. By moving the qubit to a region of the transmission line with a higher electric field and using a tunable SQUID (superconducting quantum interference device) as a qubit, we will be able to realize strong photon-photon interactions for use in quantum simulators.