Quantum Simulation with Coplanar-Waveguide Lattices*

Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit [1] capable of realizing non-Euclidean geometries [2] and unconventional unit cells [3]. Combined with strong qubit-photon interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, and spin models in driven-dissipative systems. These lattices permit the creation of unique devices which host photons in curved spaces, gapped flat bands, and novel forms of qubit-qubit interaction. Here I will present measurements from a next-generation CPW lattice device featuring multiple transmon qubits coupled to a quasi-1D lattice which features not only conventional quadratic band edges, but also flat and linearly-dispersing bands. I will show that presence of the transmon qubits allows enhanced characterization of the distribution of lattice modes and observation of interacting photon effects in the flat bands of the lattice. Alternatively, the lattice modes endow the qubits with an extended interaction, which has different spatial profiles depending on the type of band mediating the interaction. Flux tunability of the qubits allows them to be brought into proximity with all of the different types of bands present in the device.

[1]    D. Underwood et al., Phys. Rev. A 86, 023837 (2012)

[2]    A. J. Koll'{a}r et al., Nature 571, 45 (2019)

[3]    A. J. Koll'{a}r et al., Comm. Math. Phys. 376,1909 (2019)