Dissipatively Stabilized Mott insulator of Photons
How can we create interesting many-body phases with photons when intrinsic losses are inevitable? Can dissipation be turned into a resource to create and even protect fragile quantum states?

We created a highly coherent, low-disorder circuit lattice. By using engineered dissipation to create a reservoir for photons, we realize a Mott insulator of photons in a Bose-Hubbard lattice where the photons self-organize into a “crystal“ due to strong quantum interactions. Nature 566, 51–57 (2019).
The engineered reservoirs we realized experimentally are based on our theoretical proposal in Phys. Rev. A 95, 043811 (2017), and provide a versatile method for stabilizing a broad range of gapped, incompressible photonic phases.

Topological lattice for microwave photons
Can we create an strong effective magnetic field for photons moving on a lattice?

We create a topological lattice build from coupled arrays of 3D microwave cavities. The Hofstadter lattice has an insulating bulk (Chern insulator) with topologically protected chiral edge states that we observe in time- and site- resolved measurements. - Phys. Rev. A 97, 013818 (2018).

Towards strongly interactions
Can we realize fractional quantum Hall states of photon by adding superconducting qubits to mediate strong interactions in our topological photonic lattices? We explore the possibilities in a theory paper published in Phys. Rev. X 6, 041043 (2016).

Hamiltonian Tomography for Photonic Lattices
As we scale up our quantum simulator to larger lattice sizes, how can we efficiently characterize the parameters of the lattice, e.g. to control lattice disorder?

Here develop robust spectroscopic methods for extracting individual parameters and topological properties of photonic lattices. - Phys. Rev. A 95, 062120 (2017).

Previous research: ultracold atoms in optical lattices

We create and study strongly-correlated phases of ultracold atoms in optical lattices. Using our Quantum Gas Microscope, we can engineer, manipulate and detect these states with the ultimate single-site resolution.

Quantum gas microscope (Greiner Lab)

Single-site resolved images of Mott insulator shells in a trap - Science 329, 547-550 (2010)

Quantum magnetism in optical lattices: transition from a paramagnet to an anti-ferromagnet - Nature 472, 307-312 (2011)

Photon assisted tunneling: engineering lattice dynamics on demand - Phys. Rev. Lett. 107, 095301 (2011)

Bilayer quantum gases: engineered coupling between two 2D planes, and techniques for site-resolved imaging of bilayers, - Phys. Rev. A 91, 041602(R) (2015)

Direct measurement of entanglement entropy in an itinerant lattice, using many-body quantum interference. - Nature 528: 7783 (2015)