**Quantum many-body physics and quantum information science in superconducting circuits**

We will be developing new methods to create and study synthetic quantum materials made of interacting microwave photons in superconducting circuits. Taking advantage of the coherent control and flexibility of the superconducting circuit platform, we will build “analog quantum simulators” to gain microscopic understanding of novel material properties arising from the competition between quantum fluctuation, interactions and topology; and investigate many-body dynamics in non-equilibrium and open quantum systems.

We are excited to be part of a vibrant community in quantum science and technologies research here at Purdue, check out: Purdue Quantum Science and Engineering Institute.

Our research remains at the intersection of condensed matter, AMO physics, and quantum information science. We will also be exploring potentials of building more versatile analog quantum simulators by integrating superconducting circuits with other solid state or AMO systems.

### Recent Highlights

Can we build a new platform for studying synthetic quantum materials made out of microwave photons?

How can we control, prepare, and measure quantum many-body states in such a platform?

**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 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)

In-lattice cooling of quantum gases using an excitation blockade effect - *Nature *480, 500-503 (2011)

Quantum walks in 1D lattice: dynamics of few particles reveal signatures of quantum coherence, quantum statistics and interaction effects -*Science *347: 12291233 (2015)

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)