# Quantum simulation with superconducting circuits

## The use of superconducting circuits as building blocks for studying light matter interactions at the fundamental level was introduced more than a decade ago and named Circuit Quantum ElectroDynamics (circuitQED). With this project, we are taking these ideas to the next level and building complex circuits to explore many-body physics using circuits. These “quantum simulators” allow us to understand many-body phenomena in highly controlled experimental setups and to challenge the most advanced numerical and theoretical techniques.

### Josephson junction chains as quantum many-body simulator

When a highly non-linear Josephson junction is wired to a high-impedance transmission line, the phase fluctuation across the junction becomes very large. As a result, the resonance of the junction is renormalized due to highly non-linear and quantum effects. The environmental modes of the transmission lines inherit the large non-linearity of the junction creating a strongly interacting multi-mode system. In practice, we build the system by embedding a small superconducting quantum interference device into a large Josephson junction array. We observe that photons in the system spontaneously decay into lower energy entangled photons due to multi-photon conversions processes. Our experiments open many exciting prospects for the observation of exotic phenomena specific to many-body Hamiltonians in the strongly non-linear regime, and for the development of high-impedance qubits.

### Metrology

The voltage standard is based on the AC Josephson effect and the associated Shapiro steps, where a microwave tone applied to a Josephson junction yields a constant voltage plateaus solely defined by the frequency of the tone and fundamental physics constants. Theory suggested for a long time the possibility of a dual effect — that a Josephson junction device could produce current steps with heights determined only on the applied frequency when embedded in a very high impedance environment. We carried out a recent experiment demonstrating this effect which is an important step towards the long-sought closure of the quantum metrology electrical triangle.

Quantum simulation with superconducting circuits © CNRS / INSTITUT NÉEL

### Some of our recent publications

S. Léger, Revealing the finite-frequency response of a bosonic quantum impurity, SciPost Phys. (2023)

N. Crescini, Evidence of dual Shapiro steps in a Josephson junction array, Nat. Phys. (2023)

S. Léger, Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits, Nature Communications (2019)