# Nonlinear light-matter interaction: from superconducting qubits to spins in diamond

Cavity quantum electrodynamics (CQED) is the study of the interaction between matter and photons confined in a cavity. In the Jaynes-Cummings model the matter is described using the two-level approximation, and only a single cavity mode is taken into account. The interaction has a relatively large effect when the ratio *E*/ℏω between the energy gap *E* separating the two levels and the cavity mode photon energy ℏω is tuned close to unity.

The talk is devoted to the study of the light-matter interaction in the nonlinear regime using three different CQED systems. In the first experiment a Josephson flux qubit serves as a two-level system and a superconducting resonator as the cavity [1]. We experimentally find that the cavity response exhibits higher order resonances (called *super-harmonic* resonances) in the nonlinear regime when the ratio *E*/ℏω is tuned close to an integer value larger than unity. Moreover, we observe is significant narrowing in the cavity resonance that is induced by qubit driving, and which is attributed to quantum jumps. In the second experiment the interaction between a spin ensemble of diphenylpicrylhydrazyl (DPPH) molecules and a superconducting resonator is explored in the region where *E*/ℏω≫1 [2]. We find that the cavity response is significantly modified when the spins are intensively driven close to their Larmor frequency. Retardation in the response of the spin ensemble gives rise to effects such as cavity mode cooling and heating. In the third experiment the interaction between nitrogen-vacancy (NV) and nitrogen substitutional (P1) spin defects in diamond and a superconducting resonator is studied [3]. We find that nonlinearity imposes a fundamental limit upon sensitivity of CQED-based spin detection. Moreover, multi-photon resonances are observed when the ratio between the Larmor frequency and the driving frequency is tuned close to an integer value and the CQED system is tuned close to its resonance *E*/ℏω=1. In addition, other experimentally observed multi-photon resonances are attributed to the dipolar coupling between NV and P1 defects.

**References**

1. Eyal Buks, Chunqing Deng, Jean-Luc F.X. Orgazzi, Martin Otto and Adrian Lupascu, Phys. Rev. A 94, 033807 (2016).

2. Hui Wang, Sergei Masis, Roei Levi, Oleg Shtempluk and Eyal Buks, Phys. Rev. A 95, 053853 (2017).

3. Nir Alfasi, Sergei Masis, Roni Winik, Demitry Farfurnik, Oleg Shtempluck, Nir Bar-Gill and Eyal Buks, Phys. Rev. A 97 (2018).