I will give a pedagogical introduction to circuit quantum electrodynamics (circuit-QED), which describes fundamental interactions between light and matter on a chip with superconducting quantum circuits (SQCs) [1]. Here, the matter is represented by superconducting artificial atoms (SQCs) and photons are generated and stored in on-chip microwave resonators (like transmission line resonators). Thus, circuit-QED can be considered analogous to cavity-QED, but with SQCs instead of natural atoms and standard optical cavities. The interaction between matter (SQCs) and light (i.e., single microwave photons) can reach the regimes beyond weak and strong coupling to make the coupling strength comparable to the transition frequencies of a given system. Such regimes are referred to as ultrastrong and deep-strong coupling regimes, which enable the observation of fundamentally new phenomena [2]. I will describe some of these effects (including the generation of giant Schrödinger cats [3]) together with their applications for quantum information processing.

[1] X. Gu, A. F. Kockum, A. Miranowicz, Y.-X. Liu, and F. Nori:
Microwave photonics with superconducting quantum circuits, Physics Reports, 718–719, 1–102 (2017).

[2] A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori:
Ultrastrong coupling between light and matter, Nature Reviews Physics, 1, 19–40 (2019).

[3] Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori:
Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled Cat States via Parametric Amplification, Phys. Rev. Lett. 126, 023602 (2021).