Related Experiment Video
Updated: Apr 29, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Controlling discrete and continuous symmetries in "superradiant" phase transitions with circuit QED systems
Alexandre Baksic1, Cristiano Ciuti1
1Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7 and CNRS, Bâtiment Condorcet, 10 Rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
Abstract:
We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the nonstandard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We show that such an unusual coupling scheme can be implemented in circuit QED systems, where artificial Josephson atoms are coupled both capacitively and inductively to a superconducting resonator. We demonstrate that it is possible to pass from a discrete, paritylike Z(2) symmetry to a continuous U(1) with the appearance of photonic Goldstone and amplitude modes above a critical point even in the ultrastrong coupling regime (where the rotating wave approximation for the interaction between field and two-level systems is no longer applicable). We determine the rich phase diagram showing "superradiant" phases with different symmetries and phase boundaries of both first and second order.
Related Concept Videos
Woodward–Hoffmann Selection Rules and Microscopic Reversibility
Second-Order Circuits
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Phase Transitions
Phase Transitions
First-Order Circuits
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
Symmetry in Maxwell's Equations

