Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?

TL;DR

This paper proves that superradiant quantum phase transitions are forbidden in cavity QED with electric dipole atoms due to the oscillator strength sum rule, but can occur in circuit QED with Cooper pair boxes due to their unique properties.

Contribution

It establishes a no-go theorem for superradiant phase transitions in cavity QED and identifies conditions under which they can be realized in circuit QED.

Findings

Superradiant phase transitions are forbidden in electric dipole atomic systems due to sum rules.

Circuit QED with Cooper pair boxes can bypass the no-go theorem.

The Hilbert space topology influences the possibility of superradiant transitions.

Abstract

In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $\Omega_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $\Omega_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is considered, a superradiant quantum critical point is forbidden for electric dipole atomic transitions due to the oscillator strength sum rule. In circuit QED, the capacitive coupling is analogous to the electric dipole one: yet, such no-go property can be circumvented by Cooper pair boxes capacitively coupled to a resonator, due to their peculiar Hilbert space topology and a violation of the corresponding sum rule.