Comments on "Controlling Discrete and Continuous Symmetries in Superradiant Phase Transitions with Circuit QED Systems "

TL;DR

This paper critiques a recent solution to the $U(1)/Z_2$ Dicke model, emphasizing the importance of quantum fluctuations and experimental feasibility in circuit QED systems.

Contribution

It clarifies the relation between parameter regimes, highlights the significance of quantum fluctuations, and discusses experimental implementations of the model.

Findings

The $N= ightarrow ext{infinity}$ classical limit has been achieved in prior work.

Quantum fluctuations at order $1/N$ lead to new phenomena.

Experimental setups with 2-9 qubits can test these effects.

Abstract

Recently, the authors of the commented PRL presented the $ N=\infty $ solution of the $ U(1)/Z_2 $ Dicke model studied by us previously. Here we point out that (1) The authors missed an important transformation relating the two parameter regimes, so their separate discussions on the two regimes is redundant. (2) Both $ N=\infty $ classical limit and $ 1/N $ quantum fluctuations have been achieved in two of our previously published papers. It is the $ 1/N $ quantum fluctuations which lead to the non-trivial new quantum phenomena. In view of only a few $ N=2\sim 9 $ qubits inside a circuit QED microwave cavity, they can be tested in near future experiments. (3) Several possible experimental implementations of the $ U(1)/Z_2 $ Dicke model have been proposed before and recently experimentally realized.