Parity oscillations and photon correlation functions in the $ Z_2/U(1) $ Dicke model at a finite number of atoms or qubits

TL;DR

This paper investigates the parity oscillations and photon correlation functions in the finite-atom $ Z_2/U(1) $ Dicke model, revealing how anisotropy affects parity oscillations and providing measurable optical signatures.

Contribution

It introduces a detailed analysis of the $ Z_2/U(1) $ Dicke model at finite $ N $, highlighting the effects of anisotropy on parity oscillations and validating strong coupling expansion with exact diagonalization.

Findings

Parity doublets in super-radiant phase exhibit oscillations with anisotropy.

Parity oscillations are pushed to infinite coupling in the isotropic limit.

Photon correlation functions and squeezing spectra are computed for experimental relevance.

Abstract

In this work, by using the strong coupling expansion and exact diagonization (ED), we study the $ Z_2/U(1) $ Dicke model with independent rotating wave (RW) coupling $ g $ and counter-rotating wave (CRW) coupling $ g^{\prime} $ at a finite $ N $. This model includes the four standard quantum optics model: Rabi, Dicke, Jaynes-Cummings ( JC ) and Tavis-Cummings (TC) model as its various special limits. We show that in the super-radiant phase, the system's energy levels are grouped into doublets with even and odd parity. Any anisotropy $ \beta=g/g^{\prime} \neq 1 $ leads to the oscillation of parities in both the ground and excited doublets as the atom-photon coupling strength increases. The oscillations will be pushed to the infinite coupling strength in the isotropic $ Z_2 $ limit $ \beta=1 $. We find nearly perfect agreements between the strong coupling expansion and the ED in the super-radiant regime. We also compute the photon correlation functions, squeezing spectrum, number correlation functions which can be measured by various standard optical techniques.