Phase transitions in an Ising chain interacting with a single mode cavity field

TL;DR

This paper explores the complex phase behavior of a combined Dicke- and Ising-model system, revealing multiple phase transitions and analyzing its thermodynamics to understand its potential for high-precision metrology.

Contribution

It provides a detailed phase diagram of the combined model, identifying both first- and second-order phase transitions and their implications for system sensitivity.

Findings

Identifies first- and second-order phase transitions in the system.

Shows the cavity mean-field acts as an effective magnetic field.

Demonstrates sensitivity reaches the 1/N Heisenberg limit.

Abstract

We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using mean field theory, and the free energy is analyzed in detail to determine the complete phase diagram for the system. The analysis reveals both first- and second-order Dicke phase transitions into a super-radiant state, and the cavity mean-field in this regime acts as an effective magnetic field, which restricts the Ising chain dynamics to parameter ranges away from the Ising phase transition. Physical systems with a first order phase transitions are natural candidates for metrology and calibration purposes, and we apply filter theory to show that the sensitivity of the physical system to temperature and external fields reaches the 1/N Heisenberg limit.