Quantum Critical Regime in a Quadratically Driven Nonlinear Photonic Lattice

Area of Science:

• Quantum optics
• Condensed matter physics
• Open quantum systems

Background:

• Coupled optical cavities are fundamental systems for studying quantum phenomena.
• Dissipation and driving are crucial for understanding the dynamics of open quantum systems.
• Quantum Ising models exhibit critical behavior relevant to phase transitions.

Purpose of the Study:

• Investigate the critical behavior of coupled optical cavities under two-photon driving and dissipation.
• Determine the universality class of the observed critical phenomena.
• Explore the transition from quantum criticality to a classical-quantum regime with increasing dissipation.

Main Methods:

• Utilized the corner-space renormalization method for steady-state property calculations.
• Analyzed finite lattices in both one and two dimensions.
• Performed finite-size scaling analysis of photon number parity to identify critical points.

Main Results:

• Observed critical behavior analogous to the quantum Ising model at finite temperatures.
• Identified a quantum critical point in regimes of low dissipation, belonging to the quantum Ising universality class.
• Demonstrated a departure from universal behavior at higher photon loss rates, indicating a quantum critical regime.

Conclusions:

• Coupled optical cavities can exhibit quantum criticality similar to the quantum Ising model.
• Dissipation plays a key role in shaping the system's behavior, transitioning it from quantum to classical-quantum regimes.
• The findings provide insights into the interplay of quantum correlations and classical fluctuations in driven-dissipative systems.