Critical quantum geometric tensors of parametrically-driven nonlinear resonators

Area of Science:

• Quantum physics
• Nonlinear dynamics
• Condensed matter theory

Background:

• Parametrically driven nonlinear resonators are key for quantum computation and sensing.
• Critical phenomena in these systems are fundamental but less explored in ground state wavefunctions.
• Previous studies focused on eigenspectrum, leaving ground state wavefunction behaviors largely uninvestigated.

Purpose of the Study:

• To investigate the unexplored critical phenomena associated with the ground state wavefunction of parametrically driven nonlinear resonators.
• To establish a comprehensive phase diagram using the quantum ground state geometric tensor.
• To determine the universality class and critical exponents of the observed quantum phase transition.

Main Methods:

• Utilized the quantum ground state geometric tensor to analyze system behavior.
• Established a phase diagram by varying the driving parameter (ε) and phase (ϕ).
• Employed exact numerical methods to calculate critical exponents and scaling dimensions.

Main Results:

• A quantum phase transition from a normal to a symmetry-breaking phase was identified as the driving parameter (ε) increased.
• The critical point of the phase transition was found to be independent of the phase parameter (ϕ).
• Numerical results confirmed the transition falls within the universality class of the quantum Rabi model, with diverging quantum metric and Berry curvature.

Conclusions:

• The study successfully mapped the phase diagram and characterized the quantum phase transition in nonlinear resonators.
• The findings indicate that these systems exhibit critical phenomena in their ground state wavefunction, independent of external interactions.
• This research provides insights into quantum phase transitions and their universality, relevant for quantum technologies.