Parametrically driving a quantum oscillator into exceptionality

Area of Science:

• Quantum Physics
• Non-Hermitian Physics
• Condensed Matter Physics

Background:

• Singularities are common in physical theories, including spacetime, condensed matter, and wave physics.
• Exceptional points (EPs) in dissipative systems are where eigenvalues and eigenvectors coalesce.
• The behavior of EPs in open quantum systems remains less explored.

Purpose of the Study:

• Investigate exceptional points in a parametrically driven, lossy quantum oscillator.
• Analyze the influence of EPs on quantum system dynamics and observable properties.
• Examine dissipative phase transitions and their relation to the Liouvillian gap.

Main Methods:

• Analysis of a quantum oscillator model with parametric driving and dissipation.
• Study of the dynamical equations for the first and second moments of the system.
• Investigation of eigenvalue coalescence and Liouvillian gap closure.

Main Results:

• An exceptional point was identified in the moments' dynamics, acting as a phase boundary.
• System properties like populations, correlations, and spectra depend on the position relative to the EP.
• A dissipative phase transition was observed, linked to the closing of the Liouvillian gap.

Conclusions:

• Exceptional points serve as critical boundaries in open quantum systems.
• The findings highlight the distinct physical consequences of being above or below an EP.
• The study suggests experimental verification and a broader re-evaluation of EPs in dissipative quantum mechanics.