Detecting critical behavior in systems with PT and anti-PT symmetry using trace speed

Area of Science:

• Quantum mechanics
• Non-Hermitian physics

Background:

• Exceptional points (EPs) are critical in non-Hermitian quantum systems.
• Locating EPs is crucial for applications in quantum sensing and photonics.
• Existing methods for EP detection have limitations in precision and experimental accessibility.

Purpose of the Study:

• To introduce and validate trace speed (TS) as a novel statistical measure for detecting exceptional points (EPs).
• To compare the efficacy of TS against the Hilbert-Schmidt speed (HSS) for EP localization.
• To assess the experimental feasibility and sensitivity of TS for quantum applications.

Main Methods:

• Developed analytical derivations for trace speed (TS) in parity-time (PT) and anti-PT symmetric systems.
• Utilized numerical simulations to benchmark TS against Hilbert-Schmidt speed (HSS).
• Analyzed characteristic changes in TS dynamics near exceptional points.

Main Results:

• Trace speed (TS) accurately and unambiguously determines the positions of exceptional points (EPs).
• TS exhibits distinct dynamic changes when traversing EPs, facilitating precise localization.
• TS is shown to be more experimentally accessible than HSS due to simpler measurement requirements.

Conclusions:

• Trace speed (TS) is a robust and precise tool for locating exceptional points in quantum systems.
• The experimental accessibility and high sensitivity of TS make it ideal for ultra-sensitive quantum sensing.
• TS offers a promising approach for optimizing EP-based photonic architectures and exploring complex non-Hermitian systems.