The Kibble-Zurek mechanism at exceptional points

Area of Science:

• Quantum physics
• Non-Hermitian systems
• Complex systems

Background:

• Exceptional points (EPs) are critical points in non-Hermitian systems.
• The Kibble-Zurek mechanism describes defect formation when crossing critical points in Hermitian systems.
• Generalizing defect production dynamics to non-Hermitian systems is an open challenge.

Purpose of the Study:

• To generalize the Kibble-Zurek mechanism to non-Hermitian systems by studying ramps across exceptional points (EPs).
• To investigate the scaling of defect density when driving a system through an EP.
• To compare defect production in non-Hermitian systems with conventional Hermitian systems.

Main Methods:

• Analyzing adiabatic time evolution across an EP.
• Deriving defect density scaling laws in terms of critical exponents and drive speed (1/τ).
• Mapping the dynamics to a Lindblad master equation with continuous measurement.

Main Results:

• Adiabatic evolution drives the system to an eigenstate of the final non-Hermitian Hamiltonian.
• Defect density scales as τ^{-(d + z)ν/(zν + 1)}, where τ is related to the drive speed.
• Defect production is suppressed in non-Hermitian systems compared to Hermitian systems due to decay to the ground state near the EP.

Conclusions:

• The Kibble-Zurek mechanism can be generalized to non-Hermitian systems, offering insights into defect formation dynamics.
• The study reveals a suppression of defect production in non-Hermitian systems, contrasting with Hermitian counterparts.
• The findings provide a physical picture of the dynamics through a mapping to a measurement-based quantum master equation.