Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space

Abstract

We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. The basic idea of the complex time method is using complex contour integration to perform the first-order adiabatic perturbation integral. In this way, the quantum dynamical problem is transformed to a study of singularities in the complex time plane -- transition points -- which represent complex degeneracies of the adiabatic Hamiltonian as the time-dependent parameters defining the encircling contour are analytically continued to complex plane. As an underlying illustration of the approach we discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.

arXiv commentMy paper includes 71 pages and 24 figures out of which 21 pages and 4 figures are Appendixes

References in corpus (20)

• The physics of exceptional points
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Loss-induced suppression and revival of lasing
• Topological energy transfer in an optomechanical system with exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Landau-Zener-Stuckelberg interferometry
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Pump-induced Exceptional Points in Lasers
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• A review of progress in the physics of open quantum systems: theory and experiment
• Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Nonlinear level crossing models
• Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
• Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions
• A simple approach to the Landau-Zener formula
• Exotic states in the strong field control of H${}_2^{+}$ dissociation dynamics: From exceptional points to zero-width resonances
• Ab-initio Theory of Photoionization via Resonances
• Instanton versus traditional WKB approach to Landau - Zener problem
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields