Classical-quantum correspondence for two-level pseudo-Hermitian systems

TL;DR

This paper establishes a classical-quantum correspondence for two-level pseudo-Hermitian systems, demonstrating how complex external fields can be effectively described and quantized, with applications to a damped Rabi model and potential experimental verification.

Contribution

It introduces a covariant quantization scheme for pseudo-Hermitian two-level systems linking classical and quantum descriptions, and applies it to a damped Rabi problem with experimental implications.

Findings

Pseudo-Hermitian Hamiltonians describe complex external fields.

A covariant quantization maps classical theories to quantum realizations.

Damping can be completely suppressed in a modified Rabi system.

Abstract

In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed. The experimental viability of the proposal is studied within a specific context. We suggest that the main theoretical results developed in the present work could be experimentally verified.