Exactly solvable time-dependent models of two interacting two-level systems

TL;DR

This paper presents exactly solvable models for two interacting two-level quantum systems under time-dependent magnetic fields, enabling precise analysis of their dynamics and revealing intriguing physical phenomena.

Contribution

It introduces a general Hamiltonian with symmetry that reduces the complex system into two solvable sub-dynamics, allowing exact time evolution analysis.

Findings

Exact solutions for the time evolution of the coupled systems.

Identification of intriguing phenomena in the dynamics.

Method to engineer magnetic fields for solvability.

Abstract

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.