Effective Hamiltonian theory of the geometric evolution of quantum systems

TL;DR

This paper introduces an effective Hamiltonian approach to describe the geometric evolution of quantum systems, specifically generalized Lambda systems, simplifying calculations by avoiding Berry connection computations.

Contribution

It presents a novel method that models holonomic quantum evolution as standard Hamiltonian dynamics without needing dark subspace parametrization or Berry connection calculations.

Findings

Provides a new framework for quantum holonomic evolution

Eliminates complex Berry connection calculations

Applicable to larger quantum systems

Abstract

In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic evolution can be viewed as a conventional Hamiltonian dynamics in an appropriately chosen extended Hilbert space. In contrast to the existing approaches, our method does not require the calculation of the non-Abelian Berry connection and can be applied without any parametrization of the dark subspace, which becomes a challenging problem with increasing system size.