In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized $\mathrm{\Lambda }$ 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.

• Received 20 February 2020
• Accepted 6 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.042101