Effective Hamiltonian theory of the geometric evolution of quantum systems

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Physical Review A. American Physical Society (APS). 2020, 101(4), 042101. ISSN 2469-9926. eISSN 2469-9934. Available under: doi: 10.1103/PhysRevA.101.042101
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In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Λ 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.

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ISO 690SHKOLNIKOV, Vladislav O., Guido BURKARD, 2020. Effective Hamiltonian theory of the geometric evolution of quantum systems. In: Physical Review A. American Physical Society (APS). 2020, 101(4), 042101. ISSN 2469-9926. eISSN 2469-9934. Available under: doi: 10.1103/PhysRevA.101.042101
BibTex
@article{Shkolnikov2020Effec-49247,
  year={2020},
  doi={10.1103/PhysRevA.101.042101},
  title={Effective Hamiltonian theory of the geometric evolution of quantum systems},
  number={4},
  volume={101},
  issn={2469-9926},
  journal={Physical Review A},
  author={Shkolnikov, Vladislav O. and Burkard, Guido},
  note={Article Number: 042101}
}
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