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<p>Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators where eigenvalues and eigenvectors coalesce. Open quantum systems have recently been explored as EP testbeds due to their non-Hermitian nature. However, most studies focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. This work addresses this gap by proposing a general framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode equation of motion (PMEOM) and the hierarchical equations of motion (HEOM). The PMEOM is particularly useful due to its Lindblad-type structure, aligning with previous studies in the Markovian regime while offering deeper insights into EP identification. This framework incorporates non-Markovian effects through auxiliary degrees of freedom, enabling the discovery of additional or higher-order EPs that are inaccessible in the Markovian regime. We demonstrate the utility of this approach using the spin-boson model and linear bosonic systems.</p>

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Non-Markovian quantum exceptional points

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Jhen-Dong Lin,
  • Po-Chen Kuo,
  • Neill Lambert,
  • Adam Miranowicz,
  • Franco Nori,
  • Yueh-Nan Chen

摘要

Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators where eigenvalues and eigenvectors coalesce. Open quantum systems have recently been explored as EP testbeds due to their non-Hermitian nature. However, most studies focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. This work addresses this gap by proposing a general framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode equation of motion (PMEOM) and the hierarchical equations of motion (HEOM). The PMEOM is particularly useful due to its Lindblad-type structure, aligning with previous studies in the Markovian regime while offering deeper insights into EP identification. This framework incorporates non-Markovian effects through auxiliary degrees of freedom, enabling the discovery of additional or higher-order EPs that are inaccessible in the Markovian regime. We demonstrate the utility of this approach using the spin-boson model and linear bosonic systems.