Non-Markovian quantum exceptional points

Jhen-Dong Lin, Po-Chen Kuo, Neill Lambert, Adam Miranowicz, Franco Nori () and Yueh-Nan Chen ()
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Jhen-Dong Lin: National Cheng Kung University
Po-Chen Kuo: National Cheng Kung University
Neill Lambert: Cluster for Pioneering Research, RIKEN
Adam Miranowicz: Cluster for Pioneering Research, RIKEN
Franco Nori: Cluster for Pioneering Research, RIKEN
Yueh-Nan Chen: National Cheng Kung University

Nature Communications, 2025, vol. 16, issue 1, 1-10

Abstract: Abstract 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.

Date: 2025
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DOI: 10.1038/s41467-025-56242-w

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