Exceptional point structure and chiral state transfer in a rate-operator-engineered š¯’«š¯’Æ-symmetric Bose-Hubbard dimer
Abstract
The rate operator quantum jumps (ROQJ) is a general method to unravel a master equation describing the dynamics of an open quantum system into stochastic pure state trajectories. By post-selecting on no jumps occurring, one obtains a trajectory generated by a non-Hermitian Hamiltonian. The ROQJ allows for versatile modification of this non-Hermitian evolution, with each non-Hermitian Hamiltonian corresponding to a different continuous measurement scheme. We apply the ROQJ to modify the non-Hermitian dynamics of the open three-particle Bose-Hubbard dimer model under environmental non-local dephasing to construct a PT-symmetric non-Hermitian Hamiltonians with a general two parameter PT-symmetric imaginary diagonal part, which generalizes the well-known gain-loss Bose-Hubbard dimer. We characterize the symmetry structure of the spectrum for different on-site interaction strengths. For vanishing on-site interaction, we find the unbroken PT-symmetry region enclosed by order two exceptional lines of different character and four order four exceptional points, two of which are not found in the usual gain-loss Bose-Hubbard dimer. Additionally, we find regions with degenerate imaginary parts of the eigenvalues, also not found in the gain-loss Bose-Hubbard dimer. In this parameter space, we use time-dependent rate operator transformations to investigate state transfer under slowly varying parameter loops. Loops encircling an order four exceptional point exhibit chiral state transfer. Because the loops cross exceptional lines, the final states are superpositions of eigenstates. Chiral state transfer is also found with non-zero homogeneous on-site interaction when the loop crosses over broken PT-symmetry regions of different character. Using inhomogeneous on-site interactions, we find direction dependent state transfer between eigenstates without crossing or encircling exceptional points.
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BibTeX
@misc{luomala2026exceptional,
title = {{Exceptional point structure and chiral state transfer in a rate-operator-engineered $\mathcalPT$-symmetric Bose-Hubbard dimer}},
author = {Jaakko Luomala and Federico Settimo and Kimmo Luoma and Iiro Vilja and Jyrki Piilo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30836},
eprint = {2610.30836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30836},
}
RIS
TY - UNPB
TI - Exceptional point structure and chiral state transfer in a rate-operator-engineered š¯’«š¯’Æ-symmetric Bose-Hubbard dimer
AU - Jaakko Luomala
AU - Federico Settimo
AU - Kimmo Luoma
AU - Iiro Vilja
AU - Jyrki Piilo
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30836
UR - https://arxiv.org/abs/2610.30836
AB - The rate operator quantum jumps (ROQJ) is a general method to unravel a master equation describing the dynamics of an open quantum system into stochastic pure state trajectories. By post-selecting on no jumps occurring, one obtains a trajectory generated by a non-Hermitian Hamiltonian. The ROQJ allows for versatile modification of this non-Hermitian evolution, with each non-Hermitian Hamiltonian corresponding to a different continuous measurement scheme. We apply the ROQJ to modify the non-Hermitian dynamics of the open three-particle Bose-Hubbard dimer model under environmental non-local dephasing to construct a PT-symmetric non-Hermitian Hamiltonians with a general two parameter PT-symmetric imaginary diagonal part, which generalizes the well-known gain-loss Bose-Hubbard dimer. We characterize the symmetry structure of the spectrum for different on-site interaction strengths. For vanishing on-site interaction, we find the unbroken PT-symmetry region enclosed by order two exceptional lines of different character and four order four exceptional points, two of which are not found in the usual gain-loss Bose-Hubbard dimer. Additionally, we find regions with degenerate imaginary parts of the eigenvalues, also not found in the gain-loss Bose-Hubbard dimer. In this parameter space, we use time-dependent rate operator transformations to investigate state transfer under slowly varying parameter loops. Loops encircling an order four exceptional point exhibit chiral state transfer. Because the loops cross exceptional lines, the final states are superpositions of eigenstates. Chiral state transfer is also found with non-zero homogeneous on-site interaction when the loop crosses over broken PT-symmetry regions of different character. Using inhomogeneous on-site interactions, we find direction dependent state transfer between eigenstates without crossing or encircling exceptional points.
ER -