Spectral Twisting in a Common Bosonic Reservoir: Fragility of Two-Qubit Dark-State Protection
Abstract
The interaction of two qubits with a common bosonic reservoir is encoded by a matrix-valued spectral density J(ω), whose diagonal entries describe the local spectra, while the off-diagonal entries encode cross-correlations. Even when J(ω) has rank one, a frequency-independent dark channel need not exist because the family {J(ω)}ω may have a trivial common kernel. We term the frequency-dependent rotation of the bright and dark directions \textit{spectral twisting} and quantify it through the Fubini--Study speed τ(ω) of the bright spectral projector. We analyze how twisting modifies two-qubit dynamics and quantify the loss of dark-state protection through the leakage Pleak(t). Comparisons with untwisted asymmetric reservoirs and rotating-wave dynamics, together with detuned and finite-temperature calculations, distinguish spectral twisting from coupling asymmetry, counter-rotating processes, and thermal absorption. For resonant qubits tuned to the crossing of the two local spectra ω×, the singlet is locally dark at the transition frequency but couples to off-resonant components whose bright directions are rotated. In the weak-twisting regime, the fixed-time leakage scales as Pleak(t)∝[ω×τ(ω×)]2. We test this prediction for mismatched Drude-Lorentz spectra using nonperturbative hierarchical equations of motion generalized to cross-correlated bath forces. These results provide a geometric framework for dark-state engineering in structured reservoirs.
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BibTeX
@misc{borrelli2026spectral,
title = {{Spectral Twisting in a Common Bosonic Reservoir: Fragility of Two-Qubit Dark-State Protection}},
author = {Fabio Borrelli and Giovanni Miano and Carlo Forestiere},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06802},
eprint = {2609.06802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06802},
}
RIS
TY - UNPB
TI - Spectral Twisting in a Common Bosonic Reservoir: Fragility of Two-Qubit Dark-State Protection
AU - Fabio Borrelli
AU - Giovanni Miano
AU - Carlo Forestiere
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.06802
UR - https://arxiv.org/abs/2609.06802
AB - The interaction of two qubits with a common bosonic reservoir is encoded by a matrix-valued spectral density J(ω), whose diagonal entries describe the local spectra, while the off-diagonal entries encode cross-correlations. Even when J(ω) has rank one, a frequency-independent dark channel need not exist because the family {J(ω)}_ω may have a trivial common kernel. We term the frequency-dependent rotation of the bright and dark directions \textit{spectral twisting} and quantify it through the Fubini--Study speed τ(ω) of the bright spectral projector. We analyze how twisting modifies two-qubit dynamics and quantify the loss of dark-state protection through the leakage P_leak(t). Comparisons with untwisted asymmetric reservoirs and rotating-wave dynamics, together with detuned and finite-temperature calculations, distinguish spectral twisting from coupling asymmetry, counter-rotating processes, and thermal absorption. For resonant qubits tuned to the crossing of the two local spectra ω_×, the singlet is locally dark at the transition frequency but couples to off-resonant components whose bright directions are rotated. In the weak-twisting regime, the fixed-time leakage scales as P_leak(t)∝[ω_×τ(ω_×)]^2. We test this prediction for mismatched Drude-Lorentz spectra using nonperturbative hierarchical equations of motion generalized to cross-correlated bath forces. These results provide a geometric framework for dark-state engineering in structured reservoirs.
ER -