Microscopic exceptional points in the post-selected open Jaynes--Cummings model

• URL: http://arxiv.org/abs/2606.14982v1
• Date: Fri, 12 Jun 2026 22:04:36 GMT
• Title: Microscopic exceptional points in the post-selected open Jaynes--Cummings model
• Abstract summary: Phenomenological non-Hermitian Hamiltonians track selected signatures of complex reservoir dynamics.<n>Post-selected no-jump effective Hamiltonians derived from microscopic open-system theory reveal the underlying system--reservoir physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Phenomenological non-Hermitian Hamiltonians track selected signatures of complex reservoir dynamics, while post-selected no-jump effective Hamiltonians derived from microscopic open-system theory reveal the underlying system--reservoir physics. We derive such a Hamiltonian for the open Jaynes--Cummings model using a Moore--Penrose normalized $\mathrm{su}(2)$ representation that removes the vacuum-sector singularity and diagonalizes the full Hamiltonian by one operator rotation. Starting from a zero-temperature bosonic reservoir, we obtain a Gorini--Kossakowski--Sudarshan--Lindblad master equation under the Born--Markov approximation with full Bohr-frequency resolution. We use partial Bohr-frequency resolution to build a consistent post-selected no-jump Hamiltonian near exceptional points, where decay rates become comparable to Rabi frequencies and remove the scale separation behind full resolution. The normalized $\mathrm{su}(2)$ form of the resulting non-Hermitian Jaynes--Cummings Hamiltonian reveals the effects of Lamb-shifted detuning, diagonal loss imbalance, and reservoir-modified coupling. Our microscopic exceptional-point analysis recovers the experimentally reported single-excitation exceptional point for unequal independent losses and identifies regimes absent from the standard phenomenological model; for example, equal correlated losses with orthogonal channel phase produce a second-order exceptional point at the same loss-to-coupling ratio in every excitation sector.

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