The non-Hermitian landscape of autoionization

TL;DR

The paper identifies exceptional points (EPs) in single-resonance autoionization within a non-Hermitian framework and derives analytic EP positions in terms of the Fano asymmetry parameter $q$. It shows EPs occur at $(\tilde{\Omega}_{\pm}, \Delta^s_{\pm})$ with $q^2 = 4 \tilde{\Omega}^2 /(\gamma\Gamma)$ and $\Delta^s \equiv 2 q \gamma \Gamma /(\Gamma - \gamma)$, and that $\Delta$ must be tuned to $\Delta^s$ for real radicands. The authors connect EPs to the maxima of the asymmetric autoionization profile and to the effective decay rate of the ground state, proposing an experimental route to locate EPs from ionization probability $P(t)$, validated numerically for the Helium $2s2p({}^1P)$ resonance. They discuss practical feasibility with current light sources and highlight implications for broader non-Hermitian/PT-symmetric physics in Fano-profile materials, along with avenues for future work on fluctuations and multi-resonance extensions.

Abstract

We report on the existence of exceptional points (EPs) in single-resonance autoionization and provide analytical expressions for their positions in parameter space, in terms of the Fano asymmetry parameter. We additionally propose a reliable method for the experimental determination of EPs, based solely on information about their ionization probability as a function of the system parameters. The links between EPs, the maxima of the asymmetric profile and the effective decay rate of the ground state are investigated in detail. Quantitative numerical examples pertaining to the doubly excited $2s2p({}^1P)$ state of Helium confirm the validity of our formulation and results. In addition to unveiling hidden aspects of autoionization, our treatment and results provide a benchmark for the exploration of EPs and their properties in a variety of materials exhibiting Fano profiles with a broad perspective of possible applications.

Figures (6)

• Figure 1: Schematic representation of the system at study. The ground state $\ket{g}$ of an atom that is ionized with a rate $\gamma$, is coupled to an AR $\ket{a}$ via a linearly polarized field that drives the $\ket{g} \longleftrightarrow \ket{a}$ transition with a generalized Rabi frequency $\tilde{\Omega}$. The frequency of the driving field is detuned by $\Delta$ from the energy separation of the two states and the AR decays into the continuum with an autoionization rate $\Gamma$.
• Figure 2: Dependence of the exceptional points $( \tilde{Ω}_{\pm}, \Delta^s_{\pm} )$ on the asymmetry parameter $q$. Solid teal line: $\Tilde{\Omega}_{+}$, dashed teal line: $\Delta^s_{+}$, solid orange line: $\Tilde{\Omega}_{-}$ and dashed orange line: $\Delta^s_{-}$. For each value of q there exist two exceptional points.
• Figure 3: (a) Real and (b) imaginary parts of the eigenvalues $λ_1$ (red surface) and $λ_2$ (black surface) a function of the parameters $\Tilde{\Omega}$ and $Δ$, for $q=-2.79$. The yellow arrows mark the positions of the exceptional points at $( \Tilde{\Omega}, Δ) = ( \Tilde{\Omega}_{-}, \Delta^s_{-} ) = ( 0.2424Γ, -0.1738Γ )$ and $( \Tilde{\Omega}, Δ) = ( \tilde{\Omega}_{+}, \Delta^s_{+} ) = ( 8.0265Γ, 5.7538Γ )$, where the real and imaginary parts of the eigenvalues coalesce.
• Figure 4: Ionization probability as a function of $\Delta$ for various interaction times $T$, $q=-2.79$ and $\tilde{\Omega}=\tilde{\Omega}_{-}=0.2424Γ$. The vertical dashed line marks the position of the detuning $\Delta^s_{-}=-0.1738 Γ$. Inset: Position of the peak of the asymmetric profile ($\Delta_m$) as a function of the interaction time $T$ (logarithmic scale) for $q=-2.79$ and $\tilde{\Omega}=\tilde{\Omega}_{-}$. The horizontal dotted line marks the position of the detuning $\Delta^s_-$.
• Figure 5: (a) Effective decay rate of the ground state as a function of $\Tilde{\Omega}$ for $q=2.79$ and $\Delta=\Delta^s$. The dashed lines mark the positions of the exceptional points at $\Tilde{\Omega}=\Tilde{\Omega}_{-}=0.2424Γ$ and $\Tilde{\Omega}=\Tilde{\Omega}_{+}=8.0265Γ$. (b) Effective decay rate of the ground state as a function of $\Tilde{\Omega}$ and $\Delta$ for $q=-2.79$. The curved dashed line marks the $\Delta = \Delta^s ( \tilde{\Omega} )$ curve, over which the effective decay rate is maximum. An exceptional point lies at the position $( \tilde{\Omega}, \Delta ) = ( \Tilde{\Omega}_{-}, \Delta^s_{-} ) = ( 0.2424Γ, -0.1738Γ )$.