Laser Stabilised Ionising Transitions

TL;DR

The paper addresses stabilising electronic states in a bound-to-continuum system via resonant laser pumping. It develops a minimal model with a single bound state coupled to a continuum, analyzed in a rotating frame and diagonalised to reveal a discrete metastable resonance below the ionization threshold, accompanied by a continuum of dressed states. Open-system dynamics are treated with a Lindblad master equation, yielding rate equations that show the discrete state decays into the continuum through two-photon (photon-polariton) ionisation, while the resonance fluorescence spectrum comprises two surviving channels: discrete-to-discrete and discrete-to-continuum. This work demonstrates a novel mechanism to stabilise electronic states with intense, resonant fields and provides a spectroscopic handle to measure their populations, offering a path to engineer non-classical light–matter states in atomic, molecular, and solid-state systems.

Abstract

We investigate a ionising electronic transition under resonant pumping. We demonstrate that, above a critical value of the pump intensity, a novel metastable electronic bound state is created, which can decay into the free electron continuum by two-photon ionization. We calculate the system's resonant fluorescence spectrum, finding results qualitatively different from the Mollow triplet expected in a bound-to-bound transition. The fluorescent emission can be used to measure the time-resolved population of the novel metastable state. Contrary to Kramers-Hennenberger atoms, stabilised by non-perturbative, non-resonant laser pulses, the physics we observe is inherently resonant and relies on perturbative level repulsion. In analogy to how the AC-Stark shift is a semiclassical version of the single-photon Rabi splitting observed in photonic cavity, the phenomenon we describe is better understood as a semiclassical version of recently observed excitons bound by a single cavity photon. Our results demonstrate a novel way to stabilise electronic states with intense laser fields, increasing our capability to design and engineer non-classical states of matter.

Figures (6)

• Figure 1: Different Light-stabilised Frameworks. (a) Schematic representation of Floquet quasistationary (QS) stabilisation for a single bound state of energy $-\chi$ (blue dashed line), nonperturbatively photoexcited by a coherent drive of frequency $\omega_0$ into the continuum via multiphoton channel interference in the low-frequency, high-intensity regime (laser amplitude $E_0$ much larger than a critical amplitude $E_M$ depending on the parameters of the matter system). The resulting Floquet–Gamow quasienergies $\mathcal{E}_n$ possess a real part $W$ and an imaginary part $\Gamma_n$, corresponding to the $n$-photon ionization rate (indicated by the width of the cyan shaded regions). Destructive interference among different photon channels leads to a total ionization rate $\Gamma = \sum_n \Gamma_n$ that decays to zero in an oscillatory manner at increasing amplitude. (b) High-frequency limit illustrated in the Kramers--Henneberger (KH) frame. For moderate to large $E_0$, the effective potential develops new minima that support light-induced bound states (blue solid lines). Expanding the laser-dressed potential, only the zeroth-order term, referred to as KH potential, dominates, while multiphoton processes mediated by higher-order terms become negligible ($\Gamma_n \rightarrow 0$). (c) Photon-bound exciton (PBE, blue solid line) emerging from resonant level repulsion between the ionising transition and a photonic resonator as light-matter normalised coupling $\eta$ increases. The discrete resonance, protected by single-photon ionization, becomes visible in the strong coupling regime when the cavity linewidth $\gamma_c$ is smaller than a critical linewidth $\gamma_M$ depending on the parameters of the matter system. (d) Semiclassical analogue of the PBE, under investigation in this work, where resonant level repulsion occurs between coherently driven ionizing transitions as the parameter quantifying the coupling strength $\eta$ increases.
• Figure 2: Light-dressed states framework. (a) Schematic representation of a single bound state $|\Phi_{\text{b}}\rangle$ coupled to a continuum of free states $|\Phi_\omega\rangle$ (blue shaded region) via a semiclassical monochromatic laser field, with the ionisation threshold $\chi$. (b) Corresponding light-dressed states, where the discrete state $|\Psi_{\text{d}}\rangle$ and the continuum of states $|\Psi_{\bar{\omega}}\rangle$ (black shaded region) are arranged in adjacent photon ladders, characterised by photon numbers $n$ and $n+1$.
• Figure 3: Quasi-classical laser-stabilised discrete resonances. Dispersion of the dressed modes as a function of the normalised coupling strength for three pumping regimes: below two-photon threshold ($\omega_{0}<\chi/2$, a), below threshold ($\chi/2<\omega_{0}<\chi$, b), and above threshold ($\omega_{0}>\chi$, c). The solid black line tracks the discrete level $\omega_{\text{d}}$; the black-shaded region marks the continuum that begins at the edge of the continuum $\chi$, with the internal grey scale indicating how the dipole moment varies across the continuum. The blue dashed line shows the laser-pump frequency $\omega_{0}$. The purple, orange, and green vertical dash-dotted lines mark three values of the coupling which will be used as reference in the rest of the paper.
• Figure 4: Dynamics of the discrete-state population. The panels in the top row (a-c) schematically sketch two replica of the spectrum of the system separated by the energy of a laser photon. In all the present Figure purple, orange, and green colors mark the values of the normalised coupling highlighted in Fig. \ref{['Fig:2']}. The red arrows indicate the allowed decay channels in the case $\eta=0.2$ (green). Each of the other panels (d-i) represents on the left the time evolution of the discrete-state population $N_{\text{d}}(t)$ and on the right the total discrete-to-continuum emission rate $\gamma(\omega_{\text{d}},\bar{\omega})$. Each column corresponds to a different value of the pump frequency, corresponding to the three cases shown in Fig. \ref{['Fig:2']}: $\omega_{0}<\chi/2$ (d,g), $\chi/2<\omega_{0}<\chi$ (e,h), and $\omega_{0}>\chi$ (f,i). The second row (d-f) describes a system where a weak radiative loss channel dominates $(1 \gg \gamma^{\text{r}}(\omega_{\text{d}},\bar{\omega})\gg\gamma^{\text{nr}}(\omega_{\text{d}},\bar{\omega}))$, while the third (g-i) a system where a large non-radiative channel dominates $(0.1\approx\gamma^{\text{nr}}(\omega_{\text{d}},\bar{\omega})\gg\gamma^{\text{r}}(\omega_{\text{d}},\bar{\omega}) )$. All the times have been normalised over the maximum value of the decay rate over the three values of the normalised couplings and the laser frequencies considered $\tilde{t}=t \max_{\eta=\{0.05,0.1,0.2\}, \omega_0} \Gamma_{\text{d}}$.
• Figure 5: Dipole fluorescence spectra for the for dominant radiative losses ($1\gg\gamma^{\text{r}}(\omega_{\text{d}}, \bar{\omega})\gg\gamma^{\text{nr}}(\omega_{\text{d}}, \bar{\omega})$): Panels (a–c) show the calculated spectra $\tilde{S}(\omega_\textrm{f})$ for the below two-photon threshold regime $(\omega_{0} < \chi/2)$; panels (d–f) for the below-threshold regime $(\chi/2 < \omega_{0} < \chi)$; and panels (g–i) for the above-threshold regime $(\omega_{0} > \chi)$. The tilde $\tilde{}$ denotes the normalisation of $S(\omega_\textrm{f})$ to its peak amplitude in each panel (including any unphysical negative frequency peaks). Each column corresponds to a different normalised coupling strength $\eta$: $\eta = 0.20$ in panels (a, d, g), $\eta = 0.10$ in (b, e, h), and $\eta = 0.05$ in (c, f, i). In every spectrum the red curve represents the discrete-to-continuum component $S_{\text{d-c}}(\omega_{\text{f}})$, while the blue curve shows the discrete-to-discrete component $S_{\text{d-d}}(\omega_{\text{f}})$. The blue dashed vertical line marks the laser energy $\omega_{0}$, and the red dashed vertical line indicates the energy at which the hybridisation $|c_{\text{b}}(\bar{\omega})|^2$ reaches its maximum. Curve colors follow the same coding used in panel (l), which sketches the decay channels in the dressed-state picture.