Enhanced multiphoton ionization driven by quantum light

TL;DR

The paper addresses enhancing resonant multiphoton ionization (REMPI) using quantum states of light produced by nanoscale sources, where conventional paraxial models underestimate ionization gains. It develops a nonparaxial S-matrix framework that defines the $n$-photon cross section $\sigma^{(n)}$ and the photon flux $\phi$ for arbitrary quantum states, and analyzes how momentum entanglement can boost REMPI through the dipole channel. The authors derive an analytical enhancement ratio $\mathcal{R}^{(2)} = (V_{ent}/V_{sep})(f_{ent}^{(2)}/f_{sep}^{(2)})$ and demonstrate, via sodium atom simulations, that nonparaxial effects yield orders-of-magnitude increases, with a plateau at ultrathin crystal lengths due to phase-matching. They also explore higher multipole channels where the enhancement becomes sample-dependent and show that momentum correlations can still substantially improve cross sections, albeit with channel-specific behavior. The work suggests practical routes for entanglement-enhanced sensing, spectroscopy, and imaging using modern nanoscale light sources.

Abstract

We present a framework for multiphoton ionization driven by arbitrary quantum states of light. Our simulations predict that cross sections can be enhanced by more than two orders of magnitude with momentum-entangled photons produced by modern nanoscale quantum light sources. The enhancement is tied to the broad angular spectrum of such sources, and is severely underestimated by conventional approaches using the paraxial approximation. Reasonable estimates of the resonant two-photon ionization cross section in sodium atoms indicate that these effects should be observable with current technology.

Figures (3)

• Figure 1: (a) Schematic presentation of two-photon ionization of the sample with momentum entangled photons. A pump field beam waist $\Omega_{p}$ interacts with a birefringent crystal with length $L$, where spontaneous parametric downconversion generates pairs of momentum-entangled photons. These photon pairs trigger resonant two-photon ionization in the sample. The paraxial approximation accounts only for the narrow emission angles of entangled photons and is valid for sufficiently large crystals, whereas short crystals allow much larger momentum mismatches and correspondingly broader angular spectra, where a careful treatment is necessary. (b) Enhancement ratio of the REMPI cross sections, \ref{['R_dip']}, of entangled photons compared to two separable photons as a function of the pump beam waist $\Omega_p$ and length of the crystal $L$ for the ionization through dipole channel: (upper panel) nonparaxial approach and (lower panel) paraxial approximation. We consider the central frequencies of signal and idler photons to match the energy of the ($3^2 S_{1 / 2}-4^2 P_{3 / 2}$) transition in a neutral sodium atom Sansonetti2008. The graphs are plotted on a logarithmic scale with base $10$.
• Figure 2: (a) The enhancement ratio of the REMPI cross sections ($\mathcal{R}^{(2)}$) \ref{['R']} of a neutral sodium atom for dipole (black lines), quadrupole (red lines), octupole (blue lines), and hexadecapole (purple lines) as a function of the crystal length $L$ (which quantifies angular emissions of entangled photons). The considered beam waists of the pump field are $\Omega_{p}=3$$\mu$m (solid lines), $\Omega_{p}=10$$\mu$m (dashed lines), and $\Omega_{p}=50$$\mu$m (dotted-dashed lines). (b) The enhancement ratio of the cross-section of neutral sodium atoms for dipole (solid black line), quadrupole (dashed red line), octupole (dotted-dashed blue line), and hexadecapole (dotted blue line) as a function of the beam waists of the pump field ($\Omega_{p}$) for crystal length $L =10$ nm. (c) Total REMPI cross sections, $\sigma_{ent}^{(2)}$, with entangled (black lines) and separable (blue lines) photons via dipole channel as a function of crystal length $L$ for different beam waist. The transverse beam waist is $\Omega_y = 50~\mu\mathrm{m}$, chosen large enough that the transverse momentum can be neglected. The pulse duration is $T = 1.33~\mathrm{ps}$, corresponding to a photon bandwidth smaller than the $4^2 P_{3/2}\!-\!4^2 P_{1/2}$ splitting, ensuring exclusive population of $4^2 P_{3/2}$ . All the graphs are plotted on a logarithmic scale with base 10.
• Figure A1: Enhancement ratio of the dipole channel as a function of the crystal length for three different beam waists: $\Omega_p = 3~\mu\text{m}$ (solid line), $\Omega_p = 10~\mu\text{m}$ (dashed line), and $\Omega_p = 50~\mu\text{m}$ (dash-dotted line). The curves are obtained from Eq. \ref{['R_dip']}, while the discrete markers represent the numerical evaluation of Eq. \ref{['R']}, showing excellent agreement between analytical and numerical results.