Harnessing Time Symmetry to Fundamentally Alter Entanglement in Photoionization

TL;DR

This work shows that time-symmetry, implemented via odd (zero-area) envelopes, can fundamentally alter entanglement in strong-field photoionization by blocking resonant pathways and delaying entanglement generation. Using a semi-classical two-level model with time-symmetric envelopes, the authors derive compact expressions for final-state amplitudes and demonstrate that channel-resolved photoelectron spectra from the ground and excited ionic states avoid each other, enabling coincidence-based entanglement detection. The study combines analytical zero-flattop and stationary-phase analyses with numerical results to reveal how odd envelopes slow entanglement buildup (by a factor of two in absolute pulse area) while still allowing near-maximal entanglement ( $S_ ext{vN} o 1$ ), and it discusses experimental routes to exploit these effects. The findings establish time symmetry as a controllable resource for shaping entanglement in strong-field ionization and have implications for temporal decoherence, spectroscopy, and quantum-information applications in attosecond contexts.

Abstract

The Grobe--Eberly doublet phenomenon occurs in photoelectron distributions when a field dresses the remaining ion. Its manifestation is due to entanglement between a free electron and a hybrid state of light and matter. Direct detection of such entanglement is however not possible by coincidence schemes due to the dressing mechanism having an inconspicuous phase correlation effect on the ion. Here, it is shown that odd envelopes fundamentally alter the entanglement, such that channel-resolved photoelectron distributions become identifiable in coincidence with the internal state of the field-free ion. This constitutes a first usage of the parity of time symmetry in strong-field interactions.

Figures (4)

• Figure 1: Grobe--Eberly doublet and odd envelopes. (a) Schematic illustrating the Grobe--Eberly doublet formation due to atomic photoionization and sequential Rabi coupling in the ion. (b) Pulse envelope for a Gaussian, $\Lambda_\tau^\text{even}(t)$, (blue) and zero-Gaussian pulse, $\Lambda_\tau^\text{zero}(t)$, (red dashed). (c) Corresponding ground state population for an atom with one-photon Rabi coupling to an excited state. (d) Same as (c), but with one-photon coupling to continuum via photoionization.
• Figure 2: Build-up of the ion dynamics and photoelectron spectra over absolute pulse area.Top row: results for Gaussian pulses. (a) shows the ion populations of the ground state (green), the excited state (black dashed) and the full ionic population (grey dotted). The photoelectron probability distribution is presented in (b) and the ion-channel-resolved photoelectron spectra corresponding to the ground state and excited state channels are presented in (c) and (d), respectively. Bottom row: corresponding results for zero-Gaussian pulses. Heat maps are saturated at high photoelectron signals. Constant peak intensity and resonant frequency are used (see main text).
• Figure 3: Photoelectron spectra for odd envelopes with varying shape and CEP. The photoelectron spectra of the odd pulse (a), smooth odd pulse (c) and double Gaussian pulse (e) are presented in (b), (d) and (f) respectively, where $\abs{\alpha(\epsilon)}^2$ is shown in red, $\abs{\beta(\epsilon)}^2$ in blue and $\abs{\alpha(\epsilon)}^2+\abs{\beta(\epsilon)}^2$ in dotted black lines. CEP values of $\phi=0$, $\phi=\frac{\pi}{4}$ and $\phi=\frac{\pi}{2}$ are represented by lines, crosses and plus signs, respectively.
• Figure 4: Entanglement resolved over absolute pulse area and detuning. Absolute-pulse-area resolved entanglement (a) for a resonant Gaussian (blue) and its corresponding zero-area pulse (red dashed) as well as a flattop (dark grey dash-dotted) and flattop zero-area pulse (light grey dotted). Detuning- and pulse-area-resolved entanglement is presented in (b) and (c) for the Gaussian and zero-Gaussian pulses, respectively.