# Interferometric recovery of a direct-SFA photoelectron wave packet

## Physical setting

Work in atomic units with atomic hydrogen, ionization potential $I_p=0.5$, and the dipole approximation. Rescattering and Coulomb-continuum corrections are outside this commission. Generate the target packet with a standard direct strong-field approximation (direct SFA), not with a TDSE calculation.

For a pulse centred at (t_j), define

\[
{\cal E}_j(t)=E_j
\exp\!\left[-\frac{8\ln 2}{\tau_j^2}(t-t_j)^2\right]
\exp\!\left[i\left(\omega_j(t-t_j)+\frac{\pi}{2}\right)\right],
\]

and

\[
\mathbf E_j(t)=\operatorname{Re}{\cal E}_j(t)\,\hat{\mathbf x}
+\operatorname{Im}{\cal E}_j(t)\,\hat{\mathbf y}.
\]

This convention describes counterclockwise circular polarization. The target pulse has

\[
t_0=0,\qquad E_0=0.05,\qquad \omega_0=0.05695,\qquad
\tau_0=7\frac{2\pi}{\omega_0},
\]

and the phase-locked isolated-attosecond reference has

\[
t_x=800,\qquad E_x=0.015,\qquad \omega_x=1.2,\qquad \tau_x=15.
\]

Use consistent field-vector-potential, continuum-normalization, phase, and final-time conventions for the target-only, reference-only, and coherent two-pulse cases. A common overall phase and common signal normalization are immaterial. Absolute photoelectron yield is not a grading target.

## Research problem

Determine whether the otherwise inaccessible complex spectral phase and birth-time content of the target direct-SFA photoelectron packet can be recovered from three observable angle- and energy-resolved photoelectron spectra. These spectra correspond to the target-only, reference-only, and coherent two-pulse cases.

Establish the energy-time structure supported by the recovered packet for this ionization case. Distinguish conclusions about the interferometric reconstruction from conclusions limited by the direct-SFA model.

The report must make the physical cases, observable definitions, phase and time conventions, and material numerical evidence auditable. You must choose the derivation, computational realization, inverse strategy, time-frequency representation, reliability argument, evidence layout, and report organization. No fixed number, order, or layout of figures is prescribed.

## Submission and resources

Submit one self-contained scientific report and an auditable offline calculation package. Include the task-specific derivation, code, numerical data underlying all material claims, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and environment information.

Resource limits are supplied exclusively by the accompanying
`resource_limits.json`. Its fixed CPU allocation, candidate-active
wall time, network boundary are binding. No separate aggregate CPU-hour limit applies. Greater computational expense
receives no additional credit.

## Reference and integrity policy

This examination is conducted without network access or live literature
retrieval. You may rely on your existing general scientific knowledge and, if any are
explicitly supplied with the examination, on those offline materials or
software documentation. Record every such source actually consulted. For formulas,
methods, constants, or conventions used from general knowledge rather than a
consulted source, state enough of the method basis, definition, value, units,
and convention to make the calculation auditable; do not invent a citation.
You are not required to identify or prove a publication date or to retrieve
literature during the examination.

The hidden target article and its identifying metadata, figures or captions,
supplementary material, author code or data, target-specific reproduction
code, solution or scoring material, online solutions, and worked
reproductions of this case must not be used. All submitted scientific figures
and numerical data must be generated by your own implementation of the stated
problem.

See [submission requirements](../../submission_requirements.md) for the common submission entry points.