| # Interferometric recovery of a direct-SFA photoelectron wave packet |
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| ## Physical setting |
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| 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. |
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| For a pulse centred at (t_j), define |
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|
| \[ |
| {\cal E}_j(t)=E_j |
| \exp\!\left[-\frac{8\ln 2}{\tau_j^2}(t-t_j)^2\right] |
| \exp\!\left[i\left(\omega_j(t-t_j)+\frac{\pi}{2}\right)\right], |
| \] |
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|
| and |
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| \[ |
| \mathbf E_j(t)=\operatorname{Re}{\cal E}_j(t)\,\hat{\mathbf x} |
| +\operatorname{Im}{\cal E}_j(t)\,\hat{\mathbf y}. |
| \] |
| |
| This convention describes counterclockwise circular polarization. The target pulse has |
| |
| \[ |
| t_0=0,\qquad E_0=0.05,\qquad \omega_0=0.05695,\qquad |
| \tau_0=7\frac{2\pi}{\omega_0}, |
| \] |
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| and the phase-locked isolated-attosecond reference has |
|
|
| \[ |
| t_x=800,\qquad E_x=0.015,\qquad \omega_x=1.2,\qquad \tau_x=15. |
| \] |
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| 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. |
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| ## Research problem |
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| 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. |
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| 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. |
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| 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. |
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| ## Submission and resources |
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| 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. |
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| 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. |
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| ## Reference and integrity policy |
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| 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. |
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| 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. |
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| See [submission requirements](../../submission_requirements.md) for the common submission entry points. |
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