Phase characterization in a weak-pulse/strong-field ionization model
Background
Directly characterizing the carrier-envelope phase (CEP) of a weak circularly polarized isolated attosecond pulse (IAP) is difficult because the pulse does not by itself provide the strongly nonlinear response used in established infrared CEP measurements. Consider ground-state hydrogen exposed to the weak IAP together with a much stronger, phase-stable circularly polarized infrared (IR) field, with the emitted photoelectrons observed in the laser-polarization plane.
Research problem
Develop and assess a reproducible angular-streaking strategy for characterizing the absolute IAP CEP, within the stated laboratory phase convention, from the final photoelectron momentum or angular distribution in this two-pulse configuration. Treat the known IR phase as the phase reference. Demonstrate, by varying the IAP CEP, whether a usable phase-to-observable relation can be established and whether the same diagnostic remains applicable at both specified IAP wavelengths. Determine the level of CEP characterization supported by the stated model and your calculated evidence.
How the strategy is constructed and substantiated is for you to decide. Assess its success from the calculated evidence rather than assuming it in advance.
Physical inputs
Use atomic units in the field and strong-field calculations. For each individual pulse $i\in{\mathrm{IAP},\mathrm{IR}}$, use the source-stated finite-support field
and $\mathbf E_i(t)=0$ outside this support. The two pulse envelopes share the same time origin. The fields rotate clockwise in the $x$-$y$ plane under this convention.
| Quantity | Value or condition |
|---|---|
| Target | Ground-state hydrogen ($1s$) |
| Ionization potential | $I_p=0.5$ a.u. |
| IAP wavelengths | 67 nm and 100 nm |
| IR wavelength | 800 nm |
| Peak intensities | $I_{\mathrm{IAP}}=2\times10^{11},\mathrm{W/cm^2}$ and $I_{\mathrm{IR}}=2\times10^{14},\mathrm{W/cm^2}$ |
| Field amplitudes | $E_{0,i}=\sqrt{I_i/(3.51\times10^{16})}$ a.u. |
| Pulse durations | Four optical cycles, $\tau_i=4(2\pi/\omega_i)$ |
| Carrier frequencies | $\omega_i=2\pi c/\lambda_i$, converted consistently to atomic units |
| Phase reference | $\theta_{\mathrm{IR}}=0$; $\theta_{\mathrm{IAP}}$ is the characterization variable |
| Momentum domain of interest | Laser-polarization plane, $p_z=0$ |
State any conversion constants and phase, vector-potential, momentum-axis, and angular conventions used in your work.
Model scope
Use a standard ground-state-hydrogen ($1s$) ADK treatment as the simplified tunnelling baseline and a standard strong-field approximation (SFA) for the coherent final photoelectron calculation. Select and cite the precise standard formulations you use. In the ADK-level model, neglect ground-state depletion and post-release Coulomb action. Do not add a full TDSE calculation to the required task.
All numerical and diagnostic choices not fixed above are yours. The same physical and phase conventions must be used consistently, and the same diagnostic strategy must be tested at both IAP wavelengths. Any normalization or display scaling must be declared and kept common wherever relative magnitudes are used as scientific evidence. Absolute photoelectron yield is not a grading target unless it is fixed by the formulation you adopt.
You are responsible for checking that your numerical results are sufficiently reliable and reproducible to support the conclusions you report. No particular grid, solver, convergence sequence, error metric, or validation procedure is prescribed.
Submission
Submit a self-contained scientific report and an offline reproduction package containing the code, the numerical data underlying the reported evidence, the 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. The scientific organization of the report and supporting evidence, as well as filenames below the common top-level collection entry points, are yours. No full exploratory history or examiner-selected numerical method is required.
The active examination resources and limits are defined in the companion
resource_limits.json. All retained production calculations must run
within that fixed allocation and active wall time. More expensive modelling
does not receive 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 for the common submission entry points.