| # Resonant EUV high-harmonic spectroscopy of correlated helium |
|
|
| ## Background |
|
|
| An intense extreme-ultraviolet pulse can drive a bound-state resonance while |
| ionization is already strong. In this regime, coherent population transfer and |
| continuum dynamics may coexist in the emitted high-harmonic radiation. |
|
|
| Work in atomic units with the following one-dimensional, two-active-electron |
| soft-core helium model: |
|
|
| $$ |
| H(t)=\sum_{j=1}^{2} |
| \left\{\frac{1}{2}\left[p_j+\frac{A(t)}{c}\right]^2 |
| -\frac{2}{\sqrt{x_j^2+a_N}}\right\} |
| +\frac{1}{\sqrt{(x_1-x_2)^2+a_{ee}}}, |
| $$ |
| |
| where $p_j=-i\partial_{x_j}$, $a_N=0.50$, $a_{ee}=0.32$, and |
|
|
| $$ |
| E(t)=-\frac{1}{c}\frac{dA(t)}{dt}. |
| $$ |
|
|
| The initial state is the normalized field-free ground state of this |
| Hamiltonian. A gauge-equivalent formulation is acceptable. |
|
|
| For the central case, use a 32-cycle pulse |
|
|
| $$ |
| E(t)=E_0\sin^2\left(\frac{\omega_0 t}{64}\right) |
| \sin(\omega_0t), |
| \qquad 0\le t\le \frac{64\pi}{\omega_0}, |
| $$ |
|
|
| and $E(t)=0$ outside this interval, with |
|
|
| $$ |
| \omega_0=0.676, |
| \qquad E_0=0.2154. |
| $$ |
|
|
| This is the model resonance between the field-free ground state and the lowest |
| dipole-coupled odd state; it corresponds to a photon energy of about $18.4$ |
| eV and a peak intensity of about $1.6\times10^{15}\ \mathrm{W\,cm^{-2}}$. |
| When varying the photon energy, retain the same cycle count and peak intensity |
| unless a clearly separated control is being studied. |
|
|
| ## Research problem |
|
|
| Using the stated correlated two-electron TDSE as the required production |
| model, determine whether near-resonant intense EUV driving sustains coherent |
| population exchange on a subfemtosecond timescale, establish how the relevant |
| dynamics is encoded in the high-harmonic response, and decide which features |
| can and cannot be accounted for by an isolated bound two-state picture. |
|
|
| Support the conclusion with an auditable calculation of the central case and |
| a comparison domain of your design that is sufficient to distinguish a |
| resonance-specific response from a generic strong-field signal. The |
| derivation, numerical realization, evidence architecture, controls, scan |
| extent, diagnostics, and report organization are for you to decide. No fixed |
| number or layout of outputs is prescribed. |
|
|
| A reduced two-state model may be used as an interpretive or falsification |
| tool, but it is not a substitute for the correlated TDSE production |
| calculation. Clearly identify any phenomenological inputs and do not present a |
| fit as an independent prediction. |
|
|
| Spatial representation, box and boundary treatment, propagation algorithm, |
| grid, time step, field-free-state construction, spectral estimator, transform |
| sign, window, post-pulse propagation, normalization, display range, and |
| comparison sampling are student choices. State the choices that affect your |
| claims and provide evidence sufficiently reliable and reconstructible to |
| support them. Absolute spectral intensity and pointwise agreement with an |
| undisclosed transform convention are not grading targets. |
|
|
| ## Submission |
|
|
| Submit one self-contained scientific report and an offline reproduction |
| package containing the derivation, code, numerical data underlying every |
| material claim, 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. No fixed file tree, filename scheme, panel count, or complete |
| exploration history is required. |
|
|
| 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. |
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|
