[rasidi3112]

Summary

Adds strong-field physics: a hydrogen atom in an intense laser pulse, which emits high harmonics and attosecond pulses (the three-step recollision model behind attosecond science).

• quantumlab.strongfield:
  • laser units (wavelength → ω, intensity → field, U_p);
  • the classical three-step model;
  • dipole acceleration from Ehrenfest's theorem;
  • harmonic spectra, windowed Gabor time–frequency maps and attosecond pulse synthesis.
• SoftCoulomb potential with an analytic gradient. In 1D with a² = 2 its ground state is −0.5 a.u., i.e. hydrogen.
• flat_top_envelope gives long pulses with well-resolved harmonics.
• Example 12: hydrogen at 800 nm and 10¹⁴ W/cm². It produces the spectrum, a Gabor map with classical short/long returns, the attosecond pulse train, the electron density in space-time, and an 8-intensity cutoff scan.
• Docs: a strong-field guide page, an API page, the examples gallery and the README.

Validation

Check	Result
Hydrogen ground state	−0.5 a.u. to 3e-14
Three-step maximum return energy	3.1731 U_p (birth 18°, return 252°)
Odd harmonics only (inversion symmetry)	even orders 2300× weaker
Emission times vs classical returns, H11–H19	median 0.02–0.08 cycle (analysis resolution 0.053 cycle)
Attosecond bursts (H11–H21)	≈ 200 as, spacing 0.499–0.503 cycle
Cutoff vs intensity	linear in U_p; fitted spectral edge (3.48 ± 0.20) U_p + (1.52 ± 0.08) I_p

The cutoff row is reported with its caveat. A single 1D atom has a plateau with deep interference minima and a gradual roll-off, so the extracted edge depends on its definition: a 2-decade drop is used. The fit is therefore compared with, not claimed to equal, the classical (3.17 U_p + I_p) and quantum-corrected (3.17 U_p + 1.32 I_p) laws. 1D models also over-estimate ionisation. Both caveats are stated in the example, the docs and the README.

The version number is not changed here, to avoid conflicting with the open release PR #8.

Test plan

• pytest: 127 passed, 12 skipped (CUDA-only), including 9 new strong-field tests
• python benchmarks/validation_suite.py: 21/21
• mkdocs build --strict: no warnings; examples page has 20 images, none broken
• README: 39/39 images referenced and present
• CI on this PR