{
  "convergence": {
    "max_internal_steps": [
      0.04,
      0.02,
      0.01
    ],
    "observable_norm": "maximum absolute rho_ee difference",
    "validation": {
      "checks": {
        "fine_difference": true,
        "fourth_order_regime": true
      },
      "largest_medium_fine_population_difference": 1.0947350803647282e-08,
      "minimum_refinement_difference_ratio": 18.793194360131942
    }
  },
  "decay_benchmarks": {
    "coherence": "u(t) = exp(-Gamma_2 t)",
    "population": "rho_ee(t) = exp(-Gamma t)",
    "validation": {
      "checks": {
        "coherence_decay": true,
        "population_decay": true
      },
      "max_coherence_decay_error": 2.2653545705964007e-12,
      "max_population_decay_error": 9.270362255620057e-13
    }
  },
  "equations": {
    "Gamma_2": "Gamma/2 + gamma_phi",
    "u_dot": "-Gamma_2 u - Delta v",
    "v_dot": "Delta u - Gamma_2 v - Omega w",
    "w_dot": "Omega v - Gamma (w + 1)"
  },
  "license": "MIT",
  "limitations": [
    "two-state and rotating-wave approximations are assumed",
    "Markovian population decay and pure dephasing only",
    "semiclassical monochromatic drive",
    "no multilevel branching or optical pumping",
    "no motion, Doppler averaging, spatial inhomogeneity, or recoil",
    "fluorescence rate excludes collection and detector efficiency",
    "no photon-counting trajectories or field-correlation spectrum"
  ],
  "line_shapes": {
    "Delta_over_Gamma_range": [
      -6.0,
      6.0
    ],
    "Omega_over_Gamma": [
      0.1,
      0.5,
      1.0,
      2.0
    ],
    "gamma_phi_over_Gamma": 0.0,
    "samples": 601,
    "validation": {
      "checks": {
        "even_in_detuning": true,
        "steady_line_shape": true
      },
      "max_detuning_reflection_asymmetry": 2.220446049250313e-16,
      "max_formula_minus_linear_population": 7.890281310263259e-17
    }
  },
  "linewidth": {
    "Omega_over_Gamma_range": [
      0.05,
      4.0
    ],
    "definition": "full width at half maximum in angular detuning",
    "root_solver": "deterministic bisection of linear steady state",
    "samples": 80,
    "validation": {
      "checks": {
        "linewidth_root": true,
        "power_broadening": true
      },
      "max_analytic_minus_numerical_FWHM": 2.0961010704922955e-13,
      "strongest_drive_FWHM_over_Gamma": 5.744562646538043,
      "weakest_drive_FWHM_over_Gamma": 1.0024968827881935
    }
  },
  "outputs": [
    "optical-bloch-transients.csv",
    "optical-bloch-saturation.csv",
    "optical-bloch-line-shapes.csv",
    "optical-bloch-linewidth.csv",
    "optical-bloch-convergence.csv",
    "optical-bloch-metadata.json"
  ],
  "provenance": {
    "optical_resonance_text": {
      "authors": "Allen and Eberly"
    },
    "quantum_optics_text": {
      "authors": "Cohen-Tannoudji, Dupont-Roc, and Grynberg"
    }
  },
  "runtime": {
    "numpy": "2.3.5",
    "platform": "Windows-11-10.0.26200-SP0",
    "python": "3.12.13",
    "random_seed": null
  },
  "saturation": {
    "Omega_over_Gamma_range": [
      0.0,
      5.0
    ],
    "gamma_phi_over_Gamma": [
      0.0,
      0.5,
      2.0
    ],
    "samples": 251,
    "validation": {
      "checks": {
        "high_drive_tends_to_half": true,
        "saturation_formula": true,
        "steady_state_linear_solve": true
      },
      "largest_gap_from_half_at_Omega_over_Gamma_5": 0.04545454545454547,
      "max_analytic_minus_linear_state": 2.220446049250313e-16,
      "max_population_formula_error": 1.1102230246251565e-16
    }
  },
  "scope": {
    "bloch_coordinates": {
      "u": "2 Re rho_eg",
      "v": "-2 Im rho_eg",
      "w": "rho_ee - rho_gg"
    },
    "claim": "optical Bloch solver and steady-response benchmark, not a species-specific fluorescence prediction",
    "detuning_convention": "Delta = omega_0 - omega_L",
    "state": "unconditional density matrix in Bloch coordinates",
    "system": "semiclassically driven dissipative two-level atom",
    "units": {
      "Gamma": 1.0,
      "frequency": "Gamma",
      "hbar": 1.0,
      "time": "1/Gamma"
    }
  },
  "transients": {
    "Gamma_t_range": [
      0.0,
      15.0
    ],
    "cases": [
      {
        "Delta_over_Gamma": 0.0,
        "Omega_over_Gamma": 0.25,
        "gamma_phi_over_Gamma": 0.0,
        "name": "resonant_weak"
      },
      {
        "Delta_over_Gamma": 0.0,
        "Omega_over_Gamma": 1.0,
        "gamma_phi_over_Gamma": 0.0,
        "name": "resonant_saturated"
      },
      {
        "Delta_over_Gamma": 0.0,
        "Omega_over_Gamma": 3.0,
        "gamma_phi_over_Gamma": 0.0,
        "name": "resonant_oscillatory"
      },
      {
        "Delta_over_Gamma": 1.5,
        "Omega_over_Gamma": 1.0,
        "gamma_phi_over_Gamma": 0.0,
        "name": "detuned"
      },
      {
        "Delta_over_Gamma": 0.5,
        "Omega_over_Gamma": 1.0,
        "gamma_phi_over_Gamma": 0.75,
        "name": "dephased"
      }
    ],
    "initial_state": {
      "u": 0.0,
      "v": 0.0,
      "w": -1.0
    },
    "integrator": "classical explicit Runge-Kutta order 4",
    "max_internal_step": 0.005,
    "samples": 601,
    "validation": {
      "checks": {
        "bloch_ball": true,
        "physical_population": true,
        "steady_state_reached": true
      },
      "max_bloch_radius_excess": 0.0,
      "max_final_state_minus_steady_state": 9.553601065342976e-05,
      "maximum_excited_population": 0.689062915313342,
      "minimum_excited_population": 0.0
    }
  },
  "validation": {
    "all_checks_passed": true,
    "sections": {
      "convergence": {
        "fine_difference": true,
        "fourth_order_regime": true
      },
      "decay": {
        "coherence_decay": true,
        "population_decay": true
      },
      "line_shapes": {
        "even_in_detuning": true,
        "steady_line_shape": true
      },
      "linewidth": {
        "linewidth_root": true,
        "power_broadening": true
      },
      "saturation": {
        "high_drive_tends_to_half": true,
        "saturation_formula": true,
        "steady_state_linear_solve": true
      },
      "transients": {
        "bloch_ball": true,
        "physical_population": true,
        "steady_state_reached": true
      }
    }
  }
}