{
  "collapse_revival": {
    "g": 1.0,
    "initial_atom": "excited",
    "initial_field": "coherent state with real amplitude",
    "mean_photon_number": 16.0,
    "photon_cutoffs": [
      20,
      30,
      40,
      60
    ],
    "reference_cutoff": 100,
    "samples": 1201,
    "validation": {
      "checks": {
        "cutoff_converges": true,
        "excitation_conservation": true,
        "reference_cutoff": true,
        "revival_resolved": true,
        "unit_norm": true
      },
      "collapse_time_1_over_e_estimate": 1.4142135623730951,
      "largest_revival_window_abs_inversion": 0.5610658124611343,
      "largest_revival_window_time": 25.597696941449634,
      "largest_state_norm_error": 1.4432899320127035e-15,
      "largest_total_excitation_drift": 2.4868995751603507e-14,
      "max_reference_minus_infinite_sum": 6.564193633096238e-15,
      "mean_photon_number": 16.0,
      "reference_cutoff": 100,
      "revival_time_estimate": 25.132741228718345
    }
  },
  "dressed_spectrum": {
    "Delta_over_g_range": [
      -6.0,
      6.0
    ],
    "g": 0.1,
    "manifold_n": [
      0,
      1
    ],
    "omega_c": 1.0,
    "samples": 401,
    "validation": {
      "checks": {
        "analytic_dressed_energies": true,
        "orthonormal_eigenvectors": true,
        "sqrt_two_splitting": true,
        "vacuum_splitting": true
      },
      "max_block_energy_error": 5.551115123125783e-17,
      "max_eigenvector_orthonormality_error": 4.440892098500626e-16,
      "resonance_splitting_errors": {
        "n0": 5.551115123125783e-17,
        "n1": 1.6653345369377348e-16
      }
    }
  },
  "license": "MIT",
  "limitations": [
    "one two-level emitter and one bosonic mode",
    "rotating-wave Jaynes-Cummings interaction",
    "closed calculations omit all loss and drive",
    "loss extension is restricted to zero and one excitation",
    "Markovian cavity and emitter decay only",
    "no pure dephasing, coherent cavity drive, or thermal photons",
    "no input-output spectrum or detector model",
    "no counter-rotating or diamagnetic terms"
  ],
  "loss_extension": {
    "cases": [
      {
        "gamma_over_g": 0.0,
        "kappa_over_g": 0.0,
        "name": "closed"
      },
      {
        "gamma_over_g": 0.2,
        "kappa_over_g": 0.2,
        "name": "balanced"
      },
      {
        "gamma_over_g": 0.2,
        "kappa_over_g": 1.0,
        "name": "leaky_cavity"
      }
    ],
    "g": 1.0,
    "gamma_convention": "emitter population-decay rate",
    "integrator": "classical explicit Runge-Kutta order 4",
    "kappa_convention": "cavity energy-decay rate",
    "max_internal_step": 0.0025,
    "model": "unconditional Lindblad master equation in the zero- and one-excitation sectors",
    "photon_cutoff": 2,
    "samples": 501,
    "validation": {
      "balanced_final_total_excitation": 0.13533528323661304,
      "checks": {
        "closed_limit": true,
        "hermitian": true,
        "loss_removes_excitation": true,
        "positive": true,
        "trace_one": true
      },
      "largest_hermiticity_error": 0.0,
      "largest_trace_error": 4.107825191113079e-15,
      "leaky_final_total_excitation": 0.0028497499050227386,
      "max_closed_population_error": 3.6909142409058404e-11,
      "minimum_density_eigenvalue": -3.301997564264525e-12
    }
  },
  "outputs": [
    "cavity-qed-dressed-spectrum.csv",
    "cavity-qed-vacuum-rabi.csv",
    "cavity-qed-collapse-revival.csv",
    "cavity-qed-truncation.csv",
    "cavity-qed-loss.csv",
    "cavity-qed-metadata.json"
  ],
  "provenance": {
    "Jaynes_Cummings": {
      "doi": "10.1109/PROC.1963.1664"
    },
    "collapse_revival": {
      "doi": "10.1103/PhysRevLett.44.1323"
    }
  },
  "runtime": {
    "numpy": "2.3.5",
    "platform": "Windows-11-10.0.26200-SP0",
    "python": "3.12.13",
    "random_seed": null
  },
  "scope": {
    "basis_order": "atom [excited, ground] tensor photon [0,...,N-1]",
    "claim": "finite-basis Jaynes-Cummings and small Lindblad benchmark, not a device-specific cavity-QED prediction",
    "closed_model": "Jaynes-Cummings Hamiltonian",
    "detuning": "Delta = omega_a - omega_c",
    "units": {
      "closed_dynamics_g": 1.0,
      "hbar": 1.0,
      "time": "1/g"
    }
  },
  "vacuum_rabi": {
    "g": 1.0,
    "g_t_range": [
      0.0,
      12.566370614359172
    ],
    "initial_state": "|e,0>",
    "photon_cutoff": 4,
    "samples": 801,
    "validation": {
      "checks": {
        "excitation_conservation": true,
        "one_excitation_exchange": true,
        "unit_norm": true,
        "vacuum_photon_probability": true,
        "vacuum_rabi_probability": true
      },
      "max_exchange_sum_error": 6.661338147750939e-16,
      "max_excited_population_error": 4.440892098500626e-16,
      "max_photon_number_error": 4.440892098500626e-16,
      "max_state_norm_error": 6.661338147750939e-16,
      "max_total_excitation_drift": 3.3306690738754696e-16
    }
  },
  "validation": {
    "all_checks_passed": true,
    "sections": {
      "collapse_revival": {
        "cutoff_converges": true,
        "excitation_conservation": true,
        "reference_cutoff": true,
        "revival_resolved": true,
        "unit_norm": true
      },
      "dressed_spectrum": {
        "analytic_dressed_energies": true,
        "orthonormal_eigenvectors": true,
        "sqrt_two_splitting": true,
        "vacuum_splitting": true
      },
      "loss_extension": {
        "closed_limit": true,
        "hermitian": true,
        "loss_removes_excitation": true,
        "positive": true,
        "trace_one": true
      },
      "vacuum_rabi": {
        "excitation_conservation": true,
        "one_excitation_exchange": true,
        "unit_norm": true,
        "vacuum_photon_probability": true,
        "vacuum_rabi_probability": true
      }
    }
  }
}