ClickBackground

Phase 5b: Raman and Rayleigh flux as one per-gate floor beside the dark

9/9 passed in 257ms

Test	What it does	Result
test_background_reads_as_dark	A Raman flux through bg_floor drives the DPS QBER exactly as an equal dark probability does, q.ClickDetector(dark=...) being the composition point with no separate QBER term.	✅ pass
test_floor_composes	bg_floor is $1-(1-d)e^{-\eta \sum \mathrm{\Phi }}$: an empty list is the bare dark, fluxes sum, and one flux matches click_prob at that photon number.	✅ pass
test_modes_count_the_gate	The mode count is passbandgatepol, so doubling the filter width, the gate or the polarisations doubles the photons one occupancy delivers.	✅ pass
test_poisson_beats_linear	bg_floor exponentiates where Eraerds' Eq. (11) is linear, a form their note under Eq. (15) says carries no Poisson statistics, so the linear form reads high at every flux.	✅ pass
test_raman_matches_power	Kumar's Eq. (6) occupancy over passbandgate2 reproduces Eraerds' Eq. (11) $P_{ram}/(h\nu )\cdot d{t}_{gate}$, Eq. (6)'s 1/2 being the oscillator's and the 45 pm filter carrying no polarisation factor.	✅ pass
test_rayleigh_split_is_optics	The 1/2 in rayleigh_photons, the oscillator's polarisation selectivity, and the 1/2 in split, two detectors dividing an unpolarised return, cancel, so the engine takes the unpolarised number.	✅ pass
test_rayleigh_takes_the_gate	An elastic return is continuous: a gate takes gate/period of one period's photons and split this detector's share, a full-period gate at split=1 returning its input.	✅ pass
test_rejects_nonsense	The passband, gate, polarisation count, split and a saturating flux are each refused by name.	✅ pass
test_thermal_bounds_poisson	Spontaneous Raman is chaotic: the M-mode law $1-(1-d)(1+\eta n{)}^{-M}$ reads below the Poisson one at equal flux, the gap closing as the mode count rises at fixed flux.	✅ pass