Cesium Fountain Clock — Ramsey Interrogation

Fountain Setup

Launch velocity v₀ 4.0 m/s

Microwave detuning Δf 0.00 Hz

Cloud temperature 5 µK

Ramsey Fringe P(Δf)

Readouts

ground 100%excited 0%

Free evolution T

0.00 s

Fringe width

0 mHz

Detected fraction

Line Q (f₀·T)

How it works

A cesium fountain clock laser-cools a small cloud of cesium-133 atoms, tosses it upward through a microwave cavity, lets it fly freely under gravity, and catches it falling back through the same cavity. Each pass delivers a π/2 microwave pulse tuned near the 9,192,631,770 Hz hyperfine transition — together the two pulses form a Ramsey interferometer.

Free evolution time:  T = t_down − t_up
Ramsey signal:        P(δ) = ½[1 − cos(2π·Δf·T)]
Fringe half-width:    ΔfFWHM ≈ 1 / (2T)
Timing (this sim):    t_up,down solved from
  ½g·t² − v₀·t + h_cavity = 0,  g = 9.8 m/s²

Launch velocity v₀ — sets the fountain's apex height and, crucially, the free-evolution time T between the two microwave pulses. A higher toss (real fountains reach ~1 m) gives a longer T and a narrower, more precise fringe — the whole reason fountains beat tabletop cesium clocks.
Microwave detuning Δf — how far the interrogation frequency sits from the true 9,192,631,770 Hz resonance. The atoms accumulate a phase 2π·Δf·T between the two pulses, which the second pulse converts into a probability of finding the atom in the excited hyperfine state.
Cloud temperature — colder atoms (µK-scale, reached by laser cooling) drift less sideways during flight and stay inside the cavity's aperture on the way back down; hotter clouds lose atoms out the sides, lowering the detected fraction and washing out fringe contrast.
Detected fraction — the share of launched atoms whose transverse thermal drift keeps them inside the cavity aperture at the second pass; this emerges directly from the simulated trajectories, not a fudge factor.

A real cesium clock steers Δf to keep P pinned at the fringe's steepest slope (usually the two half-maximum points, alternating), which is exactly how the SI second is realized and how GPS timing chains stay synchronized.

Ground state Excited state Lost (missed cavity)

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