Rydberg RF Sensor 2D: Dressed-State Ladder & AT Susceptibility

RF Field & Atom

RF field amplitude E 12.0 V/m

Rydberg level n 50

EIT linewidth γ 1.0 MHz

Coupling Rabi Ω_c 6.0 MHz

Model vs Prediction

–

Solved-model splitting vs κ(n)·E formula

Predicted Δf = κ(n)·E

0.0 MHz

Solved from susceptibility

0.0 MHz

Coupling κ(n)

— MHz/(V/m)

Min. detectable field

— V/m

How it works

This is a native 2D re-derivation of the same Rydberg-EIT physics as the 3D sensor, not a flattened camera view of the vapor-cell scene. Instead of animated atoms and laser cylinders, this page solves the actual four-level optical Bloch continued-fraction susceptibility for the probe coherence, the standard closed form used in real Rydberg-sensor papers, and draws the three 2D tools spectroscopists use to read it: a dressed-state energy-level ladder, the computed absorption spectrum, and a complex-susceptibility phasor (Argand) plot.

D(r') = γ_r' + iΔ
D(r)  = γ_r  + iΔ + (Ω_RF/2)² / D(r')
D(e)  = γ    + iΔ + (Ω_c /2)² / D(r)
χ(Δ)  = i / D(e)          Absorption ∝ Im[χ(Δ)]

With no RF field this reduces to the textbook single EIT transparency window at line centre. Turning on a resonant RF field pumps a term into D(r) that closes that window and reopens two new ones — an Autler-Townes doublet — at a separation this page finds numerically by scanning χ(Δ) for its two transparency minima, then compares directly against the atomic-physics closed form Δf = κ(n)·E used for the field readout. The two should track each other closely once the doublet is well resolved (Δf ≳ γ); watch them diverge as E shrinks toward the sensor's noise floor.

E slider — the RF field amplitude being sensed; the solved doublet spreads apart as κ(n)·E grows.
n slider — higher principal quantum number → κ(n) ∝ n⁴ → steeper splitting per volt/metre, but a more fragile Rydberg state.
γ slider — the optical (probe) linewidth; the two peaks are only resolvable once the solved splitting exceeds roughly γ.
Ω_c slider — coupling-laser strength; it sets how deep and wide the underlying transparency feature is before the RF field splits it.
Sweep — scans a virtual probe laser across the spectrum, tracking the same point on the phasor plot below.

Probe transition |g⟩→|e⟩ Coupling |e⟩→|r⟩ RF field |r⟩→|r′⟩