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Sandbox Physics

Q020 · Phase accumulation / spectroscopy

Ramsey Frequency Measurement

Separate two half-flip pulses with a dark interval. Acquire a spectrum and a second-pulse phase scan, infer the accumulated phase from counts, and compare sensitivity against lost contrast and frequency ambiguity.

Interactive modelRamsey Frequency Measurement
Model positive probability—\text{—}
Positive / negative / rejected—\text{—}
Current-setting trials—\text{—}
Acquired positive fraction—\text{—}
95% Wilson interval—\text{—}
Output-state purity—\text{—}
Model fringe spacing—\text{—}

SIMULATED ACQUISITION

Make a prediction. Collect the evidence.

No acquired record yet.

Inference from acquired counts

Acquire a scan to estimate the signal.

—\text{—}
Density matrix and count conventions
ρ=I+r⋅σ2\rho=\frac{I+\boldsymbol r\cdot\boldsymbol\sigma}{2}

Latest raw events · full record in CSV
EventSettingOutcome

Scientific basis: Feynman III.6 · MIT 8.05 · NIST Ramsey

Physics tutorial

Trade waiting time against coherence

BackgroundThe first pulse creates transverse coherence. Darkness accumulates phase, and the second pulse converts it to population.

Why it mattersRamsey interrogation powers precision spectroscopy, but contrast, aliases and systematic shifts constrain what a finite record can prove.

Start with the essentials

Focus question
Does doubling the dark interval improve every frequency measurement?
One-sentence intuition
It narrows fringe spacing and increases phase sensitivity while shrinking the unambiguous frequency interval and reducing contrast.

Core mathematical model

Phase accumulated during darkness

Φ=2π δf T\Phi=2\pi\,\delta f\,T

Phase accumulated during darkness

Ideal instantaneous half-flip pulses with pure dephasing

Pe=12[1+e−T/T2cos⁡(Φ−φ2)]P_e=\tfrac12[1+e^{-T/T_2}\cos(\Phi-\varphi_2)]

Ideal instantaneous half-flip pulses with pure dephasing

Phase-only inference has frequency ambiguity

δf=Φ+2πk2πT,k∈Z\delta f=\frac{\Phi+2\pi k}{2\pi T},\quad k\in\mathbb Z

Phase-only inference has frequency ambiguity

Common difficulties

Linewidth is not accuracy

Typical misconceptionA narrow simulated fringe proves an accurate atomic clock.

Better mental modelThis model excludes systematic shifts, local-oscillator noise and long-term drift. Spectral width, projection-noise error and clock accuracy are distinct.

Long waits introduce aliases

Typical misconceptionAn estimate in the principal interval is the only possible frequency.

Better mental modelAdding any integer inverse dark time gives the same phase. Another independent interrogation time or prior frequency range is needed to resolve it.

Run the experiment

  1. 01

    Acquire both views

    Choose Sensitive slope and acquire a scan. Compare the spectrum with the phase scan.

    What to observe: The spectrum uses known scanned frequency settings. The estimate uses only the first harmonic of the phase counts.
  2. 02

    Lengthen darkness

    Double the dark interval and acquire again.

    What to observe: Fringe spacing halves. The phase estimate is modulo the new inverse dark time.
  3. 03

    Challenge the estimate

    Choose Lost contrast and acquire a scan. Increase shots or shorten the wait.

    What to observe: Unresolved contrast suppresses a frequency claim. More samples reduce projection noise but do not restore physical coherence.
  4. 04

    Move the working point

    Change second-pulse phase and pulse area error. Replay the sequence.

    What to observe: The second pulse converts a different quadrature. Pulse errors alter contrast and baseline in the actual evolution.