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Sandbox Physics

Q049 · Drive / monitor / compare

Quantum Zeno Monitoring

Keep the drive on. Change how often the atom is checked, then compare every final result with the histories that always read positive.

Interactive modelQuantum Zeno Monitoring
Model reference—\text{—}
Protocol reference—\text{—}

02 / READ EVERY HISTORY

A final return is not an uninterrupted stay.

Final initial state

0

Final other state

0

All-positive history

0

The latest complete measured history will appear here.

From records at the current check count

—\text{—}—\text{—}

Final initial-state fraction and final fraction within all-positive histories. Pointwise 95% Wilson intervals. At weak strength, positive is a probe label, not a certified state.

03 / CHANGE THE CHECKING RATE

Do the measured fractions move?

Final initial-state fraction versus check count NN

Blue points: records. Amber line: all trials in the model. Grey dashed line: no monitoring. A scan collects 200 independent histories at each of eight settings.

Model expectations at this setting

—\text{—}—\text{—}

The all-positive yield counts how many records enter that subset. It is not the final initial-state probability. No monitoring leaves the subset undefined.

04 / WHAT THE PROBE DISTURBS

Between checks, the drive keeps turning the state.

Model initial-state population and transverse coherence versus fraction of total time

The probe preserves instantaneous populations while reducing coherence. That changes subsequent driven evolution. Moving the preview cursor never samples an extra history.

05 / KEEP THE EVIDENCE

Save. Change one thing. Compare.

Eight saved samples maximum. Saving freezes a run; new acquisition starts another. Export includes all raw records and preparation settings. Reusing a seed reproduces draws, so repeated copies are not independent evidence.

Model, units & sources
M±=diag⁡((1±s)/2,(1∓s)/2)M_\pm=\operatorname{diag}(\sqrt{(1\pm s)/2},\sqrt{(1\mp s)/2})

A resonantly driven two-level atom, with optional detuning. The initial state is the positive longitudinal state. Instantaneous binary probes occur at equally spaced times including the final time, followed by an ideal final projective readout. Zero probes gives free unitary evolution. Weak-probe outcomes are labels, not hidden state trajectories.

The 3D trap, drive and fluorescence optics are conceptual. Probe pulse duration, scattering recoil, extra atomic levels, detector losses and environmental spectral density are not simulated. The binary Kraus model is explicitly separate from the real beryllium experiment.

Itano et al. · Physical Review A 41, 2295 (1990) · Itano · Perspectives on the quantum Zeno paradox

Physics tutorial

Quantum Zeno Monitoring

BackgroundKeep the drive on. Change how often the atom is checked, then compare every final result with the histories that always read positive.

Why it mattersCompare individual records with the declared ensemble model.

Start with the essentials

Focus question
Can repeated checks slow a quantum transition?
One-sentence intuition
Change one setting, preserve a comparison, and reconstruct from raw records.

Core mathematical model

Drive between probes

H=ℏ2(Ωσx+δσz)H=\tfrac{\hbar}{2}(\Omega\sigma_x+\delta\sigma_z)

The initial state has positive z. Time is measured in inverse resonant Rabi frequency.

Binary probe

M±=diag(1±s2,1∓s2)M_\pm=\mathrm{diag}\left(\sqrt{\tfrac{1\pm s}{2}},\sqrt{\tfrac{1\mp s}{2}}\right)

At unit strength these are projectors. At zero strength their random labels carry no state information and do not disturb the system.

Ensemble disturbance

ρ01⟼1−s2 ρ01\rho_{01}\longmapsto\sqrt{1-s^2}\,\rho_{01}

Discarding a record does not undo the coupling that generated it.

All-positive history

P+⋯+=cos⁡2N ⁣(ΩT2N)P_{+\cdots+}=\cos^{2N}\!\left(\tfrac{\Omega T}{2N}\right)

Only for resonant, equally spaced, ideal projective checks. It differs from the probability of the final state being initial.

Final initial-state probability

P0(T)=12[1+cos⁡N ⁣(ΩTN)]P_0(T)=\tfrac12\left[1+\cos^N\!\left(\tfrac{\Omega T}{N}\right)\right]

This projective resonant reference includes trajectories that leave and return.

Common difficulties

Who watches?

Typical misconceptionA conscious observer freezes the atom.

Better mental modelThe measurement interaction disturbs the state even if its record is discarded.

A universal effect?

Typical misconceptionMore checks always prevent any change.

Better mental modelThis is a declared driven two-level model. It does not model arbitrary unstable systems or anti-Zeno spectral environments.

Run the experiment

  1. 01

    Predict

    Choose no monitoring and predict the final state after a half Rabi turn.

    What to observe: The preview is a model and adds no measurements.
  2. 02

    Record

    Collect a monitoring scan. Compare final-state frequencies across equal-spacing schedules.

    What to observe: Wilson intervals describe finite independent trials at each setting.
  3. 03

    Separate histories

    Try Leave and return, then inspect the last measured history and the all-positive subset.

    What to observe: With weak probes, a positive label is not a projective state preparation.