Q049 · Repeated checks on a driven atom

Quantum Zeno Monitoring

Can repeated checks slow a quantum transition? They can. With the drive left on, each check projects the atom back toward its starting state before it gets far. The more often you check, the slower the transition goes.

The drive stays on while you change how often the atom is checked. Compare the final state of every run with the smaller set of runs in which every check read positive.

Model reference $\text{—}$

Protocol reference $\text{—}$

01 / Keep the drive on and add checks

The probe changes what happens next.

Try “No monitoring”, then “Frequent checks”. Record both. Does the atom finish where it started?

Schematic trapped atom · continuous drive · instantaneous probe pulses · no resolved photon scattering

Equally spaced checks

N=16

Drag the large probe marker to change its spacing. Zero bypasses all probes; the final state is always read.

Protocol preview · no data acquired

Ready. Preview and presets do not add records.

Make a comparison

Total drive time

\Omega T/\pi

1

Monitor strength

s

1

Detuning & sampling

Drive detuning

\delta/\Omega

0

Sampling seed

s_0

2026

Changing the number of checks keeps this sample. Any other change to the preparation starts a new sample, so save first.

An ideal two-level atom is driven continuously and checked with instantaneous two-outcome measurements. The monitor strength sets how strong each check is in a defined weak-measurement model; it is not a laser scattering efficiency. All counts are simulated. The Lab makes no general claim about the anti-Zeno effect, and none about a conscious observer.

02 / Read every history in full

Ending in the start state does not mean it never left.

Final initial state

Final other state

All-positive history

The latest complete measured history will appear here.

From records at the current check count

\text{—}

\text{—}

The first value is the fraction of histories that end in the initial state; the second is that fraction among histories where every probe read positive. Pointwise 95% Wilson intervals. With weak probes, a positive reading is only a probe label and does not certify the state.

03 / Change how often you check

Do the measured fractions move?

Model reference

Final initial-state fraction versus check count $N$

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 says how many records belong to that subset. It is not the probability of ending in the initial state. Without monitoring, this subset is not defined.

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

Each probe leaves the populations unchanged at that instant but reduces the coherence, and that changes how the drive evolves the state afterward. Moving the preview cursor does not sample an extra history.

05 / Save the evidence

Save a sample, change one thing, then 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_\pm=\operatorname{diag}(\sqrt{(1\pm s)/2},\sqrt{(1\mp s)/2})

The model is a resonantly driven two-level atom, with optional detuning. It starts in the positive longitudinal state. Instantaneous binary probes act at equally spaced times, the last one at the final time, and an ideal projective readout follows. With zero probes the evolution is free and unitary. Weak-probe outcomes are labels; they do not reveal a hidden state trajectory.

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 a separate idealization, not a reproduction of the real beryllium experiment.

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

Start with the essentials

Focus question: Can repeated checks slow a quantum transition?
One-sentence intuition: Change one setting at a time, keep a saved run for comparison, and recompute the results from the raw data.

Core mathematical model

Drive between probes

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

The atom starts in the positive-z state. Time is measured in units of the inverse resonant Rabi frequency.

Two-outcome probe

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

At strength one they are projective measurements. At strength zero the labels are random: they carry no information about the state and leave the system undisturbed.

Disturbance even when the record is ignored

\rho_{01}\longmapsto\sqrt{1-s^2}\,\rho_{01}

Throwing away a measurement record does not undo the coupling that produced it.

Probability that every check reads positive

P_{+\cdots+}=\cos^{2N}\!\left(\tfrac{\Omega T}{2N}\right)

This holds only for resonant drive with equally spaced, ideal projective checks. It is not the same as the probability of ending in the initial state.

Probability of ending in the initial state

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

This reference result for resonant projective checks also counts histories that leave the initial state and come back.

Common difficulties

Does someone have to watch?

Typical misconceptionA conscious observer watching the atom freezes it.

Better mental modelThe measurement interaction itself disturbs the state, even if the record is thrown away.

Does it always work?

Typical misconceptionMore checks always stop any change.

Better mental modelThis Lab models one driven two-level system. It does not cover arbitrary unstable systems, or environments whose spectrum produces an anti-Zeno effect.

Run the experiment

01
Predict
Choose no monitoring and predict the final state after half a Rabi turn.
What to observe: The preview shows the model only; it adds no measurements.
02
Record a scan
Collect a monitoring scan. Compare how often each final state appears for different numbers of equally spaced checks.
What to observe: The Wilson intervals show the uncertainty from the finite number of independent trials at each setting.
03
Separate the histories
Try Leave and return, then look at the last measured history and at the runs in which every check read positive.
What to observe: With weak probes, a positive reading does not project the atom into the initial state.