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Sandbox Physics

Q028 · Order / transfer / count

STIRAP Dark-State Transfer

Drag two laser pulses past each other. Can an atom reach the target while barely occupying the fragile intermediate state?

Interactive modelSTIRAP Dark-State Transfer
Model at the cursor—\text{—}
Recorded at this time—\text{—}

02 / CHANGE ONE THING

Slide the pulses past each other

Δt/t∗=1.4\Delta t/t_*=1.4

Drag either peak. Positive separation means Stokes arrives first. The sliders offer the same keyboard control.

03 / EVOLUTION & MEASUREMENT

Reach the target. Avoid the middle.

Model populations at the cursor

Initial0%
Intermediate0%
Target0%
InitialIntermediateTargetLines: model · circles: records · bars: 95% Wilson intervals

Click the plot to move the cursor. Each point combines only shots recorded at that time and those settings.

Model dark-state overlap

—\text{—}

Recorded target fraction

—\text{—}

04 / TEST YOUR PREDICTION

Which order works best?

Run a scan to collect 200 new preparations at each of 13 settings.

SettingRead / totalTarget outcomes
What is simulated?

Every record is simulated. State readout is ideal when available, with state-independent missing records. Changing preparation settings clears the active data; an already acquired scan retains its own settings until you replace or reset it. Model diagnostics are separate from measured frequencies.

The intermediate state decays equally to the two lower states. No atom escapes the three-level model. This is pulsed STIRAP, not a steady-state EIT transmission calculation.

Time is in reference units; angular frequencies are in inverse reference time. No species or laboratory clock is calibrated.

Scientific sources: Vitanov et al. · STIRAP

Physics tutorial

Control a dark-state transfer

BackgroundA coherent control sequence changes the state before a final measurement.

Why it mattersChange one operation, then test it with fresh preparations.

Start with the essentials

Focus question
Can pulse order protect a transfer?
One-sentence intuition
The population curves are model predictions; the dots come only from recorded outcomes.

Core mathematical model

Reference units

τ=t/t∗,Ω,Δ,δ,γ,V in t∗−1\tau=t/t_*,\quad \Omega,\Delta,\delta,\gamma,V\ \text{in}\ t_*^{-1}

All rates are angular-frequency or population-decay rates. No physical species is calibrated.

Open-system dynamics

ρ˙=−i[H/ℏ,ρ]+∑j(LjρLj†−12{Lj†Lj,ρ})\dot\rho=-i[H/\hbar,\rho]+\sum_j\left(L_j\rho L_j^\dagger-\tfrac12\{L_j^\dagger L_j,\rho\}\right)

The full density matrix retains coherence. Fourth-order Runge–Kutta steps resolve the largest Hamiltonian scale, with pulse boundaries split explicitly.

Three coupled levels

Hℏ=(0ΩP/20ΩP/2ΔΩS/20ΩS/2δ)\frac H\hbar=\begin{pmatrix}0&\Omega_P/2&0\\\Omega_P/2&\Delta&\Omega_S/2\\0&\Omega_S/2&\delta\end{pmatrix}

Basis: initial, intermediate, target. The intermediate state decays with total rate gamma, half into each lower state. There is no lost population outside this model.

Move the pulse centers

ΩP=Ω0e−(τ−d/2)2/2,ΩS=Ω0e−(τ+d/2)2/2\Omega_P=\Omega_0e^{-(\tau-d/2)^2/2},\quad\Omega_S=\Omega_0e^{-(\tau+d/2)^2/2}

Positive separation means Stokes arrives first. Gaussian amplitude width is one reference time; the finite simulation runs from minus five to five.

The instantaneous dark state

∣D⟩=ΩS∣g⟩−ΩP∣f⟩ΩP2+ΩS2|D\rangle=\frac{\Omega_S|g\rangle-\Omega_P|f\rangle}{\sqrt{\Omega_P^2+\Omega_S^2}}

At exact two-photon resonance this eigenvector has no intermediate-state component. Finite pulse strength and detuning can prevent the evolving state from following it. The dark overlap is a model diagnostic, not a measured count.

Readout and uncertainty

p^=kNread,Nunread=N−Nread\hat p=\frac{k}{N_{\rm read}},\quad N_{\rm unread}=N-N_{\rm read}

The displayed interval is a 95% Wilson binomial interval for successful target-state or double-excitation outcomes, conditional on available state-independent readout. It is pointwise, not a simultaneous band or numerical-model error. Each shot starts from a fresh ground-state preparation.

Common difficulties

A probability is not a trajectory

Typical misconceptionThe glowing atom reveals a hidden path.

Better mental modelThe atom marker locates a fixed site. Light-beam brightness indicates drive amplitude. Only the result tiles represent sampled observations.

Reference and boundary

Typical misconceptionThis reproduces a calibrated apparatus.

Better mental modelSTIRAP follows Vitanov et al., Reviews of Modern Physics 89, 015006 (2017), section II. Blockade follows Gaëtan et al., Nature Physics 5, 115–118 (2009). These motivate the Hamiltonians; our dimensionless rates and schematic geometry are not fitted experimental values.

Run the experiment

  1. 01

    Predict

    Choose a contrasting case before collecting.

    What to observe: Keep the physical drive and measurement time in mind.
  2. 02

    Operate

    Drag pulse peaks or the separation handle, and scrub the time cursor.

    What to observe: Playing only replays the deterministic evolution; it does not manufacture observations.
  3. 03

    Acquire and compare

    Measure at the cursor, then collect a parameter scan. Export its raw outcomes.

    What to observe: The scan measures at the captured cursor time and preserves its own preparation settings.