Q028 · Order / transfer / count

STIRAP Dark-State Transfer

How can two laser pulses transfer an atom while it almost never sits in the lossy middle state? Send them in an order that looks backwards, which is the STIRAP trick: the pulse linking the intermediate and target states comes first. The atom then follows a dark state. As the pulses overlap and trade places, that dark state turns from the initial state into the target state, and the atom hardly ever occupies the fragile intermediate state.

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

Model at the cursor $\text{—}$

Recorded at this time $\text{—}$

01 / Control the atoms

The order changes the outcome.

Blue connects the initial state; amber connects the target. Drag their peaks below.

Schematic apparatus with fixed atom positions. Beam brightness shows the drive and is not a measurement.

Sequence time

t/t_*=0

Try a comparison

Every shot starts from a fresh preparation. The page opens with 200 simulated shots already recorded.

Drive strength

\Omega_0 t_*

6

Pulse separation

(t_P-t_S)/t_*

1.4

Detuning, decay & readout

Two-photon mismatch

\delta t_*

0

Single-photon detuning

\Delta t_*

0

Spontaneous decay rate

\gamma t_*

0.3

State-readout availability

\eta

1

Record seed

s

2832

Make a prediction

Which pulse order transfers more?

The model is a three-level Lindblad equation in the rotating frame. The pulses are Gaussian, the intermediate state decays equally into the two lower states, and the readout identifies the final state perfectly. Time and frequency are in arbitrary reference units, not calibrated to a real atom. The apparatus is a sketch, and the state populations are probabilities from the model.

02 / Change one condition

Slide the pulses past each other

\Delta t/t_*=1.4

Drag either peak. A positive separation means the Stokes pulse arrives first. The sliders give the same control from the keyboard.

03 / Evolve, then measure

Reach the target while staying out of the intermediate state

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.

Setting	Read / total	Target 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, and no atom leaves the three-level system. The Lab models pulsed STIRAP; it does not calculate steady-state EIT transmission.

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

From this model to the evidence

What does changing pulse order change?

Try: At the final time, compare Stokes first with Reverse the order. Then run the pulse-order scan, keeping the drive strength and detunings the same.
Read: Compare the target-state counts and the trials left unread. The population curves and the instantaneous overlap with the dark state are model diagnostics, shown separately; they are not detected trajectories.
Scope: Both rely on destructive interference that blocks excitation of the intermediate state. STIRAP moves population between internal states; the velocity-selective trapping in the article involves momentum families and recoil. In this three-level Lab the atom sits at a fixed site, and the Lab neither measures a temperature nor demonstrates subrecoil cooling.

\begin{aligned}|D\rangle&\propto\Omega_S|g\rangle-\Omega_P|f\rangle\\\delta&=0\end{aligned}

Model reference: Vitanov et al. · STIRAP, § II

How helium atoms escaped the light and formed two narrow peaks

Start with the essentials

Focus question: Can the order of the pulses protect the transfer?
One-sentence intuition: The population curves are predictions from the model; the dots come only from measured outcomes.

Core mathematical model

Reference units

\tau=t/t_*,\quad \Omega,\Delta,\delta,\gamma,V\ \text{in}\ t_*^{-1}

Every rate is either an angular frequency or a population decay rate. No real atomic species is calibrated.

Open-system dynamics

\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 is evolved, so coherences are kept. Fourth-order Runge–Kutta steps are short enough to resolve the fastest scale in the Hamiltonian, and the integration is split exactly at pulse edges.

Three coupled levels

\frac H\hbar=\begin{pmatrix}0&\Omega_P/2&0\\\Omega_P/2&\Delta&\Omega_S/2\\0&\Omega_S/2&\delta\end{pmatrix}

The basis states are initial, intermediate and target, in that order. The intermediate state decays at total rate gamma, half into each lower state. No population leaks out of these three levels.

Move the pulse centers

\Omega_P=\Omega_0e^{-(\tau-d/2)^2/2},\quad\Omega_S=\Omega_0e^{-(\tau+d/2)^2/2}

A positive separation means the Stokes pulse arrives first. Each Gaussian amplitude is one reference time wide, and the simulation runs from minus five to plus five.

The instantaneous dark state

|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 contains none of the intermediate state. If the pulses are too weak, or there is detuning, the evolving state may fail to follow it. The overlap with the dark state is computed from the model; it is not a measured count.

Readout and uncertainty

\hat p=\frac{k}{N_{\rm read}},\quad N_{\rm unread}=N-N_{\rm read}

The interval shown is a 95% Wilson binomial interval for the fraction of target-state or double-excitation outcomes. It counts only shots that were read out, and whether a readout fails does not depend on the state. The interval holds point by point; it is not a joint band for the scan and does not cover numerical error in the model. Every shot starts from a freshly prepared ground state.

Common difficulties

A probability is not a trajectory

Typical misconceptionThe glowing atom shows the path the atom really follows.

Better mental modelThe atom marker only shows a fixed site, and the brightness of a beam shows the drive amplitude. Only the result tiles show sampled measurements.

Sources and limits

Typical misconceptionThis Lab reproduces a real, calibrated apparatus.

Better mental modelThe STIRAP model follows Vitanov et al., Reviews of Modern Physics 89, 015006 (2017), section II. The blockade model follows Gaëtan et al., Nature Physics 5, 115–118 (2009). These papers motivate the Hamiltonians, but our dimensionless rates and schematic geometry are not fitted to experimental values.

Run the experiment

01
Predict
Before collecting data, choose a contrasting case.
What to observe: Keep in mind which drive is applied and when the measurement is made.
02
Run the sequence
Drag pulse peaks or the separation handle, and scrub the time cursor.
What to observe: Playing replays the deterministic evolution. It does not create any measurement data.
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 cursor time captured when it started, and it keeps the preparation settings from that moment.