Tutorial 1: Rabi Oscillations

In this tutorial, you will learn how to manipulate the state of a single neutral atom. This is the “Hello World” of quantum computing, demonstrating coherent control over a qubit.

1. The Physics: What are Rabi Oscillations?

By shining a constant laser light on an atom at a specific amplitude Ω, the qubit’s state oscillates periodically between its ground state (0) and its excited Rydberg state (r). This oscillation happens at frequency Ω/2π, Ω is therefore named the Rabi frequency.

• At 𝑡 = 0: the atom is in the ground state (0). If you measure it 1000 times, you will always get 0.

• At 𝑡 = π/Ω: the atom reaches its maximum probability of being in the Rydberg state. If you measure it 1000 times, you will always get 1

• At 𝑡 = π/(2Ω): the atom stops mid-oscillation, forming a balanced superposition of the two states. If you measure the atom 1000 times, you should get 500 times 0 and 500 times 1.

  Let’s modify the state of one atom to have it in superposition of the ground and rydberg state !

2. Step-by-Step Implementation

1. Set up the Register

   After creating a new experiment, go to the Register tab. Create a column and a row with a single atom, then click on generate pattern. This atom will be our qubit.

   
   

2. Channel Selection

   By default, there are already 3 channels created : RAMAN CHANNEL | LOCAL, RYDBERG CHANNEL | LOCAL and RYDBERG CHANNEL | GLOBAL, but you can create, delete or update the channels if you need to on the right panel. In the Channels timeline at the bottom, identify the RYDBERG CHANNEL | GLOBAL. This channel allows us to excite atoms to their Rydberg state using a laser that covers the entire register.

   
   

3. Create the Pulse

   Add a pulse to the timeline by clicking the (+) button on the Rydberg Global row.

   
   

4. Configure the Pulse Settings

   When you create a pulse, the Pulse Tab opens on the right. For this tutorial, we will use the default settings, that provide the pulses with the highest fidelity :

   • Amplitude Waveform: Blackman is selected by default. This bell-shaped curve helps minimize unwanted transitions.
   • Max Value: Set to 4 π rad/µs to ensure strong driving.
   • Detuning Waveform: Set to Constant with value 0 π rad/µs (resonance).
   • Duration: Set to 250 ns.

   Why detuning = 0?

   The detuning must be zero (the pulse is said to be “on-resonance” or ‘resonant’). If you have a non-zero detuning, you will never reach 100% Rydberg state probability. What matters for the probability to measure the atom in the Rydberg state is the area under the curve of the amplitude: the probability is sin²(∫₀^duration Ω(t) dt/1000). With the current settings (Blackman waveform with max 4π rad/µs over 250ns), the area is approximately 0.4π, which gives a high probability of being in the Rydberg state.

   Optional: Perfect Superposition

   If you want to create a perfect superposition (50% ground, 50% Rydberg), you can set the Area field to 0.25 π with a longer duration like 1000 ns. This will give you sin²(0.25π) = 0.5, meaning equal probability for both states.

   

   Why use Blackman?

   Unlike a simple square pulse, a Blackman pulse starts and ends at zero amplitude. This waveform is used to guarantee that the execution of a sequence made with Pulser Studio is close enough to reality when run on the QPU, because the modulation effect is not taken into account on Pulser Studio. With the Blackman waveform, the duration of the waveform post-modulation is close to the asked one.

   
   

5. Visualize and Run

   Now that you have designed the pulse, you should see the purple bell-shaped pulse and the white detuning ramp in your timeline.

   You should be on the Local Emulation tab on the right panel. Since there is only one atom in the register the emulation will be instantaneous, you can now press the Play button to run the simulation.

   The histogram and state evolution will show you the probability of the atom being in the excited state. You have just performed a fundamental quantum operation: you have modified the state of your atom to be in a superposition of the ground and rydberg state !

   

Interpreting Results

Quantum computing is about probabilities: the final amplitude of the rydberg state is sin(∫₀^duration Ω(t) dt/1000) up to a given phase, and the final amplitude of the ground state is cos(∫₀^duration Ω(t) dt/1000).

• The Quantum State panel displays the complex numbers (amplitudes and phases) that describe your qubit’s superposition.
• The Histogram shows the probability of measurement in the ground (0) and rydberg (1) state. That’s the square of the modulus of the complex amplitude of the final state (e.g., cos²(0.4π) = 0.095 ground vs sin²(0.4π) = 0.905 Rydberg).