Bloch Sphere & Rabi Drive
A pure two-level state maps to a unit vector u on the Bloch sphere. The simulator integrates **du/dt = u × ω** with **ω = (0, Ω, Δ)**, matching the usual rotating-frame picture of a **σ_y-like** drive (nutation Ω) plus **σ_z** detuning (Δ). The canvas plots **(u_x, u_z)** with a reference circle; when **Δ = 0**, u stays in the **x–z** plane and you see clean Rabi flopping between |0⟩ (north pole) and |1⟩. The side panel lists all three components.
Who it's for: Students learning two-level systems, Rabi oscillations, and the Bloch picture.
Key terms
- Bloch Sphere
- Rabi Frequency
- Detuning
- Two-Level System
- Pauli Matrices
How it works
Two-level Bloch-vector dynamics with du/dt = u × ω and ω = (0, Ω, Δ): σ_y-like drive and σ_z detuning in a rotating-frame cartoon. The u_x–u_z plot shows Rabi flopping when Δ = 0.
Frequently asked questions
- Why is only an x–z circle shown instead of a full 3D sphere?
- The circle is a guide in the u_x–u_z plane. For **Δ = 0**, ω is along y and the trajectory lies entirely in that plane, so the dot follows a true great circle. For **Δ ≠ 0**, u_y is generally nonzero and the plotted point is a projection; the text readout still shows the full vector.
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