Silicon Pulse — Interactive Spin Explorer

The Silicon Crystal

Everything starts with the world's most perfect crystal.

Silicon-28 (²⁸Si) is isotopically purified to remove magnetic noise. Unlike natural silicon — which contains ~4.7% ²⁹Si with nuclear spin — pure ²⁸Si creates a "magnetically quiet" environment where quantum states survive far longer.

²⁹Si atoms have nuclear spin I=½, creating random magnetic fields that dephase electron spins. In enriched ²⁸Si (I=0), coherence times T₂ exceed 28 milliseconds — long enough for thousands of quantum operations.

5.43 Å lattice constant

99.99% ²⁸Si purity

Silicon crystallizes in the diamond cubic structure — two interlocking FCC lattices. Each atom is tetrahedrally bonded to 4 neighbors. This regular geometry creates precise, repeatable locations for quantum dots.

🖱 Rotate and zoom the crystal to explore. Use the toolbar below to add/remove qubits. When ready:

Building the Trap

Metal gates create electric fields that confine a single electron.

On top of the silicon crystal, nano-scale metal electrodes (gates) apply voltages that shape the electrostatic potential below. By tuning three gates, you sculpt a tiny quantum dot — a potential well small enough to hold exactly one electron.

Positive voltage on the center gate creates a potential well (electron trap). The left and right gates act as barriers, confining the electron laterally. The resulting potential is:

U(x) = −V_C · e^−x²/σ² + V_L(x+d)² + V_R(x−d)²

Gate Voltages

V_Left 0.0 mV

V_Center 0.0 mV

V_Right 0.0 mV

Potential Energy U(x)

⚡ Increase V_Center to form a deep potential well.

Capturing an Electron

When the potential well is deep enough, a single electron is confined.

The trapped electron's wavefunction |ψ|² — its probability density — is localized inside the quantum dot. This is your qubit. Its spin (↑ or ↓) encodes quantum information as |0⟩ and |1⟩.

Electron spin in silicon has exceptionally long coherence times because ²⁸Si has no nuclear magnetic moment. The two spin states |↑⟩ and |↓⟩ are split by the Zeeman energy ΔE = gμ_BB, where g ≈ 2.

Electron Unbound

Environment

Temperature 20 mK

At room temperature (~300 K), thermal energy k_BT ≈ 26 meV dwarfs the qubit energy splitting ΔE = gμ_BB ≈ 0.116 meV at 1T. Cooling to ~20 mK ensures k_BT ≈ 0.0017 meV, so thermal fluctuations cannot flip the spin.

The ratio ΔE/k_BT determines coherence: at 20 mK it's ~67x, at 1K it's ~1.3x.

Physics Parameters

T₁ (relaxation) 6.0 s

T₂ (Hahn echo) 28.0 ms

T₂* (Ramsey) 120 μs

ω_L 28.02 GHz

ΔE (Zeeman) 0.116 meV

k_BT 0.002 meV

P_thermal(|1⟩) 0.0000%

Coherence T₂ = 28.0 ms

🎯 Fine-tune the gates until the electron is trapped. Raise temperature to see decoherence.

Spin Control

Microwave pulses rotate the spin — this is quantum computing.

The Hamiltonian H = −½γB·σ governs the electron's spin precession. A static magnetic field B_z splits the energy levels. A resonant microwave pulse at the Larmor frequency drives Rabi oscillations between |0⟩ and |1⟩.

When a microwave pulse at frequency ω_L = γB is applied, the spin coherently oscillates between |0⟩ and |1⟩. A π-pulse flips the spin completely; a π/2-pulse creates an equal superposition — the starting point for quantum algorithms.

|0⟩

100%

|1⟩

θ 0π

φ 0π

P(|1⟩) 0.0000

B_z 1.00 T

0 π/2 π

B_z field 1.00 T

Ω_Rabi 0.0 MHz

ω_Larmor 28.02 GHz

Quantum Computing

|0⟩ ──

α (|0⟩): 1.0000 + 0.0000i

β (|1⟩): 0.0000 + 0.0000i

No qubit is perfectly isolated. Over time, interactions with the environment cause decoherence — the quantum state "leaks" into a classical mixture. T₁ governs energy relaxation (spin flips), while T₂ governs dephasing (loss of phase coherence). Always T₂ ≤ 2T₁.

Audio feedback

²⁸Si — Isotopically Pure

60 fps

Diamond Cubic · a = 5.43 Å

T₂ = 28.0 ms

Scroll to zoom · Drag to rotate