Driven two-state quantum dynamics University Quantum Mechanics II · Time-dependent perturbation theory
Resonance Switch
Time a coherent drive and tune its detuning to route a two-state ensemble into the excited state.
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Challenge 1 of 3
Resonant inversion
A perfectly resonant coherent drive starts with every system in its lower state.
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Stop the pulse with 95–100% expected excited-state population.
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Use the exact two-state Rabi probability, distinguish detuning's probability ceiling from timing error, and locate a later population peak.
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The physics behind the game
Use the exact two-state Rabi probability, distinguish detuning's probability ceiling from timing error, and locate a later population peak.
Pₑ(t) = Ω₀²/(Ω₀² + Δ²) · sin²[½√(Ω₀² + Δ²)t]
Model assumptions. An initially lower-state, isolated two-level system with a coherent rotating drive, or a linearly driven system within the rotating-wave approximation. Ω₀ and Δ are angular frequencies in rad/μs, and time is in μs. Probabilities describe an ensemble; relaxation, decoherence and sampling noise are omitted.