Quantum Otto Cycle: Two-Level System
|g⟩,|e⟩ qubit · isentropic strokes · thermal contact · η vs speed
W = — | Q_h = — | η = — | η_Otto = —
Quantum Otto Cycle: 4 strokes operating on a two-level system with gap ħω. (1) Isentropic compression: ω_c→ω_h with fixed populations p↑,p↓. (2) Hot isochoric: system thermalizes with T_h at ω_h. (3) Isentropic expansion: ω_h→ω_c. (4) Cold isochoric: thermalizes with T_c at ω_c.
Thermodynamics: Q_h = ħω_h·(p_h−p_h^eq), Q_c = ħω_c·(p_c^eq−p_c), W = Q_h+Q_c. Quasistatic Otto efficiency η_Otto = 1 − ω_c/ω_h (same form as classical, but ω replaces temperature!)
Finite-time effects: Short stroke time τ causes incomplete thermalization → quantum friction → η < η_Otto. The population approaches equilibrium exponentially: p(t) = p_eq + (p_0−p_eq)e^{−t/τ_relax}.
Right panel: η vs τ (stroke time) showing the tradeoff: faster = lower efficiency but higher power P = W/τ.