Quantum Otto Engine — Qubit Heat Engine Simulator

Quantum Otto Engine

1 · Hot isochore

Hot bath T_h 3.0

Cold bath T_c 1.0

Cold-side gap ω₁ 1.0

Hot-side gap ω₂ 2.2

Bath coupling γ 2.0

Cycle speed 1.0×

Efficiency η

–

Ideal Otto η

–

Carnot bound η_C

–

Friction loss/cyc

–

Q_hot in

–

Net work / cycle

–

Toggle coherent driving to see quantum friction appear (population coherence leaks out during the fast adiabatic strokes) and watch efficiency drop below the ideal Otto line — then recover it.

How it works

A single qubit with level gap ω(t) runs a 4-stroke Otto cycle: (1) hot isochore — ω held at the larger gap ω₂, the qubit thermalizes toward the Gibbs excited-state population p_eq(ω₂,T_h) = 1/(1+e^ω₂/T_h); (2) adiabatic expansion — ω swept ω₂→ω₁ decoupled from any bath; (3) cold isochore — ω held at the smaller gap ω₁, relaxation toward p_eq(ω₁,T_c); (4) adiabatic compression — ω swept back ω₁→ω₂. (The gap ω plays the role of inverse volume, as for a harmonic-oscillator working substance: compressing raises ω.)

dE = p·dω  (work, adiabatic strokes)
   + ω·dp  (heat, isochoric strokes)
η = W_net / Q_hot,  η_Otto = 1 − ω₁/ω₂ ≤ η_Carnot = 1 − T_c/T_h

Coherent driving (shortcut-to-adiabaticity) — the level population is dragged exactly along the instantaneous eigenstate, so the adiabatic strokes are friction-free and efficiency approaches the ideal Otto value.
Classical / incoherent driving — a fast sweep can't stay adiabatic; it leaks population toward a 50/50 mix (quantum friction), dumping extra waste heat and pulling efficiency below the ideal Otto line at the very same bath temperatures.
Faster cycle speed increases the sweep rate, so friction (when coherence is off) grows — a genuine power/efficiency trade-off unique to the quantum engine.

Real-world relevance: single-ion, superconducting-qubit and NV-center quantum heat engines are built and measured in labs today; shortcut-to-adiabaticity control is the actual technique used to suppress quantum friction in those experiments.

Bloch vector Hot bath active Cold bath active Adiabatic (decoupled)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.