Quantum Otto Engine | mysimulator.uk

Cycle

Adiabatic compression

Level Spacing (energy units)

Cold gap Δ_c 1.00

Hot gap Δ_h 2.60

Reservoirs

Hot bath T_h 1.80

Cold bath T_c 0.60

Cycle speed 1.00×

Last Completed Cycle

Efficiency η

—

Ideal 1−Δc/Δh

61.5%

Net work W

—

Heat absorbed Q_h

—

Excited pop. p_e

10.7%

Cycles completed

How it works

The engine is a single two-level system (a qubit) with ground state energy 0 and excited state energy Δ(t), coupled alternately to a hot bath (T_h) and a cold bath (T_c), run through four strokes — the quantum analogue of the classical Otto cycle:

1) Adiabatic compression   Δc → Δh   (gap swept, populations frozen — no heat)
2) Hot isochore             Δh fixed  (coupled to T_h, populations relax toward
                                        Gibbs equilibrium p_e = 1/(1+e^(Δh/T_h)))
3) Adiabatic expansion      Δh → Δc   (gap swept, populations frozen — no heat)
4) Cold isochore             Δc fixed (coupled to T_c, relaxes toward
                                        p_e = 1/(1+e^(Δc/T_c)))

Because the level spacing does no work while it is fixed, and no heat is exchanged while populations are frozen, energy bookkeeping is exact stroke by stroke: heat during an isochore is Q = Δ·Δp_e, and work during an adiabatic stroke is W = p_e·ΔΔ. The net work extracted per cycle is W = (Δh − Δc)(p₂ − p₁), where p₁, p₂ are the excited populations just before the hot and cold isochores.

When the isochores are long enough to fully thermalize, efficiency reduces to the compact quantum-Otto formula η = 1 − Δc/Δh — the exact analogue of 1 − 1/(compression ratio) in a classical Otto engine, and it is capped below the Carnot limit 1 − T_c/T_h. Raise the cycle speed and the isochores no longer have time to fully relax (finite-time thermodynamics): the actual per-cycle efficiency and work drop visibly below the ideal value shown above, exactly as they do in real solid-state and trapped-ion quantum engines.

Δc / Δh sliders — the qubit's energy gap at the cold/hot ends of the cycle. Δh must exceed Δc for the engine to do net positive work.
T_h / T_c sliders — bath temperatures; a working engine additionally needs Δc/Δh < T_c/T_h, otherwise the device runs as a heat pump instead.
Cycle speed — shortens the isochore strokes relative to the fixed thermal relaxation time, demonstrating the quantum finite-time-thermodynamics trade-off between speed and efficiency.

Excited-state population Ground-state population

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