3D Quantum Otto Cycle Engine

3D Quantum Otto Engine

Hot spacing ω_hot 3.0

Cold spacing ω_cold 1.0

Hot bath T_hot 5.0

Cold bath T_cold 1.0

Cycle speed 1.0×

⟨n⟩ cold pt A

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⟨n⟩ hot pt C

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Q_hot in

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Q_cold out

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Net work / cycle

–

Power

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η (this engine)

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η_Carnot bound

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How it works

The tower's rings mark the discrete levels E_n = ω(n+½) of the working substance. Two unitary strokes slide the whole ring stack up/down the rod (spacing ω changes, no quanta are created or destroyed — pure work). Two thermalizing strokes fire glowing quanta from the cold plate (left) or hot plate (right) into the tower at fixed spacing, redistributing the orbiting population toward that bath's Gibbs distribution — pure heat, no work.

⟨n⟩(ω,T) = 1 / (exp(ω/T) − 1)
Q_hot  = ω_hot  · (⟨n⟩_C − ⟨n⟩_A)
Q_cold = ω_cold · (⟨n⟩_C − ⟨n⟩_A)
η = 1 − ω_cold/ω_hot  ≤  η_Carnot = 1 − T_cold/T_hot

ω_hot / ω_cold — how far apart the rings are pushed on each unitary stroke; only their ratio sets η.
T_hot / T_cold — reservoir temperatures feeding the particle bursts; drag them until ω_cold/ω_hot dips below T_cold/T_hot and the tower flips into refrigerator mode (bursts reverse direction, work stat turns negative).
Orbit the tower with the mouse/touch to see the ring spacing and quanta count change together — spacing narrows near the hub and widens outward exactly as ω(n+½) predicts.

Real-world relevance: trapped-ion and superconducting-circuit quantum engines implement this same stroke sequence by literally ramping a trap or qubit frequency (playing the role of ω here) while switching reservoir coupling on and off.

Stroke 1/4 — compressing

Occupied level (ring) Cold-bath quanta Hot-bath quanta

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