Quantum Battery: Charging Speed Limit

Charging Field

Rabi drive strength Ω 2.0 rad/µs

Inhomogeneous detuning σΔ 0.3

Decoherence rate γ 0.20 /µs

Battery State

Idle — fully discharged

Stored energy

Charging power

0.00

Elapsed time

0.00 µs

Speed-limit time τ_QSL

0.00 µs

■ quantum (Rabi)■ classical (RC)

How it works

Each of the 36 cells is a two-level quantum system (energy gap ħω₀ ≡ 1) driven by a resonant charging field of Rabi frequency Ω. With per-cell detuning Δᵢ (drawn from a spread σΔ, modelling fabrication disorder) and decoherence rate γ, the excited-state population follows a damped Rabi oscillation:

Ω_eff,i = √(Ω² + Δᵢ²)
P_e,i(t) = (Ω² / Ω_eff,i²) · sin²(Ω_eff,i · t / 2) · e^(−γt)
E(t) = ⟨P_e⟩ · E_max   (average over all cells)

The quantum speed limit (a Margolus–Levitin-type bound) sets the fastest possible time to fully charge a two-level battery for a given drive energy scale: τ_QSL = π / (2·Ω_eff). No unitary charging protocol can beat it — detuning spread and decoherence only push the real charging time further above this floor, never below it.

When the drive is switched off, each cell's population relaxes back toward the ground state — spontaneous emission / dephasing acting as self-discharge: P_e,i(t) = P₀,i · e^(−γ_d·t). The dashed curve compares this whole process to a conventional battery charged through a resistor, whose energy follows the classical exponential E(t) = E_max·(1 − e^(−t/τ_RC)) with no oscillation and no hard speed limit — it simply gets arbitrarily slow as you demand more instantaneous power.

Ω — drive strength; higher Ω charges faster and pushes τ_QSL down.
σΔ — disorder between cells; large spread desynchronises the oscillation and caps the peak stored energy (Dicke-style dephasing).
γ — decoherence/relaxation rate; damps the Rabi oscillation while charging and sets how fast the battery self-discharges once the field is off.

Charged cell (high P_e) Ground state cell

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