Charge Qubit Coherence — Double Quantum Dot

Qubit Parameters

Detuning ε 0.0 µeV

Tunnel coupling t_c 12.0 µeV

Charge noise σ_ε 8.0 µeV

Live Readouts

Splitting Ω/h

5.83 GHz

P(right dot)

0.0%

Dephasing time T2*

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How it works

An electron confined in a lateral double quantum dot has two low-energy charge states: localized in the left dot |L⟩ or the right dot |R⟩. In that basis the Hamiltonian is the textbook two-level form

H = ( ε/2    t_c  )
    ( t_c   -ε/2 )

Energy splitting:  Ω = √(ε² + 4t_c²)
Occupation:  P_R(t) = (4t_c² / Ω²) · sin²(Ω t / 2ħ)

ε is the electrostatic detuning between the dots (gate-voltage controlled) and t_c is the interdot tunnel coupling. Starting in |L⟩, the electron performs coherent charge oscillations at frequency Ω/h — this is the exact system realised by Hayashi et al. (PRL 2003), the first demonstration of coherent charge-qubit dynamics.

Charge noise and the sweet spot. Real devices sit in a fluctuating electrostatic environment (1/f charge noise), which this simulator models as quasi-static Gaussian jitter of ε with standard deviation σ_ε. Averaging the oscillation over many noise realizations gives an ensemble-dephased signal, with a coherence time set by how sensitive Ω is to ε:

T2* ≈ ħ / (σ_ε · |∂Ω/∂ε|),   ∂Ω/∂ε = ε / Ω

At ε = 0 the derivative vanishes — Ω depends only quadratically on ε there — so the qubit is first-order insensitive to charge noise. This "sweet spot" is why real charge- and transmon-qubit experiments are almost always operated at or near ε = 0.

ε slider — bias the double well; moves you off the sweet spot.
t_c slider — interdot tunnel coupling; sets the minimum splitting 2t_c and the barrier height in the well.
σ_ε slider — charge-noise strength; watch the oscillation visibly decay faster away from ε = 0.

Electron probability weight Double-well energy landscape

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Charge Qubit Coherence in a Double Quantum Dot