Same double-dot charge qubit as the 3D version, but integrated directly: the electron's state is a genuine complex two-component vector c = (cL, cR) in the |L〉, |R〉 basis, evolved every substep by the time-dependent Schrodinger equation with the textbook charge-qubit Hamiltonian
H(t) = ( eps(t)/2 t_c )
( t_c -eps(t)/2 )
i hbar dc/dt = H(t) c
This sim does not use the closed-form sin² solution — it numerically integrates that ODE with 4th-order Runge–Kutta at a fixed sub-nanosecond timestep, renormalizing the state each step, and reads P(left) = |cL|² straight off the propagated vector. With no noise this reproduces the analytic Rabi formula PR(t) = (4tc²/Ω²)·sin²(Ωt/2ħ), Ω = √(ε²+4tc²), to numerical precision — a genuine consistency check on the integrator.
Real charge noise, not an analytic shortcut. Sixteen independent random-telegraph fluctuators per trajectory kick eps(t) up or down by a fixed amount at random Poisson switching times (rates spread across a decade, the standard McWhorter picture of 1/f noise as a sum of two-level charge traps). Their sum is fed straight into H(t) at every RK4 substep, so dephasing emerges from the actual stochastic trajectory, not from averaging a formula. Twelve such trajectories run in parallel and are averaged live to give the smooth-but-decaying P(left, t) curve you see plotted — exactly what an ensemble of real experimental shots would produce.
T2* ~ hbar / (sigma_eps * |dOmega/deps|), dOmega/deps = eps / Omega
At ε = 0 that derivative vanishes: Ω depends only quadratically on ε there, so the qubit is first-order immune to charge noise. Watch the oscillation trace keep its amplitude far longer at the sweet spot than away from it — the dashed curve overlays the theoretical 1/e envelope for comparison with what the integrator actually produced.
- ε slider — bias the double well; moves you off the sweet spot.
- tc slider — interdot tunnel coupling; sets the minimum splitting 2tc.
- σε slider — charge-noise strength fed to the fluctuator ensemble; watch the simulated decay speed up away from ε = 0.