采采流水

An Essay Concerning Human Understanding

Notes of Quantum Optimal Control

2019-08-20


Notes of Quantum Optimal Control

The system Hamiltonian: $$ H = \Delta_p(t)|e\rangle\langle e| + \frac{1}{2}[\Omega_p(t)|e\rangle\langle 0 |+\Omega_s(t)|e\rangle\langle 1| + h.c.], $$

Pulse 1

$$ \Delta_p(t) = \Omega(t)\sin(\alpha),
\Omega_p(t) = \Omega(t)\cos(\alpha)\cos(\theta/2),
\Omega_s(t) = \Omega(t)\cos(\alpha)\sin(\theta/2)e^{-i\phi},
\Omega(t) = \Omega_0 \sin^2(\pi t/\tau).
\alpha=0,\theta=\pi/2,\phi=0
\tau=tmax=100 ns,\Omega_0\tau=4\pi $$

$\alpha=0,\theta=\pi/2,\phi=0$

$\tau=tmax=100 ns,\Omega_0\tau=4\pi$

$dt=0.5 ns$

Pulse 2

$$ \Delta_p(t) = 0,
\Omega_p(t) = \Omega(t)\cos(\theta(t)),
\Omega_s(t) = \Omega(t)\cos(\theta(t)),\