Homodyne detection is an extension of the photocurrent method where the output is mixed with a strong external source allowing to get information about the phase of the system. With this method, the resulting detection rate depends is
With \(\gamma\), the strength of the external beam and \(C\) the collapse operator. When the beam is very strong \((\gamma >> C^\dag C)\), the rate becomes a constant term plus a term proportional to the quadrature of the system.
In closed systems, the resulting stochastic differential equation is
Here \(\delta \omega\) is a Wiener increment.
In QuTiP, this is available with the function
In : times = np.linspace(0.0, 10.0, 201) In : psi0 = tensor(fock(2, 0), fock(10, 5)) In : a = tensor(qeye(2), destroy(10)) In : sm = tensor(destroy(2), qeye(10)) In : H = 2 * np.pi * a.dag() * a + 2 * np.pi * sm.dag() * sm + 2 * np.pi * 0.25 * (sm * a.dag() + sm.dag() * a) In : data = ssesolve(H, psi0, times, sc_ops=[np.sqrt(0.1) * a], e_ops=[a.dag() * a, sm.dag() * sm], method="homodyne") Total run time: 0.03s In : figure()