def test_nonzero_unitary_dynamics_mixed_spin_operator(self):
rhox = la.CartesianSpinOperator((0.5, 0.5, 0., 0.))
rhoy = la.CartesianSpinOperator((0.5, 0., 0.5, 0.))
rhoxy = la.CartesianSpinOperator((0.5, 0.5, 0.5, 0.))
rhoxdot_expected = la.CartesianSpinOperator((0., 0., 1., 0.))
rhoydot_expected = la.CartesianSpinOperator((0., -1., 0., 0.))
rhoxydot_expected = la.CartesianSpinOperator((0., -1., 1., 0.))
ham = la.SphericalSpinOperator((0, 1, 0, 0))
rhoxdot_calc = hbar * unitary_derivative(rhox, ham)
rhoydot_calc = hbar * unitary_derivative(rhoy, ham)
rhoxydot_calc = hbar * unitary_derivative(rhoxy, ham)
self.assertAlmostEqual(rhoxdot_calc, rhoxdot_expected)
self.assertAlmostEqual(rhoydot_calc, rhoydot_expected)
self.assertAlmostEqual(rhoxydot_calc, rhoxydot_expected)
def test_nonzero_unitary_dynamics_cartesian_spin_operator(self):
rhox = la.CartesianSpinOperator((0.5, 0.5, 0., 0.))
rhoy = la.CartesianSpinOperator((0.5, 0., 0.5, 0.))
rhoxy = la.CartesianSpinOperator((0.5, 0.5, 0.5, 0.))
rhoxdot_expected = 1 / hbar * la.CartesianSpinOperator((0., 0., 1., 0.))
rhoydot_expected = 1 / hbar * la.CartesianSpinOperator((0., -1., 0., 0.))
rhoxydot_expected = 1 / hbar * la.CartesianSpinOperator((0., -1., 1., 0.))
ham = la.CartesianSpinOperator((0, 0, 0, 1))
rhoxdot_calc = unitary_derivative(rhox, ham)
rhoydot_calc = unitary_derivative(rhoy, ham)
rhoxydot_calc = unitary_derivative(rhoxy, ham)
self.assertEqual(rhoxdot_calc, rhoxdot_expected)
self.assertEqual(rhoydot_calc, rhoydot_expected)
self.assertEqual(rhoxydot_calc, rhoxydot_expected)
def test_nonzero_unitary_dynamics_spherical_spin_operator(self):
rhox = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, 0.))
rhoy = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, np.pi/2))
rhoxy = la.SphericalSpinOperator((0.5, 0.5, np.pi/2, np.pi/4))
rhoxdot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, np.pi/2))
rhoydot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, np.pi))
rhoxydot_expected = 1 / hbar * la.SphericalSpinOperator((0., 1., np.pi/2, 3*np.pi/4))
ham = la.SphericalSpinOperator((0, 1, 0, 0))
rhoxdot_calc = unitary_derivative(rhox, ham)
rhoydot_calc = unitary_derivative(rhoy, ham)
rhoxydot_calc = unitary_derivative(rhoxy, ham)
self.assertEqual(rhoxdot_calc, rhoxdot_expected)
self.assertEqual(rhoydot_calc, rhoydot_expected)
self.assertEqual(rhoxydot_calc, rhoxydot_expected)
def test_bloch_derivative_all(self):
ham = la.CartesianSpinOperator((0, 0, 0, 1))
rho = la.CartesianSpinOperator((0.5, 0, 0.5, 0))
bd_c = bloch_derivative(rho, ham, gdiss=0., gdeph=1.)
ud = unitary_derivative(rho, ham)
nud = -1 * la.CartesianSpinOperator((0, 0, 0.5, 0))
bd_e = ud + nud
self.assertEqual(bd_c, bd_e)
def bloch_derivative(rho, ham, gdiss, gdeph, rpump=0.):
ud = unitary_derivative(rho, ham)
i, x, y, z = rho.convert_cartesian()
xdot = -(gdeph + 0.5 * gdiss + 0.5 * rpump) * x
ydot = -(gdeph + 0.5 * gdiss + 0.5 * rpump) * y
zdot = rpump * (1 - z) - gdiss * (1 + z)
bd = la.CartesianSpinOperator((0, xdot, ydot, zdot))
return ud + bd
def test_steady_state_unitary_dynamics_numpy_array(self):
rho0 = np.array([[0.5, 0.], [0., 0.5]])
rhodot_expected = np.array([[0., 0.], [0., 0.]])
ham = np.array([[1., 0.], [0., -1.]])
self.assertTrue(np.array_equal(unitary_derivative(rho0, ham), rhodot_expected))
def test_steady_state_unitary_dynamics_mixed_spin_operator(self):
rho0 = la.SphericalSpinOperator((1 / 2, 0, 0, 0))
rhodot_expected = la.SphericalSpinOperator((0, 0, 0, 0))
ham = la.CartesianSpinOperator((0, 0, 0, 1))
self.assertEqual(unitary_derivative(rho0, ham), rhodot_expected)
def test_bloch_derivative_unitary_consistency(self):
ham = la.CartesianSpinOperator((0, 0, 0, 1))
rho = la.CartesianSpinOperator((0.5, 0, 0.5, 0))
ud = unitary_derivative(rho, ham)
bd = bloch_derivative(rho, ham, gdiss=0, gdeph=0)
self.assertEqual(ud, bd)