def prop_unitarity_tester(n_pulses, pi_half_time):
# create initial state ket [1,0,0,...,0] with length 2*n_pulses
init_state = [1]
for i in range(1, 2 * n_pulses):
init_state.append(0)
atoms = create_random_thermal_atoms(100, state_kets=init_state)
intensity_profile = ais.IntensityProfile(1, 1)
wf = ais.gen_wavefront(10)
wave_vectors = ais.Wavevectors()
for n_pulse in range(n_pulses):
prop = ais.SpatialSuperpositionTransitionPropagator(
1,
intensity_profile,
n_pulses,
n_pulse + 1,
wave_vectors,
wf=wf)
matrices = prop._prop_matrix(atoms)
for matrix in matrices:
multiplied = np.matmul(matrix, np.conjugate(matrix.T))
np.testing.assert_almost_equal(multiplied,
np.eye(2 * n_pulses))
def test_intensity_profile():
r_beam = 1
pos1 = np.array([[0, 0, 0]])
pos2 = np.array([[0, 1, 0]])
intensity_profile = ais.IntensityProfile(r_beam, 1)
rabi1 = intensity_profile.get_rabi_freq(pos1)
rabi2 = intensity_profile.get_rabi_freq(pos2)
ratio = rabi2 / rabi1
# test that Rabi frequency has dropped to 1/e**2 of center value
np.testing.assert_almost_equal(ratio[0], 1 / np.e**2)
def prop_time_reversal_tester(n_pulses, pi_half_time):
# create initial state ket [1,0,0,...,0] with length 2*n_pulses
init_state = [1]
for i in range(1, 2 * n_pulses):
init_state.append(0)
atoms = create_random_thermal_atoms(100, state_kets=init_state)
atoms0 = atoms
# create Raman beam
r_beam = 29.5e-3 / 2 # 1/e^2 beam radius in m
wave_vectors = ais.Wavevectors(k1=8.052945514e6, k2=-8.052802263e6)
center_rabi_freq = 2 * np.pi / 4 / pi_half_time
intensity_profile = ais.IntensityProfile(r_beam, center_rabi_freq)
for n_pulse in range(0, n_pulses):
propagator = ais.SpatialSuperpositionTransitionPropagator(
pi_half_time, intensity_profile, n_pulses, n_pulse + 1,
wave_vectors)
atoms = propagator.propagate(atoms)
# check if trace is one for atomic ensembles density matrix
np.testing.assert_array_almost_equal(
np.trace(atoms.density_matrix), 1)
# check if rho^2 = rho for pure states
np.testing.assert_array_almost_equal(
np.matmul(atoms.density_matrices, atoms.density_matrices),
atoms.density_matrices)
# check for time-reversibility (unitarity)
for n_pulse in range(0, n_pulses):
# change counting direction to descending, e.g. 3, 2, ...
n_pulse = n_pulses - n_pulse
propagator = ais.SpatialSuperpositionTransitionPropagator(
-pi_half_time, intensity_profile, n_pulses, n_pulse,
wave_vectors)
atoms = propagator.propagate(atoms)
# check if trace is one for atomic ensembles density matrix
np.testing.assert_array_almost_equal(
np.trace(atoms.density_matrix), 1)
# check if rho^2 = rho for pure states
np.testing.assert_array_almost_equal(
np.matmul(atoms.density_matrices, atoms.density_matrices),
atoms.density_matrices)
# check if final state is initial state
np.testing.assert_array_almost_equal(atoms0.density_matrices,
atoms.density_matrices)
def test_two_level_transition_propagator():
pos_params = {
'mean_x': 1.0,
'std_x': 1.0,
'mean_y': 1.0,
'std_y': 1.0,
'mean_z': 1.0,
'std_z': 1.0,
}
vel_params = {
'mean_vx': 1.0,
'std_vx': ais.convert.vel_from_temp(3.0e-6),
'mean_vy': 1.0,
'std_vy': ais.convert.vel_from_temp(3.0e-6),
'mean_vz': 1.0,
'std_vz': ais.convert.vel_from_temp(0.2e-6),
}
atoms = ais.create_random_ensemble_from_gaussian_distribution(pos_params,
vel_params,
100,
seed=0)
intensity_profile = ais.IntensityProfile(1, 1)
wf = ais.gen_wavefront(10)
wave_vectors = ais.Wavevectors()
prop1 = ais.TwoLevelTransitionPropagator(
time_delta=1, intensity_profile=intensity_profile)
prop2 = ais.TwoLevelTransitionPropagator(
time_delta=1,
intensity_profile=intensity_profile,
wf=wf,
wave_vectors=wave_vectors,
phase_scan=np.pi)
matrices = prop1._prop_matrix(atoms)
for prop in [prop1, prop2]:
matrices = prop._prop_matrix(atoms)
for matrix in matrices:
np.testing.assert_almost_equal(
np.matmul(matrix, np.conjugate(matrix.T)), np.eye(2))
def test_two_level_transition_propagator_unitarity():
atoms = create_random_thermal_atoms(100)
intensity_profile = ais.IntensityProfile(1, 1)
wf = ais.gen_wavefront(10)
wave_vectors = ais.Wavevectors()
prop1 = ais.TwoLevelTransitionPropagator(
time_delta=1, intensity_profile=intensity_profile)
prop2 = ais.TwoLevelTransitionPropagator(
time_delta=1,
intensity_profile=intensity_profile,
wf=wf,
wave_vectors=wave_vectors,
phase_scan=np.pi)
matrices = prop1._prop_matrix(atoms)
for prop in [prop1, prop2]:
matrices = prop._prop_matrix(atoms)
for matrix in matrices:
np.testing.assert_almost_equal(
np.matmul(matrix, np.conjugate(matrix.T)), np.eye(2))