Numeric interferometer usage
What you’ll learn:
How to set up a numeric interferometer using
NumericBraggInterferometerHow to plot interferometer arm trajectories from the numeric tree
How to define beamsplitter and free-evolution functions using
propagateHow to simulate an atom cloud and compute interferometer output ellipses
How to sweep detuning and compute output port populations
[1]:
import numpy as np
from mwave.numeric import NumericBraggInterferometer
from mwave.integrate import make_kvec, make_phi, propagate, omega_fnc_gaussian, multi_omega_fnc, phase_fnc_constant, score_backends
from mwave.simulation_utils import cloud_init
import numpy as np
from numba import jit, float64
# Set interferometer parameters
omega_r_conversion = 2066*2*np.pi
nbragg = 4
T = 4.5e-3*omega_r_conversion
Tp = 8e-3*omega_r_conversion
# Initialize kvec and tree
ifr = NumericBraggInterferometer(-2*nbragg, 4*nbragg, distance=0) # Should pass in wavefunction initialization functions
ifr.split(nbragg) # Should pass in the relevant function here as well! Function will inspect input function arguments to ensure correct number and naming
ifr.propagate(T)
ifr.split(nbragg)
ifr.propagate(Tp)
ifr.split([3*nbragg, -nbragg])
ifr.propagate(T)
ifr.split([3*nbragg, -nbragg])
Plot the trajectories
[2]:
from matplotlib import pyplot as plt
nodes = ifr.get_nodes()
nA, nB, nC, nD = nodes[4*nbragg], nodes[2*nbragg], nodes[0.0*nbragg], nodes[-2*nbragg]
Ts = [0, 0, T, T, T + Tp, T + Tp, T + Tp + T, T + Tp + T]
plt.figure()
for nn in [nA, nB, nC, nD]:
for p in nn:
for node in nn[p]:
t, x = node.get_trajectory()
plt.plot(t, x)
plt.show()
Create function for simulating the full interferometer
[3]:
from mwave.integrate import propagate, omega_fnc_gaussian, multi_omega_fnc, phase_fnc_constant
from mwave.precompute import load_precomputed_gbragg
from mwave.simulation_utils import cloud_init
Omega0 = 19.5
w0 = 6.2e-3
sigma = 0.259658916
tau_factor = 5
def deltalookup(vz):
return 4*nbragg + 4*(vz/0.0035) # The modification to delta is 4 times the velocity defined in units of recoil velocities
def omegalookup(x, y, z):
return Omega0*np.exp(-2*(x**2 + y**2)/(w0**2))
def make_gbragg(sigma, use_precompute=True, tau_factor=5, tol=1e-8):
if use_precompute:
return load_precomputed_gbragg('../precomputation/gbragg_single_sig0.260.h5',
'../precomputation/gbragg_multi_sig0.260.h5',
table_sigma=sigma,
table_modulation_frequency=8*4)
tfinal = 2*tau_factor*sigma
t_center = tau_factor*sigma
def gbragg_fn(kvec, k_init, sigma, omegas, deltas, delta_phase=0.0, mod_freq=None, mod_phase=0.0):
natoms = len(omegas)
phi0_batch = np.zeros((natoms, len(kvec)), dtype=np.complex128)
phi0_batch[:, np.argmin(np.abs(kvec))] = 1.0 # start at k=0 frame
delta_eff = deltas - 4*k_init # transform detuning to k=0 frame
if mod_freq is None:
result = propagate(
kvec, phi0_batch, tfinal, delta_eff,
omega_fnc_gaussian, np.array([1.0, sigma, t_center]),
phase_fnc_constant, np.array([0.0]),
omegas=omegas, tol=tol,
)
else:
result = propagate(
kvec, phi0_batch, tfinal, delta_eff,
multi_omega_fnc, np.array([1.0, sigma, t_center, mod_freq]),
phase_fnc_constant, np.array([0.0]),
omegas=omegas, tol=tol,
)
# Apply post-hoc laser phase in k=0 frame (same convention as load_precomputed_gbragg)
phi = result.phi_final * np.exp(-1j * np.outer(delta_phase, kvec/2))
# Shift output by Deltan = k_init//2 positions (same as load_precomputed_gbragg)
Deltan = k_init // 2
if Deltan == 0:
return phi
phi_out = np.zeros_like(phi)
if Deltan < 0:
phi_out[:, :Deltan] = phi[:, -Deltan:]
else:
phi_out[:, Deltan:] = phi[:, :-Deltan]
return phi_out
return gbragg_fn
gbragg = make_gbragg(sigma, use_precompute=True)
def cpops(x0, y0, z0, vz, vx, vy, cphase=0.0, injected_dphase=0.0):
bs_lookup_dict = {}
# Define beamsplitter function
def calc_bs(x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, z, idx):
# Check if this is a multifrequency beamsplitter
multifrequency = isinstance(klattice, list)
# Load cached result
if idx in bs_lookup_dict:
if k_init in bs_lookup_dict[idx]:
if int(k_final) in bs_lookup_dict[idx][k_init]:
return bs_lookup_dict[idx][k_init][int(k_final)]
# Compute omegas and deltas
x = x0 + vx*t
y = y0 + vy*t
omegas = omegalookup(x, y, z0 + z)
deltas = deltalookup(vz)
# Set sigma
sigma = 0.259658916
# Compute phases
phases = deltas*t
# Apply common mode phase if provided and at pulse 3
if idx == 3:
phases += cphase
# Apply differential phase if provided at pulse 3. The way I am injecting this is unphysical/different from how we do in the experiment. But I'm not sure if there is a better way.
if k_init == 0.0 and k_final == -2.0*nbragg:
phases += injected_dphase
# Compute effect of Bragg beamsplitter
if not multifrequency:
phi = gbragg(ifr.kvec, int(k_init), sigma, omegas, deltas, delta_phase=phases)
else:
phi = gbragg(ifr.kvec, int(k_init), sigma, omegas, deltas, delta_phase=phases, mod_freq=8*4, mod_phase=0.0)
# Determine index of k_final state
kf_idx = np.argmin(np.abs(ifr.kvec - k_final))
# Save wavefunction to cache
if idx not in bs_lookup_dict:
bs_lookup_dict[idx] = {}
if k_init not in bs_lookup_dict[idx]:
bs_lookup_dict[idx][k_init] = {}
if int(k_final) not in bs_lookup_dict[idx][k_init]:
bs_lookup_dict[idx][k_init][int(k_final)] = phi[:,kf_idx]
else:
raise RuntimeError('Array should not have been created but it was!')
# Return
return phi[:,kf_idx]
# Define free evolution function
propfnc = lambda x0, y0, z0, vz, vx, vy, t, k: np.exp(-1j*t*k**2)
# Apply functions to interferometer
fnclst = [lambda x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x: calc_bs(x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x, 1),
propfnc,
lambda x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x: calc_bs(x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x, 2),
propfnc,
lambda x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x: calc_bs(x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x, 3),
propfnc,
lambda x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x: calc_bs(x0, y0, z0, vz, vx, vy, k_init, k_final, klattice, t, x, 4)]
ifr.set_operation_funcs(fnclst)
# Load population functions
popfnc = ifr.get_population_func([4*nbragg, 2*nbragg, 0*nbragg, -2*nbragg], lambda x1, x2, x3, x4, x5, x6: np.zeros_like(x0), lambda x1, x2, x3, x4, x5, x6: np.ones_like(x0,dtype=np.complex128), lambda x1, x2, x3, x4, x5, x6: np.zeros_like(x0,dtype=np.complex128))
# Evaluate populations and return
return popfnc(4*nbragg, [x0, y0, z0, vz, vx, vy]), popfnc(2*nbragg, [x0, y0, z0, vz, vx, vy]), popfnc(0*nbragg, [x0, y0, z0, vz, vx, vy]), popfnc(-2*nbragg, [x0, y0, z0, vz, vx, vy])
x0, y0, z0, vz, vx, vy = cloud_init(natoms=1000, sigma_cloud=1e-3, sigma_transverse_v=3.5e-3, sigma_vertical_v=0.1*3.5e-3)
pA, pB, pC, pD = cpops(x0, y0, z0, vz, vx, vy, cphase=np.pi/4)
Loading single frequency Bragg precompute table, this could take a while...
Precompute table loaded! Performing checks...
Checks passed!
Loading multifrequency Bragg precompute table, this could take a while...
Precompute table loaded! Performing checks...
Checks passed!
Make ellipse
[4]:
def calc_xy(a, b, c, d):
return (a-b)/(a+b), (c-d)/(c+d)
x0, y0, z0, vz, vx, vy = cloud_init(natoms=1000, sigma_cloud=1e-3, sigma_transverse_v=0.1*3.5e-3/omega_r_conversion, sigma_vertical_v=0.1*3.5e-3)
cphases = np.linspace(0, 2*np.pi, 12)
x, y = np.full_like(cphases, np.nan), np.full_like(cphases, np.nan)
for i in range(len(cphases)):
pA, pB, pC, pD = cpops(x0, y0, z0, vz, vx, vy, cphase=cphases[i], injected_dphase=np.pi/8)
x[i], y[i] = calc_xy(np.sum(pA), np.sum(pB), np.sum(pC), np.sum(pD))
plt.plot(x, y, '.')
plt.gca().set_aspect('equal')
plt.xlim(-1,1)
plt.ylim(-1,1)
plt.show()
