MAJOR REWRITE
This commit is contained in:
parent
64132018e2
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ac5aeb4a3e
@ -1,7 +1,8 @@
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import math
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import math
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import numpy as np
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.pyplot as plt
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from scipy import signal
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import matplotlib.ticker as mtick
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from scipy import signal, interpolate
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from scipy.optimize import curve_fit
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from scipy.optimize import curve_fit
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from astropy import units as u, constants as ac
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from astropy import units as u, constants as ac
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@ -43,6 +44,8 @@ def modulation_function(mod_amp, n_points, func = 'arccos'):
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phi = np.linspace(0, 2*np.pi, n_points)
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phi = np.linspace(0, 2*np.pi, n_points)
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mod_func = mod_amp * np.sin(phi)
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mod_func = mod_amp * np.sin(phi)
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elif func == 'arccos':
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elif func == 'arccos':
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# phi = np.linspace(0, 2*np.pi, n_points)
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# mod_func = mod_amp * (2/np.pi * np.arccos(phi/np.pi-1) - 1)
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phi = np.linspace(0, 2*np.pi, int(n_points/2))
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phi = np.linspace(0, 2*np.pi, int(n_points/2))
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tmp_1 = 2/np.pi * np.arccos(phi/np.pi-1) - 1
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tmp_1 = 2/np.pi * np.arccos(phi/np.pi-1) - 1
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tmp_2 = np.flip(tmp_1)
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tmp_2 = np.flip(tmp_1)
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@ -80,11 +83,61 @@ def w(pos, w_0, lamb):
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def meanThermalVelocity(T, m = 164*u.u):
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def meanThermalVelocity(T, m = 164*u.u):
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return 4 * np.sqrt((ac.k_B * T) /(np.pi * m))
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return 4 * np.sqrt((ac.k_B * T) /(np.pi * m))
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def particleDensity(w_x, w_z, Power, Polarizability, N, T, m = 164*u.u): # For a thermal cloud
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def particleDensity(w_x, w_z, Power, Polarizability, N, T, m = 164*u.u, use_measured_tf = False): # For a thermal cloud
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v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
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if not use_measured_tf:
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v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
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v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
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v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
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v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
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return N * (2 * np.pi)**3 * (v_x * v_y * v_z) * (m / (2 * np.pi * ac.k_B * T))**(3/2)
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v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
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return N * (2 * np.pi)**3 * (v_x * v_y * v_z) * (m / (2 * np.pi * ac.k_B * T))**(3/2)
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else:
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fin_mod_dep = [0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]
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v_x = [0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813] * u.kHz
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dv_x = [0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024] * u.kHz
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v_z = [1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643] * u.kHz
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dv_z = [0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033] * u.kHz
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sorted_fin_mod_dep, sorted_v_x = zip(*sorted(zip(fin_mod_dep, v_x)))
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sorted_fin_mod_dep, sorted_dv_x = zip(*sorted(zip(fin_mod_dep, dv_x)))
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sorted_fin_mod_dep, sorted_v_z = zip(*sorted(zip(fin_mod_dep, v_z)))
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sorted_fin_mod_dep, sorted_dv_z = zip(*sorted(zip(fin_mod_dep, dv_z)))
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fin_mod_dep = [1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1]
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v_y = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02] * u.Hz
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dv_y = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31] * u.Hz
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sorted_fin_mod_dep, sorted_v_y = zip(*sorted(zip(fin_mod_dep, v_y)))
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sorted_fin_mod_dep, sorted_dv_y = zip(*sorted(zip(fin_mod_dep, dv_y)))
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alpha_x = [(v_x[0]/x)**(2/3) for x in v_x]
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dalpha_x = [alpha_x[i] * np.sqrt((dv_x[0]/v_x[0])**2 + (dv_x[i]/v_x[i])**2) for i in range(len(v_x))]
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alpha_y = [(v_z[0]/y)**2 for y in v_z]
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dalpha_y = [alpha_y[i] * np.sqrt((dv_z[0]/v_z[0])**2 + (dv_z[i]/v_z[i])**2) for i in range(len(v_z))]
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avg_alpha = [(g + h) / 2 for g, h in zip(alpha_x, alpha_y)]
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sorted_fin_mod_dep, new_aspect_ratio = zip(*sorted(zip(fin_mod_dep, (w_x * avg_alpha) / w_z)))
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fin_mod_dep = [1.0, 0.8, 0.6, 0.4, 0.2, 0.9, 0.7, 0.5, 0.3, 0.1]
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T_x = [22.1, 27.9, 31.7, 42.2, 145.8, 27.9, 33.8, 42.4, 61.9, 136.1] * u.uK
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dT_x = [1.7, 2.6, 2.4, 3.7, 1.1, 2.2, 3.2, 1.7, 2.2, 1.2] * u.uK
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T_y = [13.13, 14.75, 18.44, 26.31, 52.55, 13.54, 16.11, 21.15, 35.81, 85.8] * u.uK
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dT_y = [0.05, 0.05, 0.07, 0.16, 0.28, 0.04, 0.07, 0.10, 0.21, 0.8] * u.uK
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avg_T = [(g + h) / 2 for g, h in zip(T_x, T_y)]
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avg_dT = [0.5 * np.sqrt(g**2 + h**2) for g, h in zip(dT_x, dT_y)]
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sorted_fin_mod_dep, sorted_avg_T = zip(*sorted(zip(fin_mod_dep, avg_T)))
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sorted_fin_mod_dep, sorted_avg_dT = zip(*sorted(zip(fin_mod_dep, avg_dT)))
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pd = np.zeros(len(fin_mod_dep))
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dpd = np.zeros(len(fin_mod_dep))
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for i in range(len(fin_mod_dep)):
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particle_density = (N * (2 * np.pi)**3 * (sorted_v_x[i] * sorted_v_y[i] * sorted_v_z[i]) * (m / (2 * np.pi * ac.k_B * sorted_avg_T[i]))**(3/2)).decompose()
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pd[i] = particle_density.value
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dpd[i] = (((N * (2 * np.pi)**3 * (m / (2 * np.pi * ac.k_B * sorted_avg_T[i]))**(3/2)) * ((sorted_dv_x[i] * sorted_v_y[i] * sorted_v_z[i]) + (sorted_v_x[i] * sorted_dv_y[i] * sorted_v_z[i]) + (sorted_v_x[i] * sorted_v_y[i] * sorted_dv_z[i]) - (1.5*(sorted_v_x[i] * sorted_v_y[i] * sorted_v_z[i])*(sorted_avg_dT[i]/sorted_avg_T[i])))).decompose()).value
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pd = pd*particle_density.unit
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dpd = dpd*particle_density.unit
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return pd, dpd, sorted_avg_T, sorted_avg_dT, new_aspect_ratio, sorted_fin_mod_dep
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def thermaldeBroglieWavelength(T, m = 164*u.u):
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def thermaldeBroglieWavelength(T, m = 164*u.u):
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return np.sqrt((2*np.pi*ac.hbar**2)/(m*ac.k_B*T))
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return np.sqrt((2*np.pi*ac.hbar**2)/(m*ac.k_B*T))
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@ -141,6 +194,39 @@ def calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N, T, B): #Fo
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def calculatePSD(w_x, w_z, Power, Polarizability, N, T):
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def calculatePSD(w_x, w_z, Power, Polarizability, N, T):
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return (particleDensity(w_x, w_z, Power, Polarizability, N, T, m = 164*u.u) * thermaldeBroglieWavelength(T)**3).decompose()
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return (particleDensity(w_x, w_z, Power, Polarizability, N, T, m = 164*u.u) * thermaldeBroglieWavelength(T)**3).decompose()
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def convert_modulation_depth_to_alpha(modulation_depth):
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fin_mod_dep = [0, 0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]
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fx = [3.135, 0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813]
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dfx = [0.016, 0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024]
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fy = [2.746, 1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643]
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dfy = [0.014, 0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033]
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alpha_x = [(fx[0]/x)**(2/3) for x in fx]
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dalpha_x = [alpha_x[i] * np.sqrt((dfx[0]/fx[0])**2 + (dfx[i]/fx[i])**2) for i in range(len(fx))]
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alpha_y = [(fy[0]/y)**2 for y in fy]
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dalpha_y = [alpha_y[i] * np.sqrt((dfy[0]/fy[0])**2 + (dfy[i]/fy[i])**2) for i in range(len(fy))]
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avg_alpha = [(g + h) / 2 for g, h in zip(alpha_x, alpha_y)]
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sorted_fin_mod_dep, sorted_avg_alpha = zip(*sorted(zip(fin_mod_dep, avg_alpha)))
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f = interpolate.interp1d(sorted_fin_mod_dep, sorted_avg_alpha)
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return f(modulation_depth), fin_mod_dep, alpha_x, alpha_y, dalpha_x, dalpha_y
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def convert_modulation_depth_to_temperature(modulation_depth):
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fin_mod_dep = [1.0, 0.8, 0.6, 0.4, 0.2, 0.0, 0.9, 0.7, 0.5, 0.3, 0.1]
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T_x = [22.1, 27.9, 31.7, 42.2, 98.8, 145.8, 27.9, 33.8, 42.4, 61.9, 136.1]
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dT_x = [1.7, 2.6, 2.4, 3.7, 1.1, 0.6, 2.2, 3.2, 1.7, 2.2, 1.2]
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T_y = [13.13, 14.75, 18.44, 26.31, 52.55, 92.9, 13.54, 16.11, 21.15, 35.81, 85.8]
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dT_y = [0.05, 0.05, 0.07, 0.16, 0.28, 0.7, 0.04, 0.07, 0.10, 0.21, 0.8]
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avg_T = [(g + h) / 2 for g, h in zip(T_x, T_y)]
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sorted_fin_mod_dep, sorted_avg_T = zip(*sorted(zip(fin_mod_dep, avg_T)))
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f = interpolate.interp1d(sorted_fin_mod_dep, sorted_avg_T)
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return f(modulation_depth), fin_mod_dep, T_x, T_y, dT_x, dT_y
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#####################################################################
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#####################################################################
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# POTENTIALS #
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# POTENTIALS #
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#####################################################################
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#####################################################################
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@ -180,6 +266,23 @@ def gaussian_potential(pos, amp, waist, xoffset, yoffset):
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U_Gaussian = amp * np.exp(-2 * ((pos + xoffset) / waist)**2) + yoffset
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U_Gaussian = amp * np.exp(-2 * ((pos + xoffset) / waist)**2) + yoffset
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return U_Gaussian
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return U_Gaussian
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def crossed_beam_potential(positions, theta, waists, P, alpha, wavelength=1.064*u.um):
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beam_1_positions = positions
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A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:], waists[0][0], wavelength)*w(beam_1_positions[1,:], waists[0][1], wavelength))
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U_1_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
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U_1 = - U_1_tilde * A_1 * np.exp(-2 * ((beam_1_positions[0,:]/w(beam_1_positions[1,:], waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:], waists[0][1], wavelength))**2))
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R = rotation_matrix([0, 0, 1], np.radians(theta))
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beam_2_positions = np.dot(R, beam_1_positions)
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A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:], waists[1][0], wavelength)*w(beam_2_positions[1,:], waists[1][1], wavelength))
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U_2_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
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U_2 = - U_2_tilde * A_2 * np.exp(-2 * ((beam_2_positions[0,:]/w(beam_2_positions[1,:], waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:], waists[1][1], wavelength))**2))
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U = U_1 + U_2
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return U
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#####################################################################
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#####################################################################
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# COMPUTE/EXTRACT TRAP POTENTIAL AND PARAMETERS #
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# COMPUTE/EXTRACT TRAP POTENTIAL AND PARAMETERS #
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#####################################################################
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#####################################################################
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@ -220,6 +323,7 @@ def computeTrapPotential(w_x, w_z, Power, Polarizability, options):
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gravity = options['gravity']
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gravity = options['gravity']
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astigmatism = options['astigmatism']
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astigmatism = options['astigmatism']
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modulation = options['modulation']
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modulation = options['modulation']
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crossed = options['crossed']
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if modulation:
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if modulation:
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aspect_ratio = options['aspect_ratio']
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aspect_ratio = options['aspect_ratio']
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@ -241,14 +345,25 @@ def computeTrapPotential(w_x, w_z, Power, Polarizability, options):
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elif axis == 2:
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elif axis == 2:
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projection_axis = np.array([0, 0, 1]) # vertical direction (Z-axis)
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projection_axis = np.array([0, 0, 1]) # vertical direction (Z-axis)
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else:
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projection_axis = np.array([1, 1, 1]) # vertical direction (Z-axis)
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x_Positions = np.arange(-extent, extent, 1)*u.um
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x_Positions = np.arange(-extent, extent, 1)*u.um
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y_Positions = np.arange(-extent, extent, 1)*u.um
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y_Positions = np.arange(-extent, extent, 1)*u.um
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z_Positions = np.arange(-extent, extent, 1)*u.um
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z_Positions = np.arange(-extent, extent, 1)*u.um
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Positions = np.vstack((x_Positions, y_Positions, z_Positions)) * projection_axis[:, np.newaxis]
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Positions = np.vstack((x_Positions, y_Positions, z_Positions)) * projection_axis[:, np.newaxis]
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IdealTrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability)
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if not crossed:
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IdealTrappingPotential = IdealTrappingPotential * (np.ones((3, len(IdealTrappingPotential))) * projection_axis[:, np.newaxis])
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IdealTrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability)
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IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK)
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IdealTrappingPotential = IdealTrappingPotential * (np.ones((3, len(IdealTrappingPotential))) * projection_axis[:, np.newaxis])
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IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK)
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else:
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theta = options['theta']
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waists = np.vstack((np.asarray([w_x[0].value, w_z[0].value])*u.um, np.asarray([w_x[1].value, w_z[1].value])*u.um))
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IdealTrappingPotential = crossed_beam_potential(Positions, theta, waists, P = Power, alpha = Polarizability)
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IdealTrappingPotential = IdealTrappingPotential * (np.ones((3, len(IdealTrappingPotential))) * projection_axis[:, np.newaxis])
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IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK)
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if gravity and not astigmatism:
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if gravity and not astigmatism:
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# Influence of Gravity
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# Influence of Gravity
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@ -291,27 +406,31 @@ def computeTrapPotential(w_x, w_z, Power, Polarizability, options):
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else:
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else:
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TrappingPotential = IdealTrappingPotential
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TrappingPotential = IdealTrappingPotential
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if TrappingPotential[axis][0] > TrappingPotential[axis][-1]:
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if not crossed:
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EffectiveTrapDepthInKelvin = TrappingPotential[axis][-1] - min(TrappingPotential[axis])
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if TrappingPotential[axis][0] > TrappingPotential[axis][-1]:
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elif TrappingPotential[axis][0] < TrappingPotential[axis][-1]:
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EffectiveTrapDepthInKelvin = TrappingPotential[axis][-1] - min(TrappingPotential[axis])
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EffectiveTrapDepthInKelvin = TrappingPotential[axis][0] - min(TrappingPotential[axis])
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elif TrappingPotential[axis][0] < TrappingPotential[axis][-1]:
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EffectiveTrapDepthInKelvin = TrappingPotential[axis][0] - min(TrappingPotential[axis])
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else:
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EffectiveTrapDepthInKelvin = IdealTrapDepthInKelvin
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TrapDepthsInKelvin = [IdealTrapDepthInKelvin, EffectiveTrapDepthInKelvin]
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v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
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v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
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v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
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CalculatedTrapFrequencies = [v_x, v_y, v_z]
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v, dv, popt, pcov = extractTrapFrequency(Positions, IdealTrappingPotential, axis)
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IdealTrapFrequency = [v, dv]
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||||||
|
v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, axis)
|
||||||
|
TrapFrequency = [v, dv]
|
||||||
|
ExtractedTrapFrequencies = [IdealTrapFrequency, TrapFrequency]
|
||||||
|
|
||||||
|
return Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies
|
||||||
|
|
||||||
else:
|
else:
|
||||||
EffectiveTrapDepthInKelvin = IdealTrapDepthInKelvin
|
return TrappingPotential
|
||||||
|
|
||||||
TrapDepthsInKelvin = [IdealTrapDepthInKelvin, EffectiveTrapDepthInKelvin]
|
|
||||||
|
|
||||||
v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
|
|
||||||
v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
|
|
||||||
v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
|
|
||||||
CalculatedTrapFrequencies = [v_x, v_y, v_z]
|
|
||||||
|
|
||||||
v, dv, popt, pcov = extractTrapFrequency(Positions, IdealTrappingPotential, axis)
|
|
||||||
IdealTrapFrequency = [v, dv]
|
|
||||||
v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, axis)
|
|
||||||
TrapFrequency = [v, dv]
|
|
||||||
ExtractedTrapFrequencies = [IdealTrapFrequency, TrapFrequency]
|
|
||||||
|
|
||||||
return Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies
|
|
||||||
|
|
||||||
def extractWaist(Positions, TrappingPotential):
|
def extractWaist(Positions, TrappingPotential):
|
||||||
tmp_pos = Positions.value
|
tmp_pos = Positions.value
|
||||||
@ -321,8 +440,8 @@ def extractWaist(Positions, TrappingPotential):
|
|||||||
TrapMinimum = tmp_pot[center_idx]
|
TrapMinimum = tmp_pot[center_idx]
|
||||||
TrapCenter = tmp_pos[center_idx]
|
TrapCenter = tmp_pos[center_idx]
|
||||||
|
|
||||||
lb = int(round(center_idx - len(tmp_pot)/10, 1))
|
lb = int(round(center_idx - len(tmp_pot)/30, 1))
|
||||||
ub = int(round(center_idx + len(tmp_pot)/10, 1))
|
ub = int(round(center_idx + len(tmp_pot)/30, 1))
|
||||||
xdata = tmp_pos[lb:ub]
|
xdata = tmp_pos[lb:ub]
|
||||||
Potential = tmp_pot[lb:ub]
|
Potential = tmp_pot[lb:ub]
|
||||||
|
|
||||||
@ -330,10 +449,87 @@ def extractWaist(Positions, TrappingPotential):
|
|||||||
popt, pcov = curve_fit(gaussian_potential, xdata, Potential, p0)
|
popt, pcov = curve_fit(gaussian_potential, xdata, Potential, p0)
|
||||||
return popt, pcov
|
return popt, pcov
|
||||||
|
|
||||||
|
def computeIntensityProfileAndPotentials(Power, waists, alpha, wavelength, options):
|
||||||
|
w_x = waists[0]
|
||||||
|
w_z = waists[1]
|
||||||
|
extent = options['extent']
|
||||||
|
modulation = options['modulation']
|
||||||
|
mod_func = options['modulation_function']
|
||||||
|
|
||||||
|
if not modulation:
|
||||||
|
extent = 50
|
||||||
|
x_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
y_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
z_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
|
||||||
|
idx = np.where(y_Positions==0)[0][0]
|
||||||
|
|
||||||
|
alpha = Polarizability
|
||||||
|
wavelength = 1.064*u.um
|
||||||
|
|
||||||
|
xm,ym,zm = np.meshgrid(x_Positions, y_Positions, z_Positions, sparse=True, indexing='ij')
|
||||||
|
|
||||||
|
## Single Gaussian Beam
|
||||||
|
A = 2*Power/(np.pi*w(ym, w_x, wavelength)*w(ym, w_z, wavelength))
|
||||||
|
intensity_profile = A * np.exp(-2 * ((xm/w(ym, w_x, wavelength))**2 + (zm/w(ym, w_z, wavelength))**2))
|
||||||
|
I = intensity_profile[:, idx, :].to(u.MW/(u.cm*u.cm))
|
||||||
|
|
||||||
|
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
|
||||||
|
U = - U_tilde * I
|
||||||
|
U = (U/ac.k_B).to(u.uK)
|
||||||
|
|
||||||
|
return [x_Positions, z_Positions], [w_x.value, 0, w_z.value, 0], I, U, [0, 0, 0, 0]
|
||||||
|
|
||||||
|
else:
|
||||||
|
mod_amp = options['modulation_amplitude']
|
||||||
|
x_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
y_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
z_Positions = np.arange(-extent, extent, 1)*u.um
|
||||||
|
|
||||||
|
mod_amp = mod_amp * w_x
|
||||||
|
n_points = len(x_Positions)
|
||||||
|
dx, xmod_Positions = modulation_function(mod_amp, n_points, func = mod_func)
|
||||||
|
|
||||||
|
idx = np.where(y_Positions==0)[0][0]
|
||||||
|
|
||||||
|
xm,ym,zm,xmodm = np.meshgrid(x_Positions, y_Positions, z_Positions, xmod_Positions, sparse=True, indexing='ij')
|
||||||
|
|
||||||
|
## Single Modulated Gaussian Beam
|
||||||
|
A = 2*Power/(np.pi*w(y_Positions[idx] , w_x, wavelength)*w(y_Positions[idx], w_z, wavelength))
|
||||||
|
intensity_profile = A * 1/(2*mod_amp) * np.trapz(np.exp(-2 * (((xmodm - xm)/w(ym, w_x, wavelength))**2 + (zm/w(ym, w_z, wavelength))**2)), dx = dx, axis = -1)
|
||||||
|
I = intensity_profile[:, idx, :].to(u.MW/(u.cm*u.cm))
|
||||||
|
|
||||||
|
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
|
||||||
|
U = - U_tilde * I
|
||||||
|
U = (U/ac.k_B).to(u.uK)
|
||||||
|
|
||||||
|
poptx, pcovx = extractWaist(x_Positions, U[:, np.where(z_Positions==0)[0][0]])
|
||||||
|
poptz, pcovz = extractWaist(z_Positions, U[np.where(x_Positions==0)[0][0], :])
|
||||||
|
|
||||||
|
extracted_waist_x = poptx[1]
|
||||||
|
dextracted_waist_x = pcovx[1][1]**0.5
|
||||||
|
extracted_waist_z = poptz[1]
|
||||||
|
dextracted_waist_z = pcovz[1][1]**0.5
|
||||||
|
|
||||||
|
return [x_Positions, z_Positions], [extracted_waist_x, dextracted_waist_x, extracted_waist_z, dextracted_waist_z], I, U, [poptx, pcovx, poptz, pcovz]
|
||||||
|
|
||||||
#####################################################################
|
#####################################################################
|
||||||
# PLOTTING #
|
# PLOTTING #
|
||||||
#####################################################################
|
#####################################################################
|
||||||
|
|
||||||
|
def generate_label(v, dv):
|
||||||
|
unit = 'Hz'
|
||||||
|
if v <= 0.0:
|
||||||
|
v = np.nan
|
||||||
|
dv = np.nan
|
||||||
|
unit = 'Hz'
|
||||||
|
elif v > 0.0 and orderOfMagnitude(v) > 2:
|
||||||
|
v = v / 1e3 # in kHz
|
||||||
|
dv = dv / 1e3 # in kHz
|
||||||
|
unit = 'kHz'
|
||||||
|
tf_label = '\u03BD = %.1f \u00B1 %.2f %s'% tuple([v,dv,unit])
|
||||||
|
return tf_label
|
||||||
|
|
||||||
def plotHarmonicFit(Positions, TrappingPotential, TrapDepthsInKelvin, axis, popt, pcov):
|
def plotHarmonicFit(Positions, TrappingPotential, TrapDepthsInKelvin, axis, popt, pcov):
|
||||||
v = popt[0]
|
v = popt[0]
|
||||||
dv = pcov[0][0]**0.5
|
dv = pcov[0][0]**0.5
|
||||||
@ -379,26 +575,13 @@ def plotGaussianFit(Positions, TrappingPotential, popt, pcov):
|
|||||||
bx.set_title('Fit Residuals')
|
bx.set_title('Fit Residuals')
|
||||||
plt.plot(Positions, TrappingPotential - gapprox, 'ob')
|
plt.plot(Positions, TrappingPotential - gapprox, 'ob')
|
||||||
plt.xlabel('Distance (um)', fontsize= 12, fontweight='bold')
|
plt.xlabel('Distance (um)', fontsize= 12, fontweight='bold')
|
||||||
plt.ylabel('$U_{trap} - U_{Harmonic}$', fontsize= 12, fontweight='bold')
|
plt.ylabel('$U_{trap} - U_{Gaussian}$', fontsize= 12, fontweight='bold')
|
||||||
plt.xlim([-10, 10])
|
plt.xlim([-10, 10])
|
||||||
plt.ylim([-1, 1])
|
plt.ylim([-1, 1])
|
||||||
plt.grid(visible=1)
|
plt.grid(visible=1)
|
||||||
plt.tight_layout()
|
plt.tight_layout()
|
||||||
plt.show()
|
plt.show()
|
||||||
|
|
||||||
def generate_label(v, dv):
|
|
||||||
unit = 'Hz'
|
|
||||||
if v <= 0.0:
|
|
||||||
v = np.nan
|
|
||||||
dv = np.nan
|
|
||||||
unit = 'Hz'
|
|
||||||
elif v > 0.0 and orderOfMagnitude(v) > 2:
|
|
||||||
v = v / 1e3 # in kHz
|
|
||||||
dv = dv / 1e3 # in kHz
|
|
||||||
unit = 'kHz'
|
|
||||||
tf_label = '\u03BD = %.1f \u00B1 %.2f %s'% tuple([v,dv,unit])
|
|
||||||
return tf_label
|
|
||||||
|
|
||||||
def plotPotential(Positions, ComputedPotentials, axis, Params = [], listToIterateOver = [], save = False):
|
def plotPotential(Positions, ComputedPotentials, axis, Params = [], listToIterateOver = [], save = False):
|
||||||
|
|
||||||
plt.figure(figsize=(9, 7))
|
plt.figure(figsize=(9, 7))
|
||||||
@ -448,108 +631,195 @@ def plotPotential(Positions, ComputedPotentials, axis, Params = [], listToIterat
|
|||||||
plt.savefig('pot_' + dir + '.png')
|
plt.savefig('pot_' + dir + '.png')
|
||||||
plt.show()
|
plt.show()
|
||||||
|
|
||||||
def plotIntensityProfileAndPotentials(Power, waists, alpha, wavelength, options):
|
def plotIntensityProfileAndPotentials(positions, waists, I, U):
|
||||||
w_x = waists[0]
|
|
||||||
w_z = waists[1]
|
|
||||||
extent = options['extent']
|
|
||||||
modulation = options['modulation']
|
|
||||||
mod_func = options['modulation_function']
|
|
||||||
|
|
||||||
if not modulation:
|
x_Positions = positions[0]
|
||||||
extent = 50
|
z_Positions = positions[1]
|
||||||
x_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
y_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
z_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
|
|
||||||
idx = np.where(y_Positions==0)[0][0]
|
w_x = waists[0]
|
||||||
|
dw_x = waists[1]
|
||||||
|
w_z = waists[2]
|
||||||
|
dw_x = waists[3]
|
||||||
|
|
||||||
alpha = Polarizability
|
ar = w_x/w_z
|
||||||
wavelength = 1.064*u.um
|
dar = ar * np.sqrt((dw_x/w_x)**2 + (dw_x/w_z)**2)
|
||||||
|
|
||||||
xm,ym,zm = np.meshgrid(x_Positions, y_Positions, z_Positions, sparse=True, indexing='ij')
|
fig = plt.figure(figsize=(12, 6))
|
||||||
|
ax = fig.add_subplot(121)
|
||||||
|
ax.set_title('Intensity Profile ($MW/cm^2$)\n Aspect Ratio = %.2f \u00B1 %.2f um'% tuple([ar,dar]))
|
||||||
|
im = plt.imshow(np.transpose(I.value), cmap="coolwarm", extent=[np.min(x_Positions.value), np.max(x_Positions.value), np.min(z_Positions.value), np.max(z_Positions.value)])
|
||||||
|
plt.xlabel('X - Horizontal (um)', fontsize= 12, fontweight='bold')
|
||||||
|
plt.ylabel('Z - Vertical (um)', fontsize= 12, fontweight='bold')
|
||||||
|
ax.set_aspect('equal')
|
||||||
|
fig.colorbar(im, fraction=0.046, pad=0.04, orientation='vertical')
|
||||||
|
|
||||||
## Single Gaussian Beam
|
bx = fig.add_subplot(122)
|
||||||
A = 2*Power/(np.pi*w(ym, w_x, wavelength)*w(ym, w_z, wavelength))
|
bx.set_title('Trap Potential')
|
||||||
I = A * np.exp(-2 * ((xm/w(ym, w_x, wavelength))**2 + (zm/w(ym, w_z, wavelength))**2))
|
plt.plot(x_Positions, U[:, np.where(z_Positions==0)[0][0]], label = 'X - Horizontal')
|
||||||
I = np.transpose(I.to(u.MW/(u.cm*u.cm)))
|
plt.plot(z_Positions, U[np.where(x_Positions==0)[0][0], :], label = 'Z - Vertical')
|
||||||
|
plt.ylim(top = 0)
|
||||||
|
plt.xlabel('Extent (um)', fontsize= 12, fontweight='bold')
|
||||||
|
plt.ylabel('Depth (uK)', fontsize= 12, fontweight='bold')
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
plt.legend(prop={'size': 12, 'weight': 'bold'})
|
||||||
|
plt.show()
|
||||||
|
|
||||||
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
|
def plotAlphas():
|
||||||
U = - U_tilde * I
|
|
||||||
U = (U/ac.k_B).to(u.uK)
|
|
||||||
|
|
||||||
fig = plt.figure(figsize=(12, 6))
|
modulation_depth = np.arange(0, 1.1, 0.1)
|
||||||
ax = fig.add_subplot(121)
|
Alphas, fin_mod_dep, alpha_x, alpha_y, dalpha_x, dalpha_y = convert_modulation_depth_to_alpha(modulation_depth)
|
||||||
ax.set_title('Intensity Profile ($MW/cm^2$)\n Aspect Ratio = %.2f' %(w_x/w_z))
|
|
||||||
im = plt.imshow(I[:,idx,:].value, cmap="coolwarm", extent=[np.min(x_Positions.value), np.max(x_Positions.value), np.min(z_Positions.value), np.max(z_Positions.value)])
|
|
||||||
plt.xlabel('X - Horizontal (um)', fontsize= 12, fontweight='bold')
|
|
||||||
plt.ylabel('Z - Vertical (um)', fontsize= 12, fontweight='bold')
|
|
||||||
ax.set_aspect('equal')
|
|
||||||
fig.colorbar(im, fraction=0.046, pad=0.04, orientation='vertical')
|
|
||||||
|
|
||||||
bx = fig.add_subplot(122)
|
plt.figure()
|
||||||
bx.set_title('Trap Potential')
|
plt.errorbar(fin_mod_dep, alpha_x, yerr = dalpha_x, fmt= 'ob', markersize=5, capsize=5)
|
||||||
plt.plot(x_Positions, U[np.where(x_Positions==0)[0][0], idx, :], label = 'X - Horizontal')
|
plt.errorbar(fin_mod_dep, alpha_y, yerr = dalpha_y, fmt= 'or', markersize=5, capsize=5)
|
||||||
plt.plot(z_Positions, U[:, idx, np.where(z_Positions==0)[0][0]], label = 'Z - Vertical')
|
plt.plot(modulation_depth, Alphas, '--g')
|
||||||
plt.ylim(top = 0)
|
plt.xlabel('Modulation depth', fontsize= 12, fontweight='bold')
|
||||||
plt.xlabel('Extent (um)', fontsize= 12, fontweight='bold')
|
plt.ylabel('$\\alpha$', fontsize= 12, fontweight='bold')
|
||||||
plt.ylabel('Depth (uK)', fontsize= 12, fontweight='bold')
|
plt.tight_layout()
|
||||||
plt.tight_layout()
|
plt.grid(visible=1)
|
||||||
plt.grid(visible=1)
|
plt.show()
|
||||||
plt.legend(prop={'size': 12, 'weight': 'bold'})
|
|
||||||
plt.show()
|
|
||||||
else:
|
|
||||||
mod_amp = options['modulation_amplitude']
|
|
||||||
x_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
y_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
z_Positions = np.arange(-extent, extent, 1)*u.um
|
|
||||||
|
|
||||||
mod_amp = mod_amp * w_x
|
def plotTemperatures(w_x, w_z, plot_against_mod_depth = True):
|
||||||
n_points = len(x_Positions)
|
|
||||||
dx, xmod_Positions = modulation_function(mod_amp, n_points, func = mod_func)
|
|
||||||
|
|
||||||
idx = np.where(y_Positions==0)[0][0]
|
modulation_depth = np.arange(0, 1.1, 0.1)
|
||||||
|
w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]
|
||||||
|
new_aspect_ratio = w_xs / w_z
|
||||||
|
Temperatures, fin_mod_dep, T_x, T_y, dT_x, dT_y = convert_modulation_depth_to_temperature(modulation_depth)
|
||||||
|
measured_aspect_ratio = (w_x * convert_modulation_depth_to_alpha(fin_mod_dep)[0]) / w_z
|
||||||
|
|
||||||
xm,ym,zm,xmodm = np.meshgrid(x_Positions, y_Positions, z_Positions, xmod_Positions, sparse=True, indexing='ij')
|
plt.figure()
|
||||||
|
if plot_against_mod_depth:
|
||||||
|
plt.errorbar(fin_mod_dep, T_x, yerr = dT_x, fmt= 'ob', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(fin_mod_dep, T_y, yerr = dT_y, fmt= 'or', markersize=5, capsize=5)
|
||||||
|
plt.plot(modulation_depth, Temperatures, '--g')
|
||||||
|
xlabel = 'Modulation depth'
|
||||||
|
else:
|
||||||
|
plt.errorbar(measured_aspect_ratio, T_x, yerr = dT_x, fmt= 'ob', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(measured_aspect_ratio, T_y, yerr = dT_y, fmt= 'or', markersize=5, capsize=5)
|
||||||
|
plt.plot(new_aspect_ratio, Temperatures, '--g')
|
||||||
|
xlabel = 'Aspect Ratio'
|
||||||
|
|
||||||
## Single Modulated Gaussian Beam
|
plt.xlabel(xlabel, fontsize= 12, fontweight='bold')
|
||||||
A = 2*Power/(np.pi*w(y_Positions[idx] , w_x, wavelength)*w(y_Positions[idx], w_z, wavelength))
|
plt.ylabel('Temperature (uK)', fontsize= 12, fontweight='bold')
|
||||||
intensity_profile = A * 1/(2*mod_amp) * np.trapz(np.exp(-2 * (((xmodm - xm)/w(ym, w_x, wavelength))**2 + (zm/w(ym, w_z, wavelength))**2)), dx = dx, axis = -1)
|
plt.tight_layout()
|
||||||
I = intensity_profile[:, idx, :].to(u.MW/(u.cm*u.cm))
|
plt.grid(visible=1)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
|
def plotTrapFrequencies(v_x, v_y, v_z, modulation_depth, new_aspect_ratio, plot_against_mod_depth = True):
|
||||||
U = - U_tilde * I
|
fig, ax3 = plt.subplots(figsize=(8, 6))
|
||||||
U = (U/ac.k_B).to(u.uK)
|
|
||||||
|
|
||||||
poptx, pcovx = extractWaist(x_Positions, U[:, np.where(z_Positions==0)[0][0]])
|
if plot_against_mod_depth:
|
||||||
poptz, pcovz = extractWaist(z_Positions, U[np.where(x_Positions==0)[0][0], :])
|
ln1 = ax3.plot(modulation_depth, v_x, '-ob', label = 'v_x')
|
||||||
|
ln2 = ax3.plot(modulation_depth, v_z, '-^b', label = 'v_z')
|
||||||
|
ax4 = ax3.twinx()
|
||||||
|
ln3 = ax4.plot(modulation_depth, v_y, '-*r', label = 'v_y')
|
||||||
|
xlabel = 'Modulation depth'
|
||||||
|
else:
|
||||||
|
ln1 = ax3.plot(new_aspect_ratio, v_x, '-ob', label = 'v_x')
|
||||||
|
ln2 = ax3.plot(new_aspect_ratio, v_z, '-^b', label = 'v_z')
|
||||||
|
ax4 = ax3.twinx()
|
||||||
|
ln3 = ax4.plot(new_aspect_ratio, v_y, '-*r', label = 'v_y')
|
||||||
|
xlabel = 'Aspect Ratio'
|
||||||
|
|
||||||
extracted_waist_x = poptx[1]
|
ax3.set_xlabel(xlabel, fontsize= 12, fontweight='bold')
|
||||||
dextracted_waist_x = pcovx[1][1]**0.5
|
ax3.set_ylabel('Trap Frequency (Hz)', fontsize= 12, fontweight='bold')
|
||||||
extracted_waist_z = poptz[1]
|
ax3.tick_params(axis="y", labelcolor='b')
|
||||||
dextracted_waist_z = pcovz[1][1]**0.5
|
ax4.set_ylabel('Trap Frequency (Hz)', fontsize= 12, fontweight='bold')
|
||||||
ar = extracted_waist_x/extracted_waist_z
|
ax4.tick_params(axis="y", labelcolor='r')
|
||||||
dar = ar * np.sqrt((dextracted_waist_x/extracted_waist_x)**2 + (dextracted_waist_z/extracted_waist_z)**2)
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
lns = ln1+ln2+ln3
|
||||||
|
labs = [l.get_label() for l in lns]
|
||||||
|
ax3.legend(lns, labs, prop={'size': 12, 'weight': 'bold'})
|
||||||
|
plt.show()
|
||||||
|
|
||||||
fig = plt.figure(figsize=(12, 6))
|
def plotMeasuredTrapFrequencies(w_x, w_z, plot_against_mod_depth = True):
|
||||||
ax = fig.add_subplot(121)
|
fin_mod_dep = [0, 0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]
|
||||||
ax.set_title('Intensity Profile ($MW/cm^2$)\n Aspect Ratio = %.2f \u00B1 %.2f um'% tuple([ar,dar]))
|
fx = [3.135, 0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813]
|
||||||
im = plt.imshow(np.transpose(I.value), cmap="coolwarm", extent=[np.min(x_Positions.value), np.max(x_Positions.value), np.min(z_Positions.value), np.max(z_Positions.value)])
|
dfx = [0.016, 0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024]
|
||||||
plt.xlabel('X - Horizontal (um)', fontsize= 12, fontweight='bold')
|
fz = [2.746, 1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643]
|
||||||
plt.ylabel('Z - Vertical (um)', fontsize= 12, fontweight='bold')
|
dfz = [0.014, 0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033]
|
||||||
ax.set_aspect('equal')
|
|
||||||
fig.colorbar(im, fraction=0.046, pad=0.04, orientation='vertical')
|
|
||||||
|
|
||||||
bx = fig.add_subplot(122)
|
fin_mod_dep_y = [1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1]
|
||||||
bx.set_title('Trap Potential')
|
fy = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02]
|
||||||
plt.plot(x_Positions, U[:, np.where(z_Positions==0)[0][0]], label = 'X - Horizontal')
|
dfy = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31]
|
||||||
plt.plot(z_Positions, U[np.where(x_Positions==0)[0][0], :], label = 'Z - Vertical')
|
|
||||||
plt.ylim(top = 0)
|
alpha_x = [(fx[0]/x)**(2/3) for x in fx]
|
||||||
plt.xlabel('Extent (um)', fontsize= 12, fontweight='bold')
|
dalpha_x = [alpha_x[i] * np.sqrt((dfx[0]/fx[0])**2 + (dfx[i]/fx[i])**2) for i in range(len(fx))]
|
||||||
plt.ylabel('Depth (uK)', fontsize= 12, fontweight='bold')
|
alpha_y = [(fy[0]/y)**2 for y in fy]
|
||||||
plt.tight_layout()
|
dalpha_y = [alpha_y[i] * np.sqrt((dfy[0]/fy[0])**2 + (dfy[i]/fy[i])**2) for i in range(len(fy))]
|
||||||
plt.grid(visible=1)
|
|
||||||
plt.legend(prop={'size': 12, 'weight': 'bold'})
|
avg_alpha = [(g + h) / 2 for g, h in zip(alpha_x, alpha_y)]
|
||||||
plt.show()
|
new_aspect_ratio = (w_x * avg_alpha) / w_z
|
||||||
|
|
||||||
|
|
||||||
|
if plot_against_mod_depth:
|
||||||
|
fig, ax1 = plt.subplots(figsize=(8, 6))
|
||||||
|
ax2 = ax1.twinx()
|
||||||
|
ax1.errorbar(fin_mod_dep, fx, yerr = dfx, fmt= 'or', label = 'v_x', markersize=5, capsize=5)
|
||||||
|
ax2.errorbar(fin_mod_dep_y, fy, yerr = dfy, fmt= '*g', label = 'v_y', markersize=5, capsize=5)
|
||||||
|
ax1.errorbar(fin_mod_dep, fz, yerr = dfz, fmt= '^b', label = 'v_z', markersize=5, capsize=5)
|
||||||
|
ax1.set_xlabel('Modulation depth', fontsize= 12, fontweight='bold')
|
||||||
|
ax1.set_ylabel('Trap Frequency (kHz)', fontsize= 12, fontweight='bold')
|
||||||
|
ax1.tick_params(axis="y", labelcolor='b')
|
||||||
|
ax2.set_ylabel('Trap Frequency (Hz)', fontsize= 12, fontweight='bold')
|
||||||
|
ax2.tick_params(axis="y", labelcolor='r')
|
||||||
|
h1, l1 = ax1.get_legend_handles_labels()
|
||||||
|
h2, l2 = ax2.get_legend_handles_labels()
|
||||||
|
ax1.legend(h1+h2, l1+l2, loc=0)
|
||||||
|
else:
|
||||||
|
plt.figure()
|
||||||
|
plt.errorbar(new_aspect_ratio, fx, yerr = dfx, fmt= 'or', label = 'v_x', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(new_aspect_ratio, fz, yerr = dfz, fmt= '^b', label = 'v_z', markersize=5, capsize=5)
|
||||||
|
plt.xlabel('Aspect Ratio', fontsize= 12, fontweight='bold')
|
||||||
|
plt.ylabel('Trap Frequency (kHz)', fontsize= 12, fontweight='bold')
|
||||||
|
plt.legend(prop={'size': 12, 'weight': 'bold'})
|
||||||
|
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
def plotRatioOfTrapFrequencies(plot_against_mod_depth = True):
|
||||||
|
modulation_depth = [0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]
|
||||||
|
w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]
|
||||||
|
new_aspect_ratio = w_xs / w_z
|
||||||
|
|
||||||
|
v_x = np.zeros(len(modulation_depth))
|
||||||
|
v_y = np.zeros(len(modulation_depth))
|
||||||
|
v_z = np.zeros(len(modulation_depth))
|
||||||
|
|
||||||
|
for i in range(len(modulation_depth)):
|
||||||
|
v_x[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'x').value / 1e3
|
||||||
|
v_y[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'y').value
|
||||||
|
v_z[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'z').value / 1e3
|
||||||
|
|
||||||
|
fx = [0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813]
|
||||||
|
dfx = [0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024]
|
||||||
|
fy = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02]
|
||||||
|
dfy = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31]
|
||||||
|
fz = [1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643]
|
||||||
|
dfz = [0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033]
|
||||||
|
|
||||||
|
plt.figure()
|
||||||
|
|
||||||
|
if plot_against_mod_depth:
|
||||||
|
plt.errorbar(modulation_depth, fx/v_x, yerr = dfx/v_x, fmt= 'or', label = 'b/w horz TF', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(modulation_depth, fy/v_y, yerr = dfy/v_y, fmt= '*g', label = 'b/w axial TF', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(modulation_depth, fz/v_z, yerr = dfz/v_z, fmt= '^b', label = 'b/w vert TF', markersize=5, capsize=5)
|
||||||
|
xlabel = 'Modulation depth'
|
||||||
|
else:
|
||||||
|
plt.errorbar(new_aspect_ratio, fx/v_x, yerr = dfx/v_x, fmt= 'or', label = 'b/w horz TF', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(new_aspect_ratio, fy/v_y, yerr = dfy/v_y, fmt= '*g', label = 'b/w axial TF', markersize=5, capsize=5)
|
||||||
|
plt.errorbar(new_aspect_ratio, fz/v_z, yerr = dfz/v_z, fmt= '^b', label = 'b/w vert TF', markersize=5, capsize=5)
|
||||||
|
xlabel = 'Aspect Ratio'
|
||||||
|
|
||||||
|
plt.xlabel(xlabel, fontsize= 12, fontweight='bold')
|
||||||
|
plt.ylabel('Ratio', fontsize= 12, fontweight='bold')
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
plt.legend(prop={'size': 12, 'weight': 'bold'})
|
||||||
|
plt.show()
|
||||||
|
|
||||||
def plotScatteringLengths():
|
def plotScatteringLengths():
|
||||||
BField = np.arange(0, 2.59, 1e-3) * u.G
|
BField = np.arange(0, 2.59, 1e-3) * u.G
|
||||||
@ -572,6 +842,30 @@ def plotScatteringLengths():
|
|||||||
plt.grid(visible=1)
|
plt.grid(visible=1)
|
||||||
plt.show()
|
plt.show()
|
||||||
|
|
||||||
|
def plotCollisionRatesAndPSD(Gamma_elastic, PSD, modulation_depth, new_aspect_ratio, plot_against_mod_depth = True):
|
||||||
|
fig, ax1 = plt.subplots(figsize=(8, 6))
|
||||||
|
ax2 = ax1.twinx()
|
||||||
|
|
||||||
|
if plot_against_mod_depth:
|
||||||
|
ax1.plot(modulation_depth, Gamma_elastic, '-ob')
|
||||||
|
ax2.plot(modulation_depth, PSD, '-*r')
|
||||||
|
ax2.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.1e'))
|
||||||
|
xlabel = 'Modulation depth'
|
||||||
|
else:
|
||||||
|
ax1.plot(new_aspect_ratio, Gamma_elastic, '-ob')
|
||||||
|
ax2.plot(new_aspect_ratio, PSD, '-*r')
|
||||||
|
ax2.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.1e'))
|
||||||
|
xlabel = 'Aspect Ratio'
|
||||||
|
|
||||||
|
ax1.set_xlabel(xlabel, fontsize= 12, fontweight='bold')
|
||||||
|
ax1.set_ylabel('Elastic Collision Rate', fontsize= 12, fontweight='bold')
|
||||||
|
ax1.tick_params(axis="y", labelcolor='b')
|
||||||
|
ax2.set_ylabel('Phase Space Density', fontsize= 12, fontweight='bold')
|
||||||
|
ax2.tick_params(axis="y", labelcolor='r')
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
#####################################################################
|
#####################################################################
|
||||||
# RUN SCRIPT WITH OPTIONS BELOW #
|
# RUN SCRIPT WITH OPTIONS BELOW #
|
||||||
#####################################################################
|
#####################################################################
|
||||||
@ -587,20 +881,22 @@ if __name__ == '__main__':
|
|||||||
# Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
|
# Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
|
||||||
# w_x, w_z = 54.0*u.um, 54.0*u.um # Beam Waists in the x and y directions
|
# w_x, w_z = 54.0*u.um, 54.0*u.um # Beam Waists in the x and y directions
|
||||||
|
|
||||||
options = {
|
# options = {
|
||||||
'axis': 0, # axis referenced to the beam along which you want the dipole trap potential
|
# 'axis': 0, # axis referenced to the beam along which you want the dipole trap potential
|
||||||
'extent': 3e2, # range of spatial coordinates in one direction to calculate trap potential over
|
# 'extent': 3e2, # range of spatial coordinates in one direction to calculate trap potential over
|
||||||
'modulation': True,
|
# 'crossed': False,
|
||||||
'aspect_ratio': 3.67,
|
# 'theta': 0,
|
||||||
'gravity': False,
|
# 'modulation': True,
|
||||||
'tilt_gravity': False,
|
# 'aspect_ratio': 3.67,
|
||||||
'theta': 5, # in degrees
|
# 'gravity': False,
|
||||||
'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam
|
# 'tilt_gravity': False,
|
||||||
'astigmatism': False,
|
# 'theta': 5, # in degrees
|
||||||
'disp_foci': 3 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um # difference in position of the foci along the propagation direction (Astigmatism)
|
# 'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam
|
||||||
}
|
# 'astigmatism': False,
|
||||||
|
# 'disp_foci': 3 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um # difference in position of the foci along the propagation direction (Astigmatism)
|
||||||
|
# }
|
||||||
|
|
||||||
"""Plot ideal and trap potential resulting for given parameters only"""
|
"""Plot ideal trap potential resulting for given parameters only"""
|
||||||
# ComputedPotentials = []
|
# ComputedPotentials = []
|
||||||
# Params = []
|
# Params = []
|
||||||
|
|
||||||
@ -631,50 +927,170 @@ if __name__ == '__main__':
|
|||||||
|
|
||||||
"""Plot transverse intensity profile and trap potential resulting for given parameters only"""
|
"""Plot transverse intensity profile and trap potential resulting for given parameters only"""
|
||||||
# options = {
|
# options = {
|
||||||
# 'extent': 50, # range of spatial coordinates in one direction to calculate trap potential over
|
# 'extent': 60, # range of spatial coordinates in one direction to calculate trap potential over
|
||||||
# 'modulation': True,
|
# 'modulation': True,
|
||||||
# 'modulation_function': 'arccos',
|
# 'modulation_function': 'arccos',
|
||||||
# 'modulation_amplitude': 2.12
|
# 'modulation_amplitude': 2.16
|
||||||
# }
|
# }
|
||||||
|
|
||||||
# plotIntensityProfileAndPotentials(Power, [w_x, w_z], Polarizability, Wavelength, options)
|
# positions, waists, I, U, p = computeIntensityProfileAndPotentials(Power, [w_x, w_z], Polarizability, Wavelength, options)
|
||||||
|
# plotIntensityProfileAndPotentials(positions, waists, I, U)
|
||||||
|
|
||||||
"""Plot gaussian fit for trap potential resulting from modulation for given parameters only"""
|
"""Plot gaussian fit for trap potential resulting from modulation for given parameters only"""
|
||||||
|
# x_Positions = positions[0].value
|
||||||
|
# z_Positions = positions[1].value
|
||||||
|
# x_Potential = U[:, np.where(z_Positions==0)[0][0]].value
|
||||||
|
# z_Potential = U[np.where(x_Positions==0)[0][0], :].value
|
||||||
|
# poptx, pcovx = p[0], p[1]
|
||||||
|
# poptz, pcovz = p[2], p[3]
|
||||||
# plotGaussianFit(x_Positions, x_Potential, poptx, pcovx)
|
# plotGaussianFit(x_Positions, x_Potential, poptx, pcovx)
|
||||||
# plotGaussianFit(z_Positions, z_Potential, poptx, pcovx)
|
# plotGaussianFit(z_Positions, z_Potential, poptz, pcovz)
|
||||||
|
|
||||||
"""Calculate relevant parameters for evaporative cooling"""
|
"""Calculate relevant parameters for evaporative cooling"""
|
||||||
|
# AtomNumber = 1.00 * 1e7
|
||||||
|
# BField = 2.5 * u.G
|
||||||
|
# modulation = True
|
||||||
|
|
||||||
|
# if modulation:
|
||||||
|
# modulation_depth = 0.6
|
||||||
|
# w_x = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]
|
||||||
|
# Temperature = convert_modulation_depth_to_temperature(modulation_depth)[0] * u.uK
|
||||||
|
# else:
|
||||||
|
# modulation_depth = 0.0
|
||||||
|
# Temperature = convert_modulation_depth_to_temperature(modulation_depth)[0] * u.uK
|
||||||
|
|
||||||
|
# n = particleDensity(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, m = 164*u.u).decompose().to(u.cm**(-3))
|
||||||
|
# Gamma_elastic = calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, B = BField)
|
||||||
|
# PSD = calculatePSD(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature).decompose()
|
||||||
|
|
||||||
|
# print('Particle Density = %.2E ' % (n.value) + str(n.unit))
|
||||||
|
# print('Elastic Collision Rate = %.2f ' % (Gamma_elastic.value) + str(Gamma_elastic.unit))
|
||||||
|
# print('PSD = %.2E ' % (PSD.value))
|
||||||
|
|
||||||
|
# v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
|
||||||
|
# v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
|
||||||
|
# v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
|
||||||
|
|
||||||
|
# print('v_x = %.2f ' %(v_x.value) + str(v_x.unit))
|
||||||
|
# print('v_y = %.2f ' %(v_y.value) + str(v_y.unit))
|
||||||
|
# print('v_z = %.2f ' %(v_z.value) + str(v_z.unit))
|
||||||
|
|
||||||
|
# print('a_s = %.2f ' %(scatteringLength(BField)[0] / ac.a0))
|
||||||
|
|
||||||
|
"""Calculate relevant parameters for evaporative cooling for different modulation depths, temperatures"""
|
||||||
|
|
||||||
AtomNumber = 1.00 * 1e7
|
AtomNumber = 1.00 * 1e7
|
||||||
BField = 2.5 * u.G
|
BField = 1.4 * u.G
|
||||||
modulation = True
|
# modulation_depth = np.arange(0, 1.0, 0.02)
|
||||||
|
|
||||||
if modulation:
|
# w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]
|
||||||
aspect_ratio = 3.67
|
# new_aspect_ratio = w_xs / w_z
|
||||||
init_ar = w_x / w_z
|
# Temperatures = convert_modulation_depth_to_temperature(modulation_depth)[0] * u.uK
|
||||||
w_x = w_x * (aspect_ratio / init_ar)
|
|
||||||
Temperature = 20 * u.uK
|
|
||||||
else:
|
|
||||||
Temperature = 100 * u.uK
|
|
||||||
|
|
||||||
n = particleDensity(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, m = 164*u.u).decompose().to(u.cm**(-3))
|
plot_against_mod_depth = True
|
||||||
Gamma_elastic = calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, B = BField)
|
|
||||||
PSD = calculatePSD(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature).decompose()
|
|
||||||
|
|
||||||
print('Particle Density = %.2E ' % (n.value) + str(n.unit))
|
# # n = np.zeros(len(modulation_depth))
|
||||||
print('Elastic Collision Rate = %.2f ' % (Gamma_elastic.value) + str(Gamma_elastic.unit))
|
# Gamma_elastic = np.zeros(len(modulation_depth))
|
||||||
print('PSD = %.2E ' % (PSD.value))
|
# PSD = np.zeros(len(modulation_depth))
|
||||||
|
# v_x = np.zeros(len(modulation_depth))
|
||||||
|
# v_y = np.zeros(len(modulation_depth))
|
||||||
|
# v_z = np.zeros(len(modulation_depth))
|
||||||
|
|
||||||
v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')
|
# for i in range(len(modulation_depth)):
|
||||||
v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')
|
# # n[i] = particleDensity(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i], m = 164*u.u).decompose().to(u.cm**(-3))
|
||||||
v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')
|
# Gamma_elastic[i] = calculateElasticCollisionRate(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i], B = BField).value
|
||||||
|
# PSD[i] = calculatePSD(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i]).decompose().value
|
||||||
|
|
||||||
print('v_x = %.2f ' %(v_x.value) + str(v_x.unit))
|
# v_x[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'x').value
|
||||||
print('v_y = %.2f ' %(v_y.value) + str(v_y.unit))
|
# v_y[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'y').value
|
||||||
print('v_z = %.2f ' %(v_z.value) + str(v_z.unit))
|
# v_z[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'z').value
|
||||||
|
|
||||||
print('a_s = %.2f ' %(scatteringLength(BField)[0] / ac.a0))
|
"""Plot alphas"""
|
||||||
|
|
||||||
|
# plotAlphas()
|
||||||
|
|
||||||
|
"""Plot Temperatures"""
|
||||||
|
|
||||||
|
# plotTemperatures(w_x, w_z, plot_against_mod_depth = plot_against_mod_depth)
|
||||||
|
|
||||||
|
"""Plot trap frequencies"""
|
||||||
|
|
||||||
|
# plotTrapFrequencies(v_x, v_y, v_z, modulation_depth, new_aspect_ratio, plot_against_mod_depth = plot_against_mod_depth)
|
||||||
|
|
||||||
|
# plotMeasuredTrapFrequencies(w_x, w_z, plot_against_mod_depth = plot_against_mod_depth)
|
||||||
|
|
||||||
|
plotRatioOfTrapFrequencies(plot_against_mod_depth = plot_against_mod_depth)
|
||||||
|
|
||||||
|
"""Plot Feshbach Resonances"""
|
||||||
|
|
||||||
# plotScatteringLengths()
|
# plotScatteringLengths()
|
||||||
|
|
||||||
|
"""Plot Collision Rates and PSD"""
|
||||||
|
|
||||||
|
# plotCollisionRatesAndPSD(Gamma_elastic, PSD, modulation_depth, new_aspect_ratio, plot_against_mod_depth = plot_against_mod_depth)
|
||||||
|
|
||||||
|
"""Plot Collision Rates and PSD from only measured trap frequencies"""
|
||||||
|
|
||||||
|
pd, dpd, T, dT, new_aspect_ratio, modulation_depth = particleDensity(w_x, w_z, Power, Polarizability, AtomNumber, 0, m = 164*u.u, use_measured_tf = True)
|
||||||
|
|
||||||
|
Gamma_elastic = [(pd[i] * scatteringCrossSection(BField) * meanThermalVelocity(T[i]) / (2 * np.sqrt(2))).decompose() for i in range(len(pd))]
|
||||||
|
Gamma_elastic_values = [(Gamma_elastic[i]).value for i in range(len(Gamma_elastic))]
|
||||||
|
dGamma_elastic = [(Gamma_elastic[i] * ((dpd[i]/pd[i]) + (dT[i]/(2*T[i])))).decompose() for i in range(len(Gamma_elastic))]
|
||||||
|
dGamma_elastic_values = [(dGamma_elastic[i]).value for i in range(len(dGamma_elastic))]
|
||||||
|
|
||||||
|
PSD = [((pd[i] * thermaldeBroglieWavelength(T[i])**3).decompose()).value for i in range(len(pd))]
|
||||||
|
dPSD = [((PSD[i] * ((dpd[i]/pd[i]) - (1.5 * dT[i]/T[i]))).decompose()).value for i in range(len(Gamma_elastic))]
|
||||||
|
|
||||||
|
fig, ax1 = plt.subplots(figsize=(8, 6))
|
||||||
|
ax2 = ax1.twinx()
|
||||||
|
ax1.errorbar(modulation_depth, Gamma_elastic_values, yerr = dGamma_elastic_values, fmt = 'ob', markersize=5, capsize=5)
|
||||||
|
ax2.errorbar(modulation_depth, PSD, yerr = dPSD, fmt = '-^r', markersize=5, capsize=5)
|
||||||
|
ax2.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.1e'))
|
||||||
|
ax1.set_xlabel('Modulation depth', fontsize= 12, fontweight='bold')
|
||||||
|
ax1.set_ylabel('Elastic Collision Rate (' + str(Gamma_elastic[0].unit) + ')', fontsize= 12, fontweight='bold')
|
||||||
|
ax1.tick_params(axis="y", labelcolor='b')
|
||||||
|
ax2.set_ylabel('Phase Space Density', fontsize= 12, fontweight='bold')
|
||||||
|
ax2.tick_params(axis="y", labelcolor='r')
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.grid(visible=1)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
"""Plot ideal crossed beam trap potential resulting for given parameters only"""
|
||||||
|
|
||||||
|
# Powers = [40, 11] * u.W
|
||||||
|
# Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
|
||||||
|
# Wavelength = 1.064*u.um
|
||||||
|
# w_x = [27.5, 54]*u.um # Beam Waists in the x direction
|
||||||
|
# w_z = [33.8, 54]*u.um # Beam Waists in the y direction
|
||||||
|
|
||||||
|
# options = {
|
||||||
|
# 'axis': 3, # axis referenced to the beam along which you want the dipole trap potential
|
||||||
|
# 'extent': 1e2, # range of spatial coordinates in one direction to calculate trap potential over
|
||||||
|
# 'crossed': True,
|
||||||
|
# 'theta': 70,
|
||||||
|
# 'modulation': False,
|
||||||
|
# 'aspect_ratio': 5,
|
||||||
|
# 'gravity': False,
|
||||||
|
# 'tilt_gravity': False,
|
||||||
|
# 'theta': 5, # in degrees
|
||||||
|
# 'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam
|
||||||
|
# 'astigmatism': False,
|
||||||
|
# 'disp_foci': 3 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um # difference in position of the foci along the propagation direction (Astigmatism)
|
||||||
|
# }
|
||||||
|
|
||||||
|
# TrapPotential = computeTrapPotential(w_x, w_z, Powers, Polarizability, options)
|
||||||
|
|
||||||
|
# # plt.rcParams["figure.figsize"] = [7.00, 3.50]
|
||||||
|
# # plt.rcParams["figure.autolayout"] = True
|
||||||
|
# # fig = plt.figure()
|
||||||
|
# # ax = fig.add_subplot(111, projection='3d')
|
||||||
|
# # ax.scatter(TrapPotential[0], TrapPotential[1], TrapPotential[2], c=TrapPotential[2], alpha=1)
|
||||||
|
# # plt.show()
|
||||||
|
|
||||||
|
# plt.figure()
|
||||||
|
# plt.plot(TrapPotential[0])
|
||||||
|
# plt.show()
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
Loading…
Reference in New Issue
Block a user