Cosmetic changes
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@ -31,6 +31,11 @@ def rotation_matrix(axis, theta):
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[2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
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[2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])
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def find_nearest(array, value):
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array = np.asarray(array)
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idx = (np.abs(array - value)).argmin()
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return idx
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#####################################################################
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# BEAM PARAMETERS #
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#####################################################################
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@ -44,7 +49,7 @@ def w(pos, w_0, lamb):
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return w_0*np.sqrt(1+(pos / z_R(w_0, lamb))**2)
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#####################################################################
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# RELEVANT PARAMETERS FOR EVAPORATIVE COOLING #
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# COLLISION RATES, PSD #
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#####################################################################
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def meanThermalVelocity(T, m = 164*u.u):
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@ -59,19 +64,65 @@ def particleDensity(w_x, w_z, Power, Polarizability, N, T, m = 164*u.u): # For a
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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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def scatteringLength(B):
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a_bkg = 87 * ac.a0
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#resonanceWidth = 0.005 * u.G
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#resonanceB = 0.5 * u.G
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def scatteringLength(B, FR_choice = 1, ABKG_choice = 1):
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# Dy 164 a_s versus B in 0 to 8G range
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# should match SupMat of PhysRevX.9.021012, fig S5 and descrption
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# https://journals.aps.org/prx/supplemental/10.1103/PhysRevX.9.021012/Resubmission_Suppmat.pdf
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#return a_bkg * (1 - resonanceWidth/(B - resonanceB))
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return a_bkg
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if FR_choice == 1: # new values
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if ABKG_choice == 1:
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a_bkg = 85.5 * ac.a0
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elif ABKG_choice == 2:
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a_bkg = 93.5 * ac.a0
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elif ABKG_choice == 3:
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a_bkg = 77.5 * ac.a0
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#FR resonances
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#[B11 B12 B2 B3 B4 B51 B52 B53 B6 B71 B72 B81 B82 B83 B9]
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resonanceB = [1.295, 1.306, 2.174, 2.336, 2.591, 2.74, 2.803, 2.78, 3.357, 4.949, 5.083, 7.172, 7.204, 7.134, 76.9] * ac.G #resonance position
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#[wB11 wB12 wB2 wB3 wB4 wB51 wB52 wB53 wB6 wB71 wB72 wB81 wB82 wB83 wB9]
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resonancewB = [0.009, 0.010, 0.0005, 0.0005, 0.001, 0.0005, 0.021, 0.015, 0.043, 0.0005, 0.130, 0.024, 0.0005, 0.036, 3.1] * ac.G #resonance width
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#Get scattering length
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BField = np.arange(0, 8, 0.5) * ac.G
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tmp = np.zeros(len(resonanceB)) * ac.a0
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for idx in range(len(resonanceB)):
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tmp[idx] = [(1 - resonancewB[idx] / (BField[j] - resonanceB[idx])) for j in range(len(BField))]
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a_s_array = tmp
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#index = find_nearest(BField.value, B.value)
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a_s = 1 #a_s_array[index]
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else: # old values
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if ABKG_choice == 1:
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a_bkg = 87.2 * ac.a0
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elif ABKG_choice == 2:
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a_bkg = 95.2 * ac.a0
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elif ABKG_choice == 3:
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a_bkg = 79.2 * ac.a0
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#FR resonances
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#[B1 B2 B3 B4 B5 B6 B7 B8]
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resonanceB = [1.298, 2.802, 3.370, 5.092, 7.154, 2.592, 2.338, 2.177] * ac.G #resonance position
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#[wB1 wB2 wB3 wB4 wB5 wB6 wB7 wB8]
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resonancewB = [0.018, 0.047, 0.048, 0.145, 0.020, 0.008, 0.001, 0.001] * ac.G #resonance width
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#Get scattering length
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BField = np.arange(0,8, 0.0001) * ac.G
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a_s_array = np.zeros(len(BField)) * ac.a0
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for idx in range(len(BField)):
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a_s_array[idx] = a_bkg * (1 - resonancewB[idx] / (BField[idx] - resonanceB[idx]))
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index = find_nearest(BField.value, B.value)
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a_s = a_s_array[index]
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return a_s, a_s_array, BField
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def dipolarLength(mu = 9.93 * ac.muB, m = 164*u.u):
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return (m * ac.mu0 * mu**2) / (12 * np.pi * ac.hbar**2)
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def scatteringCrossSection(B):
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return 8 * np.pi * scatteringLength(B)**2 + ((32*np.pi)/45) * dipolarLength()**2
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return 8 * np.pi * scatteringLength(B)[0]**2 + ((32*np.pi)/45) * dipolarLength()**2
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def calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N, T, B): #For a 3D Harmonic Trap
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return (particleDensity(w_x, w_z, Power, Polarizability, N, T) * scatteringCrossSection(B) * meanThermalVelocity(T) / (2 * np.sqrt(2))).decompose()
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@ -320,17 +371,16 @@ if __name__ == '__main__':
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Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
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w_x, w_z = 27.5*u.um, 33.8*u.um # Beam Waists in the x and y directions
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AspectRatio = 4.6
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w_x = AspectRatio * w_x
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options = {
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'axis': 1, # axis referenced to the beam along which you want the dipole trap potential
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'extent': 1e4, # range of spatial coordinates in one direction to calculate trap potential over
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'modulation': True,
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'aspect_ratio': 4.6,
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'gravity': True,
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'astigmatism': False,
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'tilt_gravity': True,
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'theta': 5, # in degrees
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'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam
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'astigmatism': False,
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'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)
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}
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@ -347,23 +397,29 @@ if __name__ == '__main__':
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AtomNumber = 1.13 * 1e7
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Temperature = 30 * u.uK
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BField = 0 * u.G
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BField = 1 * u.G
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n = particleDensity(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, m = 164*u.u).decompose().to(u.cm**(-3))
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Gamma_elastic = calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, B = BField)
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PSD = calculatePSD(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature).decompose()
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print('%.2E' % (n.value)* (n.unit))
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print('%.2f' % (Gamma_elastic.value) * (Gamma_elastic.unit))
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print('%.2E' % (PSD.value))
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print('Particle Density = %.2E ' % (n.value) + str(n.unit))
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print('Elastic Collision Rate = %.2f ' % (Gamma_elastic.value) + str(Gamma_elastic.unit))
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print('PSD = %.2E ' % (PSD.value))
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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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print(v_x)
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print(v_y)
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print(v_z)
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print('v_x = %.2f ' %(v_x.value) + str(v_x.unit))
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print('v_y = %.2f ' %(v_y.value) + str(v_y.unit))
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print('v_z = %.2f ' %(v_z.value) + str(v_z.unit))
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#plt.figure()
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ret = scatteringLength(1 * ac.G)
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print(ret[1])
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#plt.plot(ret[2], ret[1])
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#plt.show()
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# v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, options['axis'])
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# plotHarmonicFit(Positions, TrappingPotential, TrapDepthsInKelvin, options['axis'], popt, pcov)
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