108 lines
6.1 KiB
Python
108 lines
6.1 KiB
Python
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import numpy as np
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from astropy import units as u, constants as ac
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from Helpers import *
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DY_POLARIZABILITY = 184.4 # in a.u, most precise measured value of Dy polarizability
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DY_MASS = 164*u.u
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DY_DIPOLE_MOMENT = 9.93 * ac.muB
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#####################################################################
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# POTENTIALS #
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#####################################################################
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def gravitational_potential(positions, m):
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return m * ac.g0 * positions
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def single_gaussian_beam_potential(positions, waists, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um):
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A = 2*P/(np.pi*w(positions[1,:], waists[0], wavelength)*w(positions[1,:], waists[1], wavelength))
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U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
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U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:], waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:], waists[1], wavelength))**2))
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return U
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def astigmatic_single_gaussian_beam_potential(positions, waists, del_y, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um):
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A = 2*P/(np.pi*w(positions[1,:] - (del_y/2), waists[0], wavelength)*w(positions[1,:] + (del_y/2), waists[1], wavelength))
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U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
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U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:] - (del_y/2), waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:] + (del_y/2), waists[1], wavelength))**2))
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return U
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def modulated_single_gaussian_beam_potential(positions, waists, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um, mod_amp=1):
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mod_amp = mod_amp * waists[0]
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n_points = len(positions[0,:])
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dx, x_mod = modulation_function(mod_amp, n_points, func = 'arccos')
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A = 2*P/(np.pi*w(positions[1,:], waists[0], wavelength)*w(positions[1,:], waists[1], wavelength))
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U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
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dU = np.zeros(2*n_points)
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for i in range(len(x_mod)):
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dU = np.vstack((dU, np.exp(-2 * (np.subtract(x_mod[i], positions[0,:])/w(positions[1,:], waists[0], wavelength))**2)))
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U = - U_tilde * A * 1/(2*mod_amp) * np.trapz(dU, dx = dx, axis = 0)
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return U
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def harmonic_potential(pos, v, xoffset, yoffset, m = DY_MASS):
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U_Harmonic = ((0.5 * m * (2 * np.pi * v*u.Hz)**2 * (pos*u.um - xoffset*u.um)**2)/ac.k_B).to(u.uK) + yoffset*u.uK
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return U_Harmonic.value
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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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return U_Gaussian
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def crossed_beam_potential(positions, waists, P, options, alpha = DY_POLARIZABILITY, wavelength=1.064*u.um):
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delta = options['delta']
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foci_shift = options['foci_shift']
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focus_shift_beam_1 = foci_shift[0]
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focus_shift_beam_2 = foci_shift[1]
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beam_disp = options['beam_disp']
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beam_1_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[0])).T * beam_disp[0].unit
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beam_2_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[1])).T * beam_disp[1].unit
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beam_1_positions = positions + beam_1_disp
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A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][0], wavelength)*w(beam_1_positions[1,:] + focus_shift_beam_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,:] + focus_shift_beam_1, waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][1], wavelength))**2))
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R = rotation_matrix([0, 0, 1], np.radians(delta))
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beam_2_positions = np.dot(R, positions + beam_2_disp)
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A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][0], wavelength)*w(beam_2_positions[1,:] + focus_shift_beam_2, 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,:] + focus_shift_beam_2, waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][1], wavelength))**2))
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U = U_1 + U_2
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return U
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def astigmatic_crossed_beam_potential(positions, waists, P, options, alpha = DY_POLARIZABILITY, wavelength=1.064*u.um):
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delta = options['delta']
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del_y = options['foci_disp_crossed']
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del_y_1 = del_y[0]
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del_y_2 = del_y[1]
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foci_shift = options['foci_shift']
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focus_shift_beam_1 = foci_shift[0]
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focus_shift_beam_2 = foci_shift[1]
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beam_disp = options['beam_disp']
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beam_1_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[0])).T * beam_disp[0].unit
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beam_2_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[1])).T * beam_disp[1].unit
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beam_1_positions = positions + beam_1_disp
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A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:] - (del_y_1/2) + focus_shift_beam_1, waists[0][0], wavelength)*w(beam_1_positions[1,:] + (del_y_1/2) + focus_shift_beam_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,:] - (del_y_1/2) + focus_shift_beam_1, waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:] + (del_y_1/2) + focus_shift_beam_1, waists[0][1], wavelength))**2))
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R = rotation_matrix([0, 0, 1], np.radians(delta))
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beam_2_positions = np.dot(R, positions + beam_2_disp)
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A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:] - (del_y_2/2) + focus_shift_beam_2, waists[1][0], wavelength)*w(beam_2_positions[1,:] + (del_y_2/2) + focus_shift_beam_2, 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,:] - (del_y_2/2) + focus_shift_beam_2, waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:] + (del_y_2/2) + focus_shift_beam_2, waists[1][1], wavelength))**2))
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U = U_1 + U_2
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return U
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