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Thermal Bose distribution
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| #!/usr/bin/env python | |
| """ | |
| Plot the Fock distribution for a thermal state at given frequency | |
| and temperature. | |
| Author: mattia | |
| Last modified: Thu Jan 21, 2021 05:20PM | |
| Version: 1.0 | |
| 3 arguments from command line: | |
| cutoff for Fock number to show, temperature in mK, | |
| frequency in GHz. | |
| """ | |
| import sys | |
| if (len(sys.argv)==1 or len(sys.argv)>6 or any(x in sys.argv for x in | |
| ['-h', '--help'])): | |
| print("""usage: | |
| ./thermal <cutoff> <temperature [mK]> <frequency [GHz]> | |
| [-p, --plot] [-s, --save]""") | |
| quit() | |
| import numpy as np | |
| def nb(freq, temp): | |
| """ | |
| Average number of excitations in thermal bath. | |
| Parameters | |
| ---------- | |
| freq: float | |
| frequency [GHz] | |
| temp: float | |
| temperature [mK] | |
| """ | |
| if temp == 0: | |
| return 0 | |
| else: | |
| return 1./(np.exp(freq/(kT_conv*temp))- 1.) | |
| def be(n, freq, temp): | |
| """ | |
| Bose-Einstein probability distribution. | |
| Parameters | |
| ---------- | |
| n : int | |
| Fock number | |
| freq : float | |
| frquency [GHz] | |
| temp : float | |
| temperature [mK] | |
| """ | |
| return np.exp(-n*freq/(kT_conv*temp))*(1 - np.exp(-freq/(kT_conv*temp))) | |
| if __name__=='__main__': | |
| N = int(sys.argv[1]) | |
| temp = float(sys.argv[2]) #mK | |
| freq = float(sys.argv[3]) #GHz | |
| # Conversion factor: from mK to GHz: | |
| kT_conv = 0.0208366 # GHz/mK | |
| plot = any(x in sys.argv for x in ['-p', '--plot']) | |
| save = any(x in sys.argv for x in ['-s', '--save']) | |
| pns = be(np.arange(N), freq, temp) | |
| print 'Cutoff = {0}.'.format(N) | |
| print 'Temperature = {0:.3f} mK. '.format(temp) | |
| print 'Frequency = {0:.3f} GHz. '.format(freq) | |
| print '\nOccupation probabilities:\n', pns | |
| print '\nAverage occupation number: ', nb(freq, temp) | |
| if save: | |
| np.savetxt('pns.dat', np.vstack((np.arange(N), pns)).T) | |
| if plot: | |
| import matplotlib | |
| matplotlib.use('Qt5Agg') | |
| import matplotlib.pyplot as plt | |
| plt.subplots() | |
| plt.bar(range(N), pns, facecolor='cornflowerblue', edgecolor=None) | |
| plt.xlabel('Fock number') | |
| plt.ylabel('Occupation probability') | |
| plt.xticks(range(N)) | |
| if save: plt.savefig('pns.pdf') | |
| plt.show() | |
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Compute the Fock probability distribution for a thermal state and view it.
Usage
chmod +x thermal;./thermal [args] [options]Options
-hor--help: print help;-sof--save: save data and figure to file;-por--plot: display plot with matplotlib.Args
In this order: