def showResult():
wavelength = float(entrystrings[0].get()) # laser wavelength in nm
beamwaist = float(entrystrings[1].get()) # beam waist in m
power = float(entrystrings[2].get()) # power in Watts
bprop = [wavelength, power, beamwaist] # collect beam properties
atomSymbol = entrystrings[3].get() # choose Rb or Cs
L = int(entrystrings[4].get()) # orbital angular momentum
J = float(entrystrings[5].get()) # total angular momentum
# choose element
if atomSymbol == "Rb":
atomObj = Rb
elif atomSymbol == "Cs":
atomObj = Cs
else:
messagebox.showinfo("Error", "You must choose Rb or Cs")
return 0
# get transition data for the given state
if L == 0:
D0, w0, lw, nlj = atomObj.D0S, atomObj.w0S, atomObj.lwS, atomObj.nljS
elif L == 1 and J == 0.5:
D0, w0, lw, nlj = atomObj.D0P1, atomObj.w0P1, atomObj.lwP1, atomObj.nljP1
elif L == 1 and J == 1.5:
D0, w0, lw, nlj = atomObj.D0P3, atomObj.w0P3, atomObj.lwP3, atomObj.nljP3
# construct the instance of the dipole class
dipoleObj = dipole(atomObj.m, (L, J),
bprop,
D0,
w0,
lw,
nlj,
nuclear_spin=atomObj.I,
symbol=atomObj.X)
messagebox.showinfo("Calculation Result", getStarkShift(dipoleObj))
return lc
#### Rb ####
# beam properties:
wavelength = 810e-9 # laser wavelength in m
power = 5e-3 # laser power in W
beamwaist = 1e-6 # tweezer trap beam waist in m
bprop = [wavelength, power, beamwaist]
# create dipole objects for ground and excited states
Rb5S = dipole(Rb.m, (0, 1 / 2.),
bprop,
Rb.D0S,
Rb.w0S,
Rb.lwS,
Rb.nljS,
nuclear_spin=Rb.I,
symbol=Rb.X,
Ahfs=Rb.AhS)
Rb5P = dipole(Rb.m, (1, 3 / 2.),
bprop,
Rb.D0P3,
Rb.w0P3,
Rb.lwP3,
Rb.nljP3,
nuclear_spin=Rb.I,
symbol=Rb.X,
Ahfs=Rb.AhP3,
Bhfs=Rb.BhP3)
def plotStarkShifts(
wavelength=880e-9, # laser wavelength in nm
beamwaist=1e-6, # beam waist in m
power=20e-3): # power in Watts
"""Find the ac Stark Shifts in Rb, Cs assuming hyperfine splitting is negligible"""
# typical optical tweezer parameters:
bprop = [wavelength, power, beamwaist] # collect beam properties
# mass, (L,J,F,MF), bprop, dipole matrix elements (Cm), resonant frequencies (rad/s),
# linewidths (rad/s), state labels, nuclear spin, atomic symbol.
Rb5S = dipole(Rb.m, (0, 1 / 2.),
bprop,
Rb.D0S,
Rb.w0S,
Rb.lwS,
Rb.nljS,
nuclear_spin=Rb.I,
symbol=Rb.X,
Ahfs=Rb.AhS)
Rb5P = dipole(Rb.m, (1, 3 / 2.),
bprop,
Rb.D0P3,
Rb.w0P3,
Rb.lwP3,
Rb.nljP3,
nuclear_spin=Rb.I,
symbol=Rb.X,
Ahfs=Rb.AhP3,
Bhfs=Rb.BhP3)
Cs6S = dipole(Cs.m, (0, 1 / 2.),
bprop,
Cs.D0S,
Cs.w0S,
Cs.lwS,
Cs.nljS,
nuclear_spin=Cs.I,
symbol=Cs.X,
Ahfs=Cs.AhS)
Cs6P = dipole(Cs.m, (1, 3 / 2.),
bprop,
Cs.D0P3,
Cs.w0P3,
Cs.lwP3,
Cs.nljP3,
nuclear_spin=Cs.I,
symbol=Cs.X,
Ahfs=Cs.AhP3,
Bhfs=Cs.BhP3)
# need a small spacing to resolve the magic wavelengths - so it will run slow
# to resolve magic wavelengths, take about 10,000 points. Hac, eigenvectors, Hhfs, F_labels, MF_labels
wavels = np.linspace(700e-9, 1100e-9, 2000)
# ac Stark Shift in Joules:
dE6S = Cs6S.acStarkShift(0, 0, 0, wavels, mj=0.5)
dE6P = Cs6P.acStarkShift(0, 0, 0, wavels, mj=1.5)
dif6P = dE6P - dE6S
magic6P = getMagicWavelengths(dif6P, dE6P, wavels)
plt.figure()
plt.title("AC Stark Shift in $^{133}$Cs")
plt.plot(wavels * 1e9,
dE6S / h * 1e-6,
'b--',
label='Ground State S$_{1/2}$')
plt.plot(wavels * 1e9,
dE6P / h * 1e-6,
'r-.',
label='Excited State P$_{3/2}$')
# plt.plot(wavels*1e9, (dif6P)/h*1e-6, 'k', label='Difference')
plt.plot([magic6P[0] * 1e9] * 2,
[min(dif6P / h / 1e6), max(dif6P / h / 1e6)],
'm:',
label='Magic Wavelength')
plt.legend()
for mw in magic6P[1:]:
plt.plot(
[mw * 1e9] * 2,
[min(dif6P / h / 1e6), max(dif6P / h / 1e6)], 'm:')
plt.ylabel("Stark Shift (MHz)")
plt.xlabel("Wavelength (nm)")
plt.xlim(wavels[0] * 1e9, wavels[-1] * 1e9)
plt.ylim(-2200, 2200)
plt.plot(wavels * 1e9, np.zeros(len(wavels)), 'k',
alpha=0.25) # show zero crossing
plt.show()
print("Magic wavelengths at:\n", magic6P)
# ac Stark Shift in Joules:
dE5S = Rb5S.acStarkShift(0, 0, 0, wavels, mj=0.5)
dE5P = Rb5P.acStarkShift(0, 0, 0, wavels, mj=1.5)
dif5P = dE5P - dE5S
plt.figure()
plt.title("AC Stark Shift in $^{87}$Rb")
plt.plot(wavels * 1e9,
dE5S / h * 1e-6,
'b--',
label='Ground State S$_{1/2}$')
plt.plot(wavels * 1e9,
dE5P / h * 1e-6,
'r-.',
label='Excited State P$_{3/2}$')
# plt.plot(wavels*1e9, (dif5P)/h*1e-6, 'k', label='Difference')
plt.legend()
plt.ylabel("Stark Shift (MHz)")
plt.xlabel("Wavelength (nm)")
plt.ylim(-500, 500)
plt.plot(wavels * 1e9, np.zeros(len(wavels)), 'k',
alpha=0.25) # show zero crossing
plt.show()
def compareArora():
"""Plot Fig. 5 - 8 in Arora et al 2007 to show that the polarisabilities
of Rb and Cs without hyperfine levels are correct"""
# beam properties: wavelength, power, beam waist
# intensity set to 1e10 MW/cm^2
bprop = [1064e-9, np.pi * 0.5e-2, 1e-6]
numpoints = 100
for ATOM in [Rb, Cs]:
if ATOM == Rb:
wavel1 = np.linspace(780, 800, numpoints) * 1e-9
Ylim1 = (-8000, 8000)
wavel2 = np.linspace(787, 794, numpoints) * 1e-9
Ylim2 = (-1000, 1000)
FP = 3
elif ATOM == Cs:
wavel1 = np.linspace(925, 1000, numpoints) * 1e-9
Ylim1 = (-1000, 5000)
wavel2 = np.linspace(927, 945, numpoints) * 1e-9
Ylim2 = (-100, 100)
FP = 5
S = dipole(ATOM.m, (0, 1 / 2.),
bprop,
ATOM.D0S,
ATOM.w0S,
ATOM.lwS,
ATOM.nljS,
nuclear_spin=ATOM.I,
symbol=ATOM.X)
P3 = dipole(ATOM.m, (1, 3 / 2.),
bprop,
ATOM.D0P3,
ATOM.w0P3,
ATOM.lwP3,
ATOM.nljP3,
nuclear_spin=ATOM.I,
symbol=ATOM.X)
# compare polarisability of excited states
plt.figure()
plt.title("Polarisability of " + ATOM.X)
plt.plot(wavel1 * 1e9, S.polarisability(wavel1) / au, 'r', label='s')
plt.plot(wavel1 * 1e9,
P3.polarisability(wavel1, mj=0.5) / au,
'g--',
label='p$_{3/2}$, mj=1/2')
plt.plot(wavel1 * 1e9,
P3.polarisability(wavel1, mj=1.5) / au,
'm:',
label='p$_{3/2}$, mj=3/2')
plt.legend()
plt.xlabel("Wavelength (nm)")
plt.ylabel("Polarisability (a.u.)")
plt.ylim(Ylim1)
plt.xlim(wavel1[0] * 1e9, wavel1[-1] * 1e9)
# calculate stark shifts between F, MF states
mfLS = ['r', 'g--', 'm:', 'c-.', 'k-.', 'y'] # line styles
plt.figure()
plt.title(
"AC Stark Shifts for transitions from P$_{3/2}$ |F'=3, m$_F'\\rangle$ to \nthe groundstate in "
+ ATOM.X)
ES = np.zeros(len(wavel2))
EP3 = np.zeros((FP + 1, len(wavel2)))
for i in range(len(wavel2)):
ES[i] = S.diagH(wavel2[i], 0, 0,
0)[0][0] # ground state shift is independent of MF
EP3vals, _, _, Fs, MFs = P3.diagH(
wavel2[i], 0, 0,
0) # get eigenvalues of excited state stark shift operator
EP3[:, i] = EP3vals[-FP - 1:] # only interested in F' = F
for MF in range(FP +
1): # the shift only depends on the magnitude of MF
plt.plot(wavel2 * 1e9, (EP3[MF] - ES) / h / 1e6,
mfLS[MF],
label='m$_F$ = $\pm$' + str(MF))
xlims = [wavel2[0] * 1e9, wavel2[-1] * 1e9]
plt.plot(xlims, [0, 0], 'k:', alpha=0.4) # show where zero is
plt.ylim(Ylim2)
plt.xlim(xlims)
plt.xlabel("Wavelength (nm)")
plt.ylabel("Stark Shift (MHz)")
plt.legend()
plt.show()
"%s,%s,%s,%.16e,%.16e,%.16e\n" %
(int(DATA[0][i][0]), int(DATA[0][i][1]),
float(DATA[0][i][2]), abs(DATA[2][i]), DATA[1][i],
(2 * np.pi / abs(DATA[1][i]))**3 * DATA[2][i]**2 /
3. / np.pi / hbar / eps0 /
(2. * DATA[0][i][2] + 1)))
else:
f.write("%s,%s,%s,%.16e,%.16e,%.16e\n" %
(int(DATA[0][i][0]), int(DATA[0][i][1]),
float(DATA[0][i][2]), abs(
DATA[2][i]), DATA[1][i], 0))
if __name__ == "__main__":
# run GUI by passing an arg:
if np.size(sys.argv) > 1 and sys.argv[1] == 'rungui':
runGUI()
sys.exit() # don't run any of the other code below
Rb5P = dipole(Rb.m, (1, 3 / 2.), [1064e-9, 20e-3, 1e-6],
Rb.D0P3,
Rb.w0P3,
Rb.lwP3,
Rb.nljP3,
nuclear_spin=Rb.I,
symbol=Rb.X,
Ahfs=Rb.AhP3,
Bhfs=Rb.BhP3)
print(getStarkShift(Rb5P))
compareArora()