def compareKien():
"""compare Kien 2013 Fig 4,5"""
bprop =[880e-9,20e-3,1e-6]
Cs = atom(atm = 'Cs133')
Cs880 = dipole(Cs, (0,1/2.,3,3), bprop)
CsP = dipole(Cs, (1,3/2.,3,3), bprop)
wls = [np.linspace(680, 690, 200)*1e-9, np.linspace(930, 940, 200)*1e-9]
ylims = [(-1200, 300), (-3000, 6000)]
for ii in range(2):
plt.figure()
plt.title("Cs Polarisabilities. Red: 6S$_{1/2}$, Blue: 6P$_{3/2}$.\nscalar: solid, vector: dashed, tensor: dotted")
a1 = Cs880.polarisability(wls[ii],mj=0.5,split=True)
a2 = 0.5*(np.array(CsP.polarisability(wls[ii],mj=1.5, split=True))+
np.array(CsP.polarisability(wls[ii],mj=0.5, split=True)))
ls = ['-', '--', ':']
for i in range(3):
plt.plot(wls[ii]*1e9, a1[i]/au, 'r', linestyle=ls[i], label="Cs")
plt.plot(wls[ii]*1e9, a2[i]/au, 'b', linestyle=ls[i], label="$P_{3/2}$")
#plt.legend()
plt.ylim(ylims[ii])
plt.xlabel("Wavelength (nm)")
plt.ylabel("Polarisablity (a.u.)")
plt.show()
def vmfSS(ATOM):
"""Return the Stark shifts of the MF states for Cs cooling/repump transitions"""
plt.figure()
if ATOM.atm == 'Cs133':
Cs = ATOM
F = 5
bprop = [938e-9, 8e-3, 1.7e-6] # wavelength, beam power, beam waist
for MFp in range(-F, F+1, 1):
P = dipole(Cs, (1,3/2.,F,MFp), bprop)
Pshift = P.acStarkShift(0,0,0, bprop[0], HF=True)/h/1e6 # interested in how the EStates shift relative to each other
plt.plot(MFp, Pshift, '_', markersize=15, linewidth=10, color = '#7E317B')
print("|F' = "+str(F)+", m_F' = "+str(MFp)+"> : %.5g MHz"%Pshift)
elif ATOM.atm == 'Rb87':
Rb = ATOM
F = 3
bprop = [940e-9, 35e-3, 1.7e-6] # wavelength, beam power, beam waist
for MFp in range(-F, F+1, 1):
P = dipole(Rb, (1,3/2.,F,MFp), bprop)
Pshift = P.acStarkShift(0,0,0, bprop[0], HF=True)/h/1e6 # interested in how the EStates shift relative to each other
s, v, t = P.polarisability(bprop[0], mj=3/2, HF=False, split=True)
# print('split ',s/au, t/au)
s, v, t = P.polarisability(bprop[0], mj=3/2, HF=True, split=True)
# print('avrge ',s/au, t/au)
plt.plot(MFp, Pshift, '_', markersize=15, linewidth=10, color = '#7E317B')
print("|F' = "+str(F)+", m_F' = "+str(MFp)+"> : %.5g MHz"%Pshift)
plt.title('Stark Shifts of ' + ATOM.atm + " |F' = " + str(F) + ', $M_F$> states' )
plt.xlabel("$M_F$")
plt.ylabel("AC Stark Shift (MHz)")
plt.show()
def getMFStarkShifts(
wavelength=1064e-9, # laser wavelength in m
power=0.00906143, # laser power in W
beamwaist=1e-6, # beam waist in m
plotit=False): # toggle to plot the results
"""Return the Stark shifts of the MF states for cooling/repump transitions.
Units are MHz"""
bprop = [wavelength, power, beamwaist] # collect beam properties
Fs = [1, 2]
numstates = sum(2 * np.array(Fs) +
1) * 3 # total number of hyperfine transitions
l1 = [6, 12] # index of lines for making legend
#
states = np.zeros((numstates, 3), dtype=int) # F, MF, MFprime
shifts = np.zeros(numstates) # differential ac Stark shifts
i = 0 # index
for F in Fs:
for MF in range(-F, F + 1):
for MFp in range(MF - 1, MF + 2):
S = dipole(Rb, (0, 1 / 2., F, MF), bprop)
P = dipole(Rb, (1, 3 / 2., F + 1, MFp), bprop)
#
states[i] = (F, MF, MFp)
# units are MHz
shifts[i] = (
S.acStarkShift(0, 0, 0, bprop[0], HF=True) -
P.acStarkShift(0, 0, 0, bprop[0], HF=True)) / h / 1e6
i += 1
#
if plotit:
plt.figure()
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
i = 0
for F, MF, MFp in states:
if MF != 0:
deltaMF = (MFp - MF) * np.sign(MF)
else:
deltaMF = (MFp - MF)
plt.plot(MF,
shifts[i],
'_',
color=colors[F - 1],
alpha=0.33 * (2 + deltaMF),
markersize=15,
linewidth=10)
i += 1
plt.xlabel("$M_F$")
plt.ylabel("AC Stark Shift (MHz)")
lines = plt.gca().lines
plt.legend(lines[l1[0]:l1[1]], [
'F=' + str(f) + r', $\Delta M_F=$' + str(-dmf)
for f in range(min(Fs),
max(Fs) + 1) for dmf in range(-1, 2)
])
plt.show()
#
return states, shifts
def getMFStarkShifts():
"""Return the Stark shifts of the MF states for Cs cooling/repump transitions"""
print(
"stark shift of Cs 6S1/2 -> 6P3/2 for different MF states at 1064nm for beam power 6 mW, beam waist 1 micron, giving trap depth 1 mK"
)
bprop = [1064e-9, 6e-3, 1e-6] # wavelength, beam power, beam waist
plt.figure()
# colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
colors = ['k', 'r']
for F in [3, 4]:
for MF in range(-F, F + 1):
print(" ----- |F = " + str(F) + ", m_F = " + str(MF) + ">")
for MFp in range(MF - 1, MF + 2):
S = dipole(Cs.m, (0, 1 / 2., F, MF),
bprop,
Cs.D0S,
Cs.w0S,
Cs.lwS,
Cs.nljS,
nuclear_spin=Cs.I,
symbol=Cs.X)
P = dipole(Cs.m, (1, 3 / 2., F + 1, MFp),
bprop,
Cs.D0P3,
Cs.w0P3,
Cs.lwP3,
Cs.nljP3,
nuclear_spin=Cs.I,
symbol=Cs.X)
shift = (S.acStarkShift(0, 0, 0, bprop[0], HF=True) -
P.acStarkShift(0, 0, 0, bprop[0], HF=True)) / h / 1e6
if MF != 0:
deltaMF = (MFp - MF) * np.sign(MF)
else:
deltaMF = (MFp - MF)
plt.plot(MF,
shift,
'_',
color=colors[F - 3],
alpha=0.33 * (2 + deltaMF),
markersize=15,
linewidth=10)
print("|F' = " + str(F + 1) + ", m_F' = " + str(MFp) +
"> : %.5g MHz" % shift)
plt.xlabel("$M_F$")
plt.ylabel("AC Stark Shift (MHz)")
lines = plt.gca().lines
plt.legend(lines[18:24], [
'F=' + str(f) + ', $\Delta M_F=$' + str(-dmf) for f in range(3, 5)
for dmf in range(-1, 2)
])
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]
for ATOM in [atom(atm = 'Rb87'), atom(atm = 'Cs133')]:
if ATOM.X == 'Rb87':
wavel1 = np.linspace(780, 800, 200)*1e-9
Ylim1 = (-8000, 8000)
wavel2 = np.linspace(787,794, 200)*1e-9
Ylim2 = (-1000, 1000)
FS, FP = 1, 3
elif ATOM.X == 'Cs133':
wavel1 = np.linspace(925, 1000, 200)*1e-9
Ylim1 = (-1000, 5000)
wavel2 = np.linspace(927, 945, 200)*1e-9
Ylim2 = (-100, 100)
FS, FP = 3, 5
S = dipole(ATOM, (0,1/2.,FS,FS), bprop)
P3 = dipole(ATOM, (1,3/2.,FP,FP), bprop)
# 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$_{3/2}$ m$_F$ to \nthe groundstate in "+ATOM.X)
dES = S.acStarkShift(0,0,0, wavel2, HF=True) # ground state stark shift
for MF in range(FP+1):
P3.MF = MF
dEPMF = P3.acStarkShift(0,0,0, wavel2, HF=True) # excited MF state stark shift
plt.plot(wavel2*1e9, (dEPMF - dES)/h/1e6, mfLS[MF], label=r'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()
def plotPolarisability():
"""Plot the polarisability of Rb 5S and Cs 6S states highlighting our laser wavelengths"""
bprop = [1064e-9, 6e-3, 1e-6] # wavelength, beam power, beam waist
wavelengths = np.linspace(700, 1100, 500) * 1e-9 # in m
ymax = 5000
# groundstate rubidium
Rb5S = dipole(Rb, (0, 1 / 2., 1, 1), bprop)
alphaRb = Rb5S.polarisability(
wavelengths) / au # polarisability in atomic units
# groundstate caesium
Cs6S = dipole(Cs, (0, 1 / 2., 4, 4), bprop)
alphaCs = Cs6S.polarisability(
wavelengths) / au # polarisability in atomic units
plt.figure()
# split up the plotting so as not to have lines at resonances:
for v in [[alphaRb, DUsea_blue, 'Rb 5S$_{1/2}$'],
[alphaCs, DUcherry_red, 'Cs 6S$_{1/2}$']]:
plus = np.where(v[0] > 0)[0] # where polarisability is positive
ind1 = plus[np.where(plus > np.arange(len(plus)) +
plus[0])[0][0]] # second positive region
plt.plot(wavelengths[:plus[0] - 1] * 1e9,
v[0][:plus[0] - 1],
color=v[1],
label=v[2])
plt.plot(wavelengths[plus[0] + 1:ind1 - 1] * 1e9,
v[0][plus[0] + 1:ind1 - 1],
color=v[1])
plt.plot(wavelengths[ind1 + 1:] * 1e9, v[0][ind1 + 1:], color=v[1])
# plot dotted lines to show where the resonances are
plt.plot([780] * 2, [-ymax, ymax], '--', color=DUsea_blue)
plt.plot([795] * 2, [-ymax, ymax], '--', color=DUsea_blue)
plt.plot([852.3] * 2, [-ymax, ymax], '--', color=DUcherry_red)
plt.plot([894.6] * 2, [-ymax, ymax], '--', color=DUcherry_red)
# show zero crossing
plt.plot([wavelengths[0] * 1e9, wavelengths[-1] * 1e9], [0, 0],
'k--',
alpha=0.4)
# show laser wavelengths
# plt.fill_between([1060,1070], ymax, -ymax, color=DUcherry_red, alpha=0.3)
# plt.fill_between([935,945], ymax, -ymax, color=DUcherry_red, alpha=0.3)
# plt.fill_between([878, 882], ymax, -ymax, color=DUsea_blue, alpha=0.3)
# plt.fill_between([805,825], ymax, -ymax, color=DUsea_blue, alpha=0.3)
plt.ylim((-ymax, ymax))
plt.ylabel('Polarisability ($a_0^3$)')
plt.xlim((wavelengths[0] * 1e9, wavelengths[-1] * 1e9))
plt.xlabel('Wavelength (nm)')
plt.legend()
plt.tight_layout()
plt.show()
def getMFStarkShifts(
wavelength=1064e-9, # laser wavelength in m
power=0.00906143, # laser power in W
beamwaist=1e-6, # beam waist in m
ATOM=Cs):
"""Return the Stark shifts of the MF states for cooling/repump transitions"""
bprop = [wavelength, power, beamwaist] # collect beam properties
if ATOM == Cs: # assign the relevant hyperfine transitions
Fs = [3, 4]
l1 = [18, 24] # index of lines for making legend
elif ATOM == Rb:
Fs = [1, 2]
l1 = [6, 12] # index of lines for making legend
# print("Stark shift of "+ATOM.X+" S1/2 F = %s, %s -> P3/2 F' = %s, %s for different MF states."%(Fs[0],Fs[0]+1,Fs[1],Fs[1]+1))
plt.figure()
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
for F in Fs:
for MF in range(-F, F + 1):
print(" ----- |F = " + str(F) + ", m_F = " + str(MF) + ">")
for MFp in range(MF - 1, MF + 2):
S = dipole(ATOM, (0, 1 / 2., F, MF), bprop)
P = dipole(ATOM(1, 3 / 2., F + 1, MFp), bprop)
shift = (S.acStarkShift(0, 0, 0, bprop[0], HF=True) -
P.acStarkShift(0, 0, 0, bprop[0], HF=True)) / h / 1e6
if MF != 0:
deltaMF = (MFp - MF) * np.sign(MF)
else:
deltaMF = (MFp - MF)
plt.plot(MF,
shift,
'_',
color=colors[F - 1],
alpha=0.33 * (2 + deltaMF),
markersize=15,
linewidth=10)
print("|F' = " + str(F + 1) + ", m_F' = " + str(MFp) +
"> : %.5g MHz" % shift)
plt.xlabel("$M_F$")
plt.ylabel("Differential AC Stark Shift (MHz)")
lines = plt.gca().lines
plt.legend(lines[l1[0]:l1[1]], [
'F=' + str(f) + r', $\Delta M_F=$' + str(-dmf)
for f in range(min(Fs),
max(Fs) + 1) for dmf in range(-1, 2)
])
plt.show()
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
F = 1
elif atomSymbol == "Cs":
atomObj = Cs
F = 3
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, (L, J, F, F), bprop)
messagebox.showinfo("Calculation Result", getStarkShift(dipoleObj))
def heatRate(wl, P, w0, trapfreq, X=Rb):
"""heating rate in units of vibrational quanta per second
wl - wavelength (m)
P - beam power (W)
w0 - beam waist (m)
trapfreq - atomic trap frequency (rad/s)
X - instance of atom() class from AtomFieldInt_V3"""
atom = dipole(X, (0,1/2.,1,1), [wl, P, w0])
return atom.scatRate() * hbar * (2*np.pi/wl)**2 / 2 / X.m / trapfreq
# compare trapping frequencies and Rabi frequencies between Rb/Cs
def wz(atom):
"""Axial trapping freq"""
return np.sqrt(
2 * np.abs(atom.acStarkShift(0, 0, 0) / atom.m / atom.field.zR**2))
def wr(atom):
"""Radial trap freq"""
return np.sqrt(
4 * np.abs(atom.acStarkShift(0, 0, 0) / atom.m / atom.field.w0**2))
rb5s = dipole(Rb, (0, 1 / 2., 1, 1), [814e-9, 1.46e-3, 1e-6])
print(rb5s.acStarkShift(0, 0, 0) / h / 1e6 / 20.7)
cs6s = dipole(Cs, (0, 1 / 2., 3, 3), [940e-9, 5.02e-3, 1.1e-6])
print(cs6s.acStarkShift(0, 0, 0) / h / 1e6 / 20.7)
print((wz(rb5s) / wz(cs6s))**2)
wl = 780.241209686e-9 # wavelength of D2 line in m 852.347065e-9
power = 100e-6 # in W
waist = 100e-6 # in m
# # calculate differential stark shifts for Raman transition
# X = Rb
# F, mF, Fp, mFp = 1, 1, 2, 2
# wl = 780.241209686e-9 # wavelength of D2 line in m 852.347065e-9
Rbwl = 814e-9 # wavelength of the Rb tweezer trap in m
power = 8e-3 # power of Cs tweezer beam in W
Cswaist = 1.5e-6 # beam waist for Cs in m
Rbpower = power*0.43 # power of Rb tweezer beam in W
Rbwaist = 1.5e-6 # beam waist fir Rb in m
minU0 = -0.6e-3*kB # min acceptable combined trap depth for Cs
factorRb = 2 # how much deeper the Rb must be in its own trap
factorCs = 2 # how much deeper the Cs must be in its own trap
wavels = np.linspace(800, 840, 400) * 1e-9 # wavelengths to consider for Rb trap, in m
# For the 1064nm trap: at Cs wavelength with Cs power and Cs beam waist
# mass, (L,J,F,MF), bprop, dipole matrix elements (Cm), resonant frequencies (rad/s),
# linewidths (rad/s), state labels, nuclear spin, atomic symbol.
# groundstate rubidium 5 S 1/2
Rb1064 = dipole(Rb, (0,1/2.,1,1), [Cswl, power, Cswaist])
# groundstate caesium 6 S 1/2
Cs1064 = dipole(Cs, (0,1/2.,4,4), [Cswl, power, Cswaist])
print("Rb tweezer wavelength: %.0f nm\t\tCs tweezer wavelength: %.0f nm\n"%(Cswl*1e9, Rbwl*1e9))
# set the power of the traps so that the trap depth experienced by each
# species in the overlapping trap is the same:
# Rbpower = (Cs1064.polarisability(Cswl,mj=0.5) - Rb1064.polarisability(Cswl, mj=0.5)
# )/ (Rb1064.polarisability(Rbwl, mj=0.5) - Cs1064.polarisability(Rbwl, mj=0.5)) * power
# Stability condition 1:
def P1Rb(wlCs, wlRb, U0min=minU0, Cspower=power):
"""Condition 1: The combined trap depth must be > 0.6mK for Cs."""
return abs((U0min*np.pi*eps0*c + Cs1064.polarisability(wlCs)*Cspower/Cswaist**2)
def combinedTrap(Cswl = 1064e-9, # wavelength of the Cs tweezer trap in m
Rbwl = 880e-9, # wavelength of the Rb tweezer trap in m
power = 6e-3, # power of Cs tweezer beam in W
Rbpower = -1, # power of Rb tweezer beam in W
beamwaist = 1e-6): # beam waist in m
"""Model tweezer traps for Rb and Cs and find the potential each experiences
when they're overlapping. Should fix the separate tweezer trap depths to >1mK.
We also want Rb to experience a deeper trap from its tweezer than from the Cs
tweezer so that there isn't too much heating during merging.
args:
Cswl = 1064e-9, # wavelength of the Cs tweezer trap in m
Rbwl = 880e-9, # wavelength of the Rb tweezer trap in m
power = 6e-3, # power of Cs tweezer beam in W
Rbpower = -1, # power of Rb tweezer beam in W (if < 0 then choose a power
such that both species experience the same trap depth when the tweezers are
overlapping)
beamwaist = 1e-6 # beam waist in m
"""
bprop = [Cswl, power, beamwaist] # collect beam properties
# For the 1064nm trap:
# mass, (L,J,F,MF), bprop, dipole matrix elements (Cm), resonant frequencies (rad/s),
# linewidths (rad/s), state labels, nuclear spin, atomic symbol.
# groundstate rubidium
Rb = atom(atm = 'Rb87')
Rb1064 = dipole(Rb, (0,1/2.,1,1), bprop)
# groundstate caesium
Cs = atom(atm = 'Cs133')
Cs1064 = dipole(Cs, (0,1/2.,4,4), bprop)
CsP = dipole(Cs, (1,3/2.,5,5), bprop)
# set the power of the traps so that the trap depth experienced by each
# species in the overlapping trap is the same:
if Rbpower < 0:
Rbpower = (Cs1064.polarisability(Cswl,mj=0.5) - Rb1064.polarisability(Cswl, mj=0.5)) / (Rb1064.polarisability(Rbwl, mj=0.5) - Cs1064.polarisability(Rbwl, mj=0.5)) * power
# for the 880nm trap:
bprop = [Rbwl, abs(Rbpower), beamwaist]
Rb880 = dipole(Rb, (0,1/2.,1,1), bprop)
Cs880 = dipole(Cs, (0,1/2.,3,3), bprop)
# in the trap with both tweezers overlapping:
U0 = abs(Rb1064.acStarkShift(0,0,0) + Rb880.acStarkShift(0,0,0))
wrRb = np.sqrt(4*U0 / Rb.m / beamwaist**2) /2. /np.pi /1e3
wrCs = np.sqrt(4*U0 / Cs.m / beamwaist**2) /2. /np.pi /1e3
print("%.0f beam power: %.3g mW\t\t%.0f beam power: %.3g mW"%(Cswl*1e9, power*1e3, Rbwl*1e9, Rbpower*1e3))
print("""In the combined %.0fnm and %.0fnm trap with a depth of %.3g mK the radial trapping frequencies are:
Rubidium: %.0f kHz \nCaesium: %.0f kHz"""%(Rbwl*1e9, Cswl*1e9, U0/kB*1e3, wrRb, wrCs))
# with just the Cs tweezer trap:
URb =abs(Rb1064.acStarkShift(0,0,0))
wrRb1064 = np.sqrt(4*URb / Rb.m / beamwaist**2) /2. /np.pi /1e3
UCs = abs(Cs1064.acStarkShift(0,0,0))
wrCs1064 = np.sqrt(4*UCs / Cs.m / beamwaist**2) /2. /np.pi /1e3
print("""\nIn just the %.0fnm trap:
Rubidium has trap depth %.3g mK
radial trapping frequency %.0f kHz
Caesium has trap depth %.3g mK
radial trapping frequency %.0f kHz"""%(Cswl*1e9, URb/kB*1e3, wrRb1064, UCs/kB*1e3, wrCs1064))
print(getStarkShift(Cs1064))
print(getStarkShift(CsP))
# plot merging traps:
n = 5 # number of time steps in merging to plot
sep = np.linspace(0, 10e-6, n) # initial separation of the tweezer traps
zs = np.linspace(-2, 10, 200)*1e-6 # positions along the beam axis
for atoms in [[Rb1064, Rb880], [Cs1064, Cs880]]:
plt.figure()
plt.subplots_adjust(hspace=0.01)
for i in range(n):
ax = plt.subplot2grid((n,1), (i,0))
U = (atoms[0].acStarkShift(0,0,zs) + atoms[1].acStarkShift(0,0,zs-sep[n-i-1]))/kB*1e3 # combined potential along the beam axis
U1064 = atoms[0].acStarkShift(0,0,zs)/kB*1e3 # potential in the 1064 trap
U880 = atoms[1].acStarkShift(0,0,zs-sep[n-i-1])/kB*1e3 # potential in the 880 trap
plt.plot(zs*1e6, U, 'k')
plt.plot(zs*1e6, U1064, color='tab:orange', alpha=0.6)
plt.plot(zs*1e6, U880, color='tab:blue', alpha=0.6)
plt.plot([0]*2, [min(U),0], color='tab:orange', linewidth=10, label='%.0f'%(Cswl*1e9), alpha=0.4)
plt.plot([sep[n-i-1]*1e6]*2, [min(U),0], color='tab:blue', linewidth=10, label='%.0f'%(Rbwl*1e9), alpha=0.4)
ax.set_xticks([])
ax.set_yticks([])
if i == 0:
ax.set_title("Optical potential experienced by "+atoms[0].X
+"\n%.0f beam power: %.3g mW %.0f beam power: %.3g mW"%(Cswl*1e9, power*1e3, Rbwl*1e9, Rbpower*1e3),
pad = 25)
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3, ncol=2, mode="expand", borderaxespad=0.)
plt.xlabel(r'Position ($\mu$m)')
ax.set_xticks(sep*1e6)
plt.ylabel('Trap Depth (mK)')
ax.yaxis.set_major_locator(AutoLocator())
plt.show()
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"""
# 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., 1, 1),
bprop,
Rb.D0S,
Rb.w0S,
Rb.lwS,
Rb.nljS,
nuclear_spin=Rb.I,
symbol=Rb.X)
Rb5P = dipole(Rb.m, (1, 3 / 2., 1, 1),
bprop,
Rb.D0P3,
Rb.w0P3,
Rb.lwP3,
Rb.nljP3,
nuclear_spin=Rb.I,
symbol=Rb.X)
Cs6S = dipole(Cs.m, (0, 1 / 2., 3, 3),
bprop,
Cs.D0S,
Cs.w0S,
Cs.lwS,
Cs.nljS,
nuclear_spin=Cs.I,
symbol=Cs.X)
Cs6P = dipole(Cs.m, (1, 3 / 2., 3, 3),
bprop,
Cs.D0P3,
Cs.w0P3,
Cs.lwP3,
Cs.nljP3,
nuclear_spin=Cs.I,
symbol=Cs.X)
# need a small spacing to resolve the magic wavelengths - so it will run slow
# to resolve magic wavelengths, take about 10,000 points.
wavels = np.linspace(700e-9, 1100e-9, 500)
# ac Stark Shift in Joules:
dE6S = Cs6S.acStarkShift(0, 0, 0, wavels, mj=0.5, HF=False)
dE6P = Cs6P.acStarkShift(0, 0, 0, wavels, mj=1.5, HF=False)
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 S$_{1/2}$')
plt.plot(wavels * 1e9, dE6P / h * 1e-6, 'r-.', label='Excited 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, HF=False)
dE5P = Rb5P.acStarkShift(0, 0, 0, wavels, mj=1.5, HF=False)
dif5P = dE5P - dE5S
plt.figure()
plt.title("AC Stark Shift in $^{87}$Rb")
plt.plot(wavels * 1e9, dE5S / h * 1e-6, 'b--', label='Ground S$_{1/2}$')
plt.plot(wavels * 1e9, dE5P / h * 1e-6, 'r-.', label='Excited 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 combinedTrap(
Cswl=1064e-9, # wavelength of the Cs tweezer trap in m
Rbwl=880e-9, # wavelength of the Rb tweezer trap in m
power=20e-3, # power in W
beamwaist=1e-6): # beam waist in m
"""Model tweezer traps for Rb and Cs and find the potential each experiences
when they're overlapping"""
bprop = [Cswl, power, beamwaist] # collect beam properties
# For the 1064nm trap:
# mass, (L,J,F,MF), bprop, dipole matrix elements (Cm), resonant frequencies (rad/s),
# linewidths (rad/s), state labels, nuclear spin, atomic symbol.
# groundstate rubidium
Rb1064 = dipole(Rb.m, (0, 1 / 2., 1, 1),
bprop,
Rb.D0S,
Rb.w0S,
Rb.lwS,
Rb.nljS,
nuclear_spin=Rb.I,
symbol=Rb.X)
# groundstate caesium
Cs1064 = dipole(Cs.m, (0, 1 / 2., 4, 4),
bprop,
Cs.D0S,
Cs.w0S,
Cs.lwS,
Cs.nljS,
nuclear_spin=Cs.I,
symbol=Cs.X)
CsP = dipole(Cs.m, (1, 3 / 2., 5, 5),
bprop,
Cs.D0P3,
Cs.w0P3,
Cs.lwP3,
Cs.nljP3,
nuclear_spin=Cs.I,
symbol=Cs.X)
# set the power of the traps so that the trap depth experienced by each
# species in the overlapping trap is the same:
P880 = (Cs1064.polarisability(Cswl, mj=0.5) - Rb1064.polarisability(
Cswl, mj=0.5)) / (Rb1064.polarisability(Rbwl, mj=0.5) -
Cs1064.polarisability(Rbwl, mj=0.5)) * power
# for the 880nm trap:
bprop = [Rbwl, abs(P880), beamwaist]
Rb880 = dipole(Rb.m, (0, 1 / 2., 1, 1),
bprop,
Rb.D0S,
Rb.w0S,
Rb.lwS,
Rb.nljS,
nuclear_spin=Rb.I,
symbol=Rb.X)
Cs880 = dipole(Cs.m, (0, 1 / 2., 3, 3),
bprop,
Cs.D0S,
Cs.w0S,
Cs.lwS,
Cs.nljS,
nuclear_spin=Cs.I,
symbol=Cs.X)
# in the trap with both tweezers overlapping:
U0 = abs(Rb1064.acStarkShift(0, 0, 0) + Rb880.acStarkShift(0, 0, 0))
wrRb = np.sqrt(4 * U0 / Rb.m / beamwaist**2) / 2. / np.pi / 1e3
wrCs = np.sqrt(4 * U0 / Cs.m / beamwaist**2) / 2. / np.pi / 1e3
print("%.0f beam power: %.3g mW\t\t%.0f beam power: %.3g mW" %
(Cswl * 1e9, power * 1e3, Rbwl * 1e9, P880 * 1e3))
print(
"""In the combined %.0fnm and %.0fnm trap with a depth of %.3g mK the radial trapping frequencies are:
Rubidium: %.0f kHz \nCaesium: %.0f kHz""" %
(Rbwl * 1e9, Cswl * 1e9, U0 / kB * 1e3, wrRb, wrCs))
# with just the Cs tweezer trap:
URb = abs(Rb1064.acStarkShift(0, 0, 0))
wrRb1064 = np.sqrt(4 * URb / Rb.m / beamwaist**2) / 2. / np.pi / 1e3
UCs = abs(Cs1064.acStarkShift(0, 0, 0))
wrCs1064 = np.sqrt(4 * UCs / Cs.m / beamwaist**2) / 2. / np.pi / 1e3
print("""\nIn just the %.0fnm trap:
Rubidium has trap depth %.3g mK
radial trapping frequency %.0f kHz
Caesium has trap depth %.3g mK
radial trapping frequency %.0f kHz""" %
(Cswl * 1e9, URb / kB * 1e3, wrRb1064, UCs / kB * 1e3, wrCs1064))
print(getStarkShift(Cs1064))
print(getStarkShift(CsP))
# plot merging traps:
n = 5 # number of time steps in merging to plot
sep = np.linspace(0, 10e-6, n) # initial separation of the tweezer traps
zs = np.linspace(-2, 10, 200) * 1e-6 # positions along the beam axis
for atoms in [[Rb1064, Rb880], [Cs1064, Cs880]]:
plt.figure()
plt.subplots_adjust(hspace=0.01)
for i in range(n):
ax = plt.subplot2grid((n, 1), (i, 0))
if i == 0:
ax.set_title(
"Optical potential experienced by " + atoms[0].X +
"\n%.0f beam power: %.3g mW %.0f beam power: %.3g mW" %
(Cswl * 1e9, power * 1e3, Rbwl * 1e9, P880 * 1e3))
U = (atoms[0].acStarkShift(0, 0, zs) +
atoms[1].acStarkShift(0, 0, zs - sep[n - i - 1])
) / kB * 1e3 # combined potential along the beam axis
U1064 = atoms[0].acStarkShift(
0, 0, zs) / kB * 1e3 # potential in the 1064 trap
U880 = atoms[1].acStarkShift(
0, 0,
zs - sep[n - i - 1]) / kB * 1e3 # potential in the 880 trap
plt.plot(zs * 1e6, U, 'k')
plt.plot(zs * 1e6, U1064, color='tab:orange', alpha=0.6)
plt.plot(zs * 1e6, U880, color='tab:blue', alpha=0.6)
plt.plot([0] * 2, [min(U), 0],
color='tab:orange',
linewidth=10,
label='%.0f' % (Cswl * 1e9),
alpha=0.4)
plt.plot([sep[n - i - 1] * 1e6] * 2, [min(U), 0],
color='tab:blue',
linewidth=10,
label='%.0f' % (Rbwl * 1e9),
alpha=0.4)
ax.set_xticks([])
ax.set_yticks([])
plt.xlabel('Position ($\mu$m)')
ax.set_xticks(sep * 1e6)
plt.ylabel('Trap Depth (mK)')
ax.yaxis.set_major_locator(AutoLocator())
plt.show()
'F=' + str(f) + ', $\Delta M_F=$' + str(-dmf) for f in range(3, 5)
for dmf in range(-1, 2)
])
plt.show()
if __name__ == "__main__":
wavelength = 1064e-9 # wavelength in m
power = 6e-3 # beam power in W
beamwaist = 1e-6 # beam waist in m
bprop = [wavelength, power, beamwaist]
Rb5P1 = dipole(Rb.m, (1, 1 / 2., 1, 1),
bprop,
Rb.D0P1,
Rb.w0P1,
Rb.lwP1,
Rb.nljP1,
nuclear_spin=Rb.I,
symbol=Rb.X)
Rb5P3 = dipole(Rb.m, (1, 3 / 2., 1, 1),
bprop,
Rb.D0P3,
Rb.w0P3,
Rb.lwP3,
Rb.nljP3,
nuclear_spin=Rb.I,
symbol=Rb.X)
# print(getStarkShift(Rb5P1))
print(getStarkShift(Rb5P3))
print(np.array(Rb5P3.polarisability(795e-9, HF=True, split=True)) / au)
from AtomFieldInt_V3 import (dipole, atom, c, eps0, h, hbar, a0, e, me, kB,
amu, Eh, au, atom)
Rb = atom(atm='Rb87')
Cs = atom(atm='Cs133')
Na = atom(atm='Na23')
Cswl = 976e-9 # wavelength of the Cs tweezer trap in m
Nawl = 700e-9 # wavelength of the Rb tweezer trap in m
Cspower = 5e-3 # power of Cs tweezer beam in W
Napower = 5e-3 # power of Rb tweezer beam in W
Cswaist = 0.8e-6 # beam waist for Cs in m
Nawaist = 0.7e-6 # beam waist fir Na in m
# Cs in its own tweezer
Cs976 = dipole(Cs, (0, 1 / 2., 4, 4), [Cswl, Cspower, Cswaist])
# Cs in the Na tweezer
Cs700 = dipole(Cs, (0, 1 / 2., 4, 4), [Nawl, Napower, Nawaist])
# Na in the Cs tweezer
Na976 = dipole(Na, (0, 1 / 2., 1, 1), [Cswl, Cspower, Cswaist])
# Na in its own tweezer
Na700 = dipole(Na, (0, 1 / 2., 1, 1), [Nawl, Napower, Nawaist])
# separated tweezer trap depths in mK:
U_cs_976 = Cs976.acStarkShift(0, 0, 0) / kB * 1e3
U_cs_700 = Cs700.acStarkShift(0, 0, 0) / kB * 1e3
U_na_976 = Na976.acStarkShift(0, 0, 0) / kB * 1e3
U_na_700 = Na700.acStarkShift(0, 0, 0) / kB * 1e3
# combined trap depths in mK:
U_cs = U_cs_976 + U_cs_700
def plotScatRate():
"""Plot the polarisability of Rb 5S and Cs 6S states and the scattering
rates within a given wavelength range (given in metres)"""
bprop = [1064e-9, 6e-3, 1e-6] # wavelength, beam power, beam waist
wl1 = np.linspace(795e-9, Cs.rwS[0],
200) # wavelength below Cs D1 line (m)
wl2 = np.linspace(Cs.rwS[0], 1100e-9,
200) # wavelength below Cs D1 line (m)
# groundstate rubidium
Rb5S = dipole(Rb, (0, 1 / 2., 1, 1), bprop)
# below Cs D1 line, use intensities such that the Rb trap depth is 1mK
I1 = 2 * kB * 1e-3 * eps0 * c / Rb5S.polarisability(wl1)
# groundstate caesium
Cs6S = dipole(Cs, (0, 1 / 2., 4, 4), bprop)
# above Cs D1 line, use intensities such that the Cs trap depth is 1mK
I2 = 2 * kB * 1e-3 * eps0 * c / Cs6S.polarisability(wl2)
fig, ax = plt.subplots(2,
2,
gridspec_kw={
'height_ratios': [3, 2],
'hspace': 0,
'wspace': 0.02
},
sharex='col')
for i, wl, I in [[0, wl1, I1], [1, wl2, I2]]:
# plot scattering rates for fixed trap depth
ax[0][i].semilogy(wl * 1e9,
Rb5S.scatRate(wl, I),
color=DUsea_blue,
label='Rb 5S$_{1/2}$') # Rb
ax[0][i].semilogy(wl * 1e9,
Cs6S.scatRate(wl, I),
color=DUcherry_red,
label='Cs 6S$_{1/2}$') # Cs
ax[0][i].plot([min(wl) * 1e9, max(wl) * 1e9], [100] * 2,
'k:') # show acceptable limit
ax[0][i].set_ylim((2, 10000))
# plot polarisability in the same wavelength range
ax[1][i].plot(wl * 1e9,
Rb5S.polarisability(wl) / au,
color=DUsea_blue,
label='Rb 5S$_{1/2}$')
ax[1][i].plot(wl * 1e9,
Cs6S.polarisability(wl) / au,
color=DUcherry_red,
label='Cs 6S$_{1/2}$')
ax[1][i].set_ylim((-6000, 6000))
if not i: # only have y label on the lhs
ax[0][i].set_ylabel('Scattering Rate (s$^{-1}$)')
ax[1][i].set_ylabel('Polarisability ($a_0^3$)')
else: # remove ticks
ax[0][i].set_yticks([])
ax[1][i].set_yticks([])
ax[1][i].set_xlim((wl[0] * 1e9, wl[-1] * 1e9))
ax[1][i].set_xlabel('Wavelength (nm)')
# calculate trap depth
# Rbdepths, Csdepths = np.zeros(len(wavelengths)), np.zeros(len(wavelengths))
# for i in range(len(wavelengths)): # power changes to keep trap depth fixed
# Rb5S.field.E0 = np.sqrt(2 * abs(Is[i]) / eps0 / c)
# Cs6S.field.E0 = np.sqrt(2 * abs(Is[i]) / eps0 / c)
# Rbdepths[i] = Rb5S.acStarkShift(0,0,0, wavelengths[i])/kB*1e3 # in mK
# Csdepths[i] = Cs6S.acStarkShift(0,0,0, wavelengths[i])/kB*1e3 # in mK
#
# ax1 = ax[0].twinx() # plot trap depth
# l3 = ax1.plot(wavelengths*1e9, Rbdepths, '--', color=DUsea_blue, label='Trap Depth', alpha=0.5)
# l4 = ax1.plot(wavelengths*1e9, Csdepths, '--', color=DUcherry_red, label='Trap Depth', alpha=0.5)
# ax1.set_ylabel('Trap Depth (mK)')
# ax1.set_ylim((-3, 3))
# lines = l1+l2+l3+l4 # order lines so that they appear next to each other in the legend
# ax[0].legend(lines, [l.get_label() for l in lines], ncol=2, fontsize=11)
plt.subplots_adjust(left=0.17, right=0.95, top=0.93, bottom=0.13)
ax[0][1].legend()
ax[0][0].set_title('Rb Trap Depth 1 mK')
ax[0][1].set_title('Cs Trap Depth 1 mK')
plt.show()
def check880Trap(wavelength = 880e-9, # wavelength in m
wavels = np.linspace(795,930,500)*1e-9, # wavelengths in m to plot
power = 5e-3, # beam power in W
beamwaist = 1e-6, # beam waist in m
species = 'Rb'): # which species to set a 1mK trap for
"""Plot graphs of the trap depth experienced by Cs around 880nm when
the ground state Rb trap depth is fixed at 1mK. Look at the scattering
rates and hence trap lifetimes that are possible."""
bprop = [wavelength, power, beamwaist]
Rb = atom(atm = 'Rb87')
Rb5S = dipole(Rb, (0,1/2.,1,1), bprop)
Rb5P = dipole(Rb, (1,3/2.,1,1), bprop)
Cs = atom(atm = 'Cs133')
Cs6S = dipole(Cs, (0,1/2.,3,3), bprop)
Cs6P = dipole(Cs, (1,3/2.,3,3), bprop)
# choose power so that Rb trap depth is fixed at 1 mK:
if species == Cs.X:
Powers = abs(1e-3*kB * np.pi * eps0 * c * beamwaist**2 / Cs6S.polarisability(wavels)) # in Watts
else:
Powers = abs(1e-3*kB * np.pi * eps0 * c * beamwaist**2 / Rb5S.polarisability(wavels)) # in Watts
_, ax1 = plt.subplots()
ax1.set_title('Fixing the trap depth of ground state '+species+' at 1 mK')
ax1.set_xlabel('Wavelength (nm)')
ax1.plot(wavels*1e9, Powers*1e3, color='tab:blue')
ax1.set_ylabel('Power (mW)', color='tab:blue')
ax1.tick_params(axis='y', labelcolor='tab:blue')
ax1.set_xlim(wavels[0]*1e9, wavels[-1]*1e9)
# ax1.set_ylim(min(Powers)*1e3-0.5, 15)
ax2 = ax1.twinx()
# now the power and the wavelength are varied:
Llabels = ['$S_{1/2}$', '$P_{3/2}$']
if species == Cs.X:
colors = ['k', 'tab:orange', 'tab:orange', 'tab:orange']
linestyles = ['--', '-.', '-', ':']
else:
colors = ['tab:orange', 'tab:orange', 'k', 'tab:orange']
linestyles = ['-', '-.', '--', ':']
trapdepths = []
for obj in [Cs6S, Cs6P, Rb5S, Rb5P]:
res = np.zeros(len(Powers))
for i in range(len(Powers)):
obj.field.E0 = 2 * np.sqrt(Powers[i] / eps0 / c / np.pi)/beamwaist
# average mj states (doesn't have any effect on j=1/2 states)
res[i] = 0.5*(obj.acStarkShift(0,0,0, wavels[i], mj=1.5) +
obj.acStarkShift(0,0,0, wavels[i], mj=0.5))
color = colors.pop(0)
ls = linestyles.pop(0)
ax2.plot(wavels*1e9, res*1e3/kB, color=color, label=obj.X+" "+Llabels[obj.L], linestyle=ls)
trapdepths.append(res)
ax2.plot(wavels*1e9, np.zeros(len(wavels)), 'k', alpha=0.1) # show zero crossing
ax2.set_ylabel('Trap Depth (mK)', color='tab:orange')
ax2.legend()
ax2.set_ylim(-3, 3)
ax2.tick_params(axis='y', labelcolor='tab:orange')
plt.tight_layout()
I = 2*Powers / np.pi / beamwaist**2
# scattering rate of Cs from the D2 line:
deltaCsD1 = 2*np.pi*c * (1/wavels - 1/Cs.rwS[0]) # detuning from D1 (rad/s)
deltaCsD2 = 2*np.pi*c * (1/wavels - 1/Cs.rwS[35]) # detuning from D2 (rad/s)
IsatCsD1 = 2.4981 *1e-3 *1e4 # saturation intensity for D1 transition, sigma polarised
IsatCsD2 = 1.1023 *1e-3 *1e4 # saturation intensity for D2 transition, pi polarised
CsRsc = 0
for vals in [[Cs.lwS[0], deltaCsD1, IsatCsD1], [Cs.lwS[35], deltaCsD2, IsatCsD2]]:
CsRsc += vals[0]/2. * I/vals[2] / (1 + 4*(vals[1]/vals[0])**2 + I/vals[2])
# Cstau = 1e-3*kB / (hbar*(2*np.pi/wavels))**2 * 2.*Cs.m / CsRsc # the lifetime is the trap depth / recoil energy / scattering rate
Cst = 4*np.sqrt(Cs.m*abs(trapdepths[0])) / (2*np.pi/wavels)**2 /hbar /beamwaist /CsRsc # duration in vibrational ground state (s) = 1/Lamb-Dicke^2 /Rsc
# scattering rate of Rb from the D1 line:
deltaRbD1 = 2*np.pi*c * (1/wavels - 1/Rb.rwS[0]) # detuning from D1 (rad/s)
IsatRbD1 = 4.484 *1e-3 *1e4 # saturation intensity for D1 transition, pi polarised
RbRsc = Rb.lwS[0]/2. * I/IsatRbD1 / (1 + 4*(deltaRbD1/Rb.lwS[0])**2 + I/IsatRbD1) # per second
# Rbtau = 1e-3*kB / (hbar*(2*np.pi/wavels))**2 * 2.*Rb.m / RbRsc # the lifetime is the trap depth / recoil energy / scattering rate
Rbt = 4*np.sqrt(Rb.m*abs(trapdepths[2])) / (2*np.pi/wavels)**2 /hbar /beamwaist /RbRsc # duration in vibrational ground state (s) = 1/Lamb-Dicke^2 /Rsc
# plot lifetime and scattering rate on the same axis:
for Rsc, ts, X in [[RbRsc, Rbt, Rb.X], [CsRsc, Cst, Cs.X]]:
fig, ax3 = plt.subplots()
ax3.set_title('Scattering rate and lifetime of ground state '+X+' in a 1 mK trap (for '+species+')')
ax3.set_xlabel('Wavelength (nm)')
ax3.semilogy(wavels*1e9, Rsc, color='tab:blue')
ax3.plot(wavels*1e9, np.zeros(len(wavels))+100, '--', color='tab:blue', alpha=0.25) # show acceptable region
ax3.set_ylabel('Scattering rate ($s^{-1}$)', color='tab:blue')
ax3.tick_params(axis='y', labelcolor='tab:blue')
ax3.set_xlim(wavels[0]*1e9, wavels[-1]*1e9)
ax3.set_ylim(1, 1e5)
ax4 = ax3.twinx()
ax4.semilogy(wavels*1e9, ts, color='tab:orange')
ax4.plot(wavels*1e9, np.ones(len(wavels))/2., '--', color='tab:orange', alpha=0.25) # show acceptable region
ax4.set_ylabel('Time in the vibrational ground state (s)', color='tab:orange')
ax4.tick_params(axis='y', labelcolor='tab:orange')
ax4.set_ylim(0.001,10)
plt.tight_layout()
plt.show()
# ax[0].legend(lines, [l.get_label() for l in lines], ncol=2, fontsize=11)
plt.subplots_adjust(left=0.17, right=0.95, top=0.93, bottom=0.13)
ax[0][1].legend()
ax[0][0].set_title('Rb Trap Depth 1 mK')
ax[0][1].set_title('Cs Trap Depth 1 mK')
plt.show()
if __name__ == "__main__":
wavelength = 1064e-9 # wavelength in m
power = 6e-3 # beam power in W
beamwaist = 1e-6 # beam waist in m
bprop = [wavelength, power, beamwaist]
Rb5P1 = dipole(Rb, (1, 1 / 2., 1, 1), bprop)
Rb5P3 = dipole(Rb, (1, 3 / 2., 1, 1), bprop)
# print(getStarkShift(Rb5P1))
# print(getStarkShift(Rb5P3))
# print(np.array(Rb5P3.polarisability(795e-9, HF=True, split=True))/au)
# combinedTrap(power=6e-3)
# getMFStarkShifts()
# plotPolarisability()
plotScatRate()
# compare Kien 2013 Fig 4,5:
# wls = [np.linspace(680, 690, 200)*1e-9, np.linspace(930, 940, 200)*1e-9]
# ylims = [(-1200, 300), (-3000, 6000)]
# for ii in range(2):
import matplotlib.pyplot as plt
import sys
sys.path.append(r'Y:\Tweezer\Code\Python 3.5\polarisability')
sys.path.append(r'Z:\Tweezer\Code\Python 3.5\polarisability')
from AtomFieldInt_V3 import dipole, atom, c, eps0, h, hbar, a0, e, me, kB, amu, Eh, au
Rb = atom(atm='Rb87')
Cs = atom(atm='Cs133')
# from scipy.constants import physical_constants
# muB = physical_constants['Bohr magneton']
wavelength = 1064e-9 # wavelength in m
power = 5e-3 # beam power in W
waist = 1.2e-6 # beam waist of tweezer in m
ehat = (2**(-0.5), 1j * 2**(-0.5), 0) # E field circular polarisation
# create dipole objects for ground state Rb / Cs
bprop = [wavelength, power, waist, ehat]
Rb5S = dipole(Rb, (0, 1 / 2., 1, 1), bprop)
# Rb5S.gJ = 2.00233113 # Fine structure Lande g-factor (from Steck)
Cs6S = dipole(Cs, (0, 1 / 2., 3, 3), bprop)
# Cs6S.gJ = 2.00254032 # Fine structure Lande g-factor (from Steck)
def get_sep(atom=Rb5S, wl=wavelength):
"""Calculate the displacement of the trap centre due to the fictitious field"""
aS, aV, aT = atom.polarisability(
wl, split=True, HF=True) # vector polarisability for |F,MF>
return aV / aS * atom.MF / atom.F * wl / 4. / np.pi # displacement of potential min.
Fs, occs = np.unique(states[:, 0], return_counts=True) # F states
if not weights: # probability of being in each MF state
weights = np.concatenate([np.ones(o) / o
for o in occs]) # equal distribution
weighted_shift = shifts * weights
aveShifts = [np.sum(weighted_shift[np.where(Fs == F)])
for F in Fs] # average
return aveShifts
if __name__ == "__main__":
# calculate the stark shifts for trap depths 0 - 2 mK
beamwaist = 1.2e-6 # beam waist of tweezer in m
wavelength = 1064e-9 # wavelength of tweezer beam in m
# make an object to calculate the groundstate polarisability
G = dipole(Rb, (0, 1 / 2., 1, 1), [wavelength, 1e-3, beamwaist])
powers = abs(
np.linspace(0, 2, 200) * 1e-3 * kB / G.polarisability(wavelength) *
np.pi * eps0 * c * beamwaist**2)
shifts = np.zeros((len(powers), 2)) # AC Stark shifts in MHz
for i in range(len(powers)):
mfstates, mfshifts = getMFStarkShifts(wavelength, powers[i], beamwaist)
shifts[i] = aveShift(mfstates, mfshifts)
plt.figure()
ax1 = plt.gca()
ax2 = ax1.twiny()
plt.title('Averaging over the hyperfine transitions of Rb D2 line')
ax1.plot(powers * 1e3, shifts[:, 0], label="F=1 $\rightarrow$ F'=2")
ax1.plot(powers * 1e3, shifts[:, 1], label="F=2 $\rightarrow$ F'=3")
