Pump-probe Spectroscopy on a Single Transition

This notebook enables you to calculate the probe absorption in the presence of a pump field having arbitrary intensity for stationary atoms, equation (7.64).   
Dephasing collisions are included, but the system is closed in that total population is conserved.

Here is a list of symbols

g2 =(Subscript[γ, 2])
d=Δ
d1=(Subscript[δ, 1])
g=γ=(Subscript[γ, 2])/2+Γ 
c=(Subscript[χ, 1])   ****

Program

mu2[g2_,d_]:=g2+ I d

mu12[g_,d_]:=g+I d

mu21p[g_,d1_]:=g+I d1

mu12prime[g_,d_,d1_]:=g+I (d-d1)

mu12bar[g_,d_,d1_]:=g+I (d+d1)

mutinv[g2_,d_]:=2/mu2[g2,d]

n0[g_,d1_,c_]:=-((1+(2 c^2)/(g^2+d1^2)))^(-1)

B[g_,g2_,d_,c_,d1_]:=mutinv[g2,d] 2 c^2 mu12[g,d]/(mu12prime[g,d,d1] mu12bar[g,d,d1])

B[g,g2,d,c,d1]

b12[g_,g2_,d1_,d_,c_]:=-n0[g,d1,c](1-2c^2 (1+(g-g2/2)/mu2[g2,d])/(mu12prime[g,d,d1] mu21p[g,d1] (1+B[g,g2,d,c,d1])))/mu12prime[g,d,d1]

**  b12 is Eq. (7.64) of text divided by (i (SuperStar[(Subscript[χ, 2])])) ; Thus absorption is proportional to Re[b12]**

Simplify[b12[g2/2+Γ,g2,d1,d,c]]

linear absorption with no pump field

Plot[Re[b12[1/2,1,0,d,0]],{d,-4,4}]

Line shape for zero pump field detuning in strong field. Note the reduced absorption

Plot[Re[b12[.5,1,0,d,5]],{d,-25,25},PlotRange->All]

general line shape with pump field detuning  there is a small dispersion contribtuion near Δ = 0

Plot[Re[b12[.5,1,20,d,10]],{d,-35,35},PlotRange->All]

adding dephasing collisions increases the dispersion component near Δ = 0

Plot[Re[b12[2,1,20,d,10]],{d,-35,35},PlotRange->All]