Constants

c=QuantityMagnitude[Quantity["SpeedOfLight"], "Meters"/"Seconds"];
ϵ=8.854 (10^(-12));
h=6.626 (10^(-34));
k=1.38 (10^(-23));
λ1=780.24 (10^(-9));λ2=776.9 (10^(-9));
ω1=2 π (c/(λ1));ω2=2 π (c/(λ2));
m=1.443 (10^(-25));(* Mass of Rb87 *)
A1=3.755 (10^7); A2=4.788 (10^5); (* Einstein A coefficient for 776 transition *)
Γ2= 4 (10^6);Γ1=3.755 (10^7);

Parameters

Δ=2 π 60 (10^6); (* Detuning *)

μ2=√(A2 ((3 ϵ h (c^3))/(2 ((ω2)^3))));(* Atomic Dipole moment *)

μ1=√(A1 ((3 ϵ h (c^3))/(2 ((ω1)^3))));

Isat2=(π/3)((h c A2)/((λ2)^3))(* Saturation intensity of 776 *)

Isat1=(π/3)((h c A1)/((λ1)^3))

TD=((h Γ1)/(4 π k))(* Doppler limit temperature *)

Γ2D= ω2√(((8 k TD Log[2])/(m (c^2))))

I1=((2 0.2 (10^(-3)))/(π (((0.5 (10^(-3))))^2)))

I2=((2 15 (10^(-3)))/(π (((0.5 (10^(-3))))^2)))

Ω1=(Sqrt[((((Γ1)^2)/2)(I1/Isat1))])

Ω2=(Sqrt[(((8 (π^2) ((μ2)^2))/(ϵ c (h^2)))I2)])

ΩR=((Ω1 Ω2)/(2  Δ))

Γ2eff=(Sqrt[(((Γ2)^2)+2 ((Γ2D)^2) + (((2 π 3 (10^6)))^2))])

ΩR=12 (10^6);

eff[δ_]=((((((2 π δ))^2)+((Γ2eff)^2)) ((Γ2)/(Γ2eff)))/((((2 π δ))^2)+((Γ2eff)^2)+(((Γ2eff)/(2 Γ2)) ((ΩR)^2))));
eff[δ_]=((((((2 π δ))^2)+((Γ2eff)^2)) ((Γ2)/(Γ2eff)))/((((2 π δ))^2)+((Γ2eff)^2)+(((Γ2eff)/(2 Γ2)) ((ΩR)^2))));

Plot[eff[x*(10^6)],{x,-60,60}, PlotRange->{{-60,60},{0.1,0.26}}]