Solve Rabi Problem Numerically

TheHamiltonianofRabiProblemis:​​
H
0
=
ℏω
0
†
σ
σ
V(t)=
ℏΩ
0
(
†
σ
+σ)(
iωt
e
+
-iωt
e
)
​​​​Thenwecansupposethewavefunctioncanbeexpandedas(intheinteractionpicture):​​|ψ〉=
a
0
(t)|0〉+
a
1
(t)
-iωt
e
|1〉​​​​Andtheequationsare:​​​​
i
d
a
0
dt
=(
-iΔt
e
+
-iΓt
e
)
a
1
i
d
a
1
dt
=(
iΔt
e
+
iΓt
e
)
a
0
whereΔ=
-8
10
,Γ=
8
10
and
a
0
(0)=1,
a
1
(0)=0​​
timeRange=2Pi;​​(*letx[t]=
a
0
[y],y[t]=a1[t]*)​​(*thefollowingcodegoeswellwhenΔ=
-4
10
,Γ=
4
10
,butbreaksdownwhentheorderdifferencegoeshigher*)​​​​solution=NDSolve[{Ix'[t]==(Exp[-IΔt]+Exp[-IΓt])y[t],Iy'[t]==(Exp[IΔt]+Exp[IΓt])x[t],x[0]==1,y[0]==0}/.{Δ->1.0
-8
10
,Γ->1.0
8
10
},{x,y},{t,0,timeRange}];​​​​​​​​Plot[{Evaluate[Norm[x[t]/.solution]^2],Evaluate[Norm[y[t]/.solution]^2]},{t,0,timeRange},PlotTheme->"Scientific",FrameLabel->{"t(s)","|a(t)​
2
|
"}]
NDSolve
:Maximum number of 871114 steps reached at the point t == 0.021293.
Out[]=