The document describes simulation and experimentation of pulsed light interacting with multilevel quantum systems. It presents two coupled differential equations modeling the interaction and applies the rotating wave approximation to neglect fast oscillating terms. It also only considers the case of exact resonance between the light frequency and the system energy levels.

1. Simulation and Experiment of the
Interaction of Pulsed Light with
Multilevel Systems
Abhijit Mondal
Y6010
Department of Chemistry
Indian Institute of Technology, Kanpur

2. ∂c1/∂t = i(E0 μ12/2ħ) (ei(ω−ω0)t + e−i(ω+ω0 )t ) c2 (t)
∂c2/∂t = i(E0 μ12/2ħ) (e-i(ω−ω0)t + ei(ω+ω0 )t ) c1 (t)
where E0 is the amplitude of the light wave,
light wave of angular frequency ω and
ω0 = (E2 − E1 )/ħ.
Rabi frequency defined by:
ΩR = |μ12 E0 /ħ |.
We apply the rotating wave approximation to neglect the
terms that oscillate at ±(ω + ω0 ),
Second, we only consider the case of exact resonance with
δω = 0.

4. NOT Gate
Hadamard
Gate

12. int main(int argc,char *argv[])
{
FILE *fp1,*fp2,*fp3,*fp4; fp1=fopen("1.txt","r"); fp2=fopen("gr 5.txt","r");
fp3=fopen("quotient.txt","w"); fp4=fopen("remainder.txt","w");
char *buffer1=new char[20]; char *buffer2=new char[20]; double *f=new double[2000];
double *g=new double[2000];
int i=0;
while(!feof(fp1)) {fseek(fp1,7,SEEK_CUR); fgets(buffer2,8,fp1); double y=atof(buffer2); f[i]=y;i+
+;
}
i=0;
while(!feof(fp2)) {fseek(fp2,7,SEEK_CUR); fgets(buffer2,8,fp2); double y=atof(buffer2); g[i]=y;i+
+;
}
int deg=i;
for(i=0;i<deg;i++) {
int j=1;double sum=0.0;
while(j<=i) {sum+=f[j]*q[i-j]; j++; }
q[i]=(g[i]-sum)/f[0]; fprintf(fp3,"%fn",q[i]);
}
}

13. Let us suppose that the original response signal be denoted
as g(x), the h(x) is the convolution of f(x) and g(x). Then
c0= a0 b0= c0 / a0
c1= a1b0 + a0b1 b1= (c1- a1b0) / a0
c 2= a2b 0 + a 1b 1 + a 0b 2 b2= (c2- a1b1- a2b0) / a0
.
.
cn-1= ∑i=0n-1 ai bn-1-i bn-1= (cn-1 - ∑i=1n-1 ai bn-1-i) / a0
Hence we use a dynamic programming approach to solve for
bi for each i as:
bi = (ci - ∑j=1i aj bi-j) / a0

14. Thank You for noticing me !!!