proton4ik
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Hey there, the task I'm working on is written below.
Find the quadrature distribution ρ(q), for an optical mode being in the coherent state |α>.
Hint: use ∑Hn(x)*(t^n)/(n!)
I really am struggling with this type of tasks :D
I tried to follow a solved example that I found in my workbook, but there are no explanations and I'm really not sure if I do anything correctly.
[tex]\rho(q)=<q|\hat{\rho}|q>=\sum_{n=0}^{\infty} <q| \hat{\rho} {{\psi}_n}^* |n> = \frac {1} {1+n_{th}} \sum_{n=0}^{\infty} (\frac{n_{th}}{1+n_{th}})^n {{\psi}_n}^* |{\psi}_n (q)|^2=\frac{e^{\frac{-q^2}{1+2n_{th}}}}{{\pi (1+2n_{th})}^{1/2}}[/tex]
I have five more exercises like that, but I can't understand the concept. Any help is much appreciated!
Find the quadrature distribution ρ(q), for an optical mode being in the coherent state |α>.
Hint: use ∑Hn(x)*(t^n)/(n!)
I really am struggling with this type of tasks :D
I tried to follow a solved example that I found in my workbook, but there are no explanations and I'm really not sure if I do anything correctly.
[tex]\rho(q)=<q|\hat{\rho}|q>=\sum_{n=0}^{\infty} <q| \hat{\rho} {{\psi}_n}^* |n> = \frac {1} {1+n_{th}} \sum_{n=0}^{\infty} (\frac{n_{th}}{1+n_{th}})^n {{\psi}_n}^* |{\psi}_n (q)|^2=\frac{e^{\frac{-q^2}{1+2n_{th}}}}{{\pi (1+2n_{th})}^{1/2}}[/tex]
I have five more exercises like that, but I can't understand the concept. Any help is much appreciated!