• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Expectation value of operators and squeezing in the even cat state

Problem Statement
I need to derive the equations 7.126 and 7.127(image posted) from Gerry/Knight's quantum optics book. The equations are the expectation values of the square of the quadrature operators for the even cat state.
Relevant Equations
<X1^2>=0.25 + ( (alpha)^2 )/(1+exp(-2alpha^2))

<X2^2>=0.25 - (exp(-2alpha^2)*(alpha)^2)/(1+exp(-2alpha^2))
I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25.

How do I derive the given equations?
 

Attachments

Last edited:

Want to reply to this thread?

"Expectation value of operators and squeezing in the even cat state" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top