fluctuation of the photon number in a coherent state
Not what you're looking for?
Problems 2.11 and 2.12 of the notes.
Purchase this Solution
Solution Summary
We give a detailed solution of the problems.
Solution Preview
Problem 2.11
We can use the expression Eq. 2.2.29 for the density matrix:
rho(n) = 1/(1+n) sum from k = 0 to infinity of r^k |k><k|
where n is the mean photon number and r = n/(1+n). To compute the variance, we need to evaluate:
<(a-dagger a)^2> = Tr[rho (a-dagger a)^2]
We can do this as follows. We first write:
(a-dagger a)^2 = a-dagger a a-dagger a
We can use the commutation relation [a, a-dagger ] = 1 to move all the a-dagger's to the left. We have that a a-dagger = 1 + a-dagger a, therefore:
a-dagger (a a-dagger) a = a-dagger (1 + a-dagger a ) a = a-dagger a + a-dagger^2 a^2.
We thus have:
Tr[rho (a-dagger a)^2] = Tr[rho ...
Purchase this Solution
Free BrainMass Quizzes
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
The Moon
Test your knowledge of moon phases and movement.
Basic Physics
This quiz will test your knowledge about basic Physics.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.