- #1
naima
Gold Member
- 938
- 54
I found this in a Phd thesis
consider a two level atom interacting with the electromagnetic field.
The atom is described by
##H_{at} = \hbar ω_0 J_z##
a monomode electric field is described by
##H_{em} = \hbar \omega (a^\dagger a + 1/2)##
We have ##E = E_0(a^\dagger + a)## and the dipolar moment is ##D = d_o(J_+ - J_-)##
We have then ##H_{int} = -DE##
So this interference hamitonian contains four terms
a) ##a J_+ and a^\dagger J_-##
but also
b) ##a J_- and a^\dagger J_+##
the author writes later a formula without the b) terms.
How can we make them disappear (mathematically)?
consider a two level atom interacting with the electromagnetic field.
The atom is described by
##H_{at} = \hbar ω_0 J_z##
a monomode electric field is described by
##H_{em} = \hbar \omega (a^\dagger a + 1/2)##
We have ##E = E_0(a^\dagger + a)## and the dipolar moment is ##D = d_o(J_+ - J_-)##
We have then ##H_{int} = -DE##
So this interference hamitonian contains four terms
a) ##a J_+ and a^\dagger J_-##
but also
b) ##a J_- and a^\dagger J_+##
the author writes later a formula without the b) terms.
How can we make them disappear (mathematically)?