#### naima

Gold Member

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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)?