I found this in a Phd thesis(adsbygoogle = window.adsbygoogle || []).push({});

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)?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Light and atom interaction hamiltonian

**Physics Forums | Science Articles, Homework Help, Discussion**