Matrix of the force on a two-level atom

[Carnot]

Hi, I am reading about forces on a two-level atom. In my textbook (p. 30 in Laser cooling and trapping by Metcalf & Straten) it says that the matrix expression for the force

F = e\frac{\partial}{\partial z}(<\vec{E}(\vec{r},t) \cdot \vec{r}>)

has only off-diagonal entries.

But how does this matrix expression look like?
I'm sorry, I'm completely lost in how to write this matrix, so I'm thankfull to any hints or explanations you may have.

Thanks

 

[Carnot]

Wow, and what happened to the equation? It looked fine in pre-view. Sorry - don't know how to fix that :-/

 

[Bill_K]

It's a 2 x 2 matrix. The rows and columns are |e> and |g>, the excited and ground state of the "atom". The diagonal elements of the interaction Hamiltonian are zero, and the off-diagonal ones are <e|H_int|g> = - e E·<e|r|g>