# Matrix of the force on a two-level atom

1. Feb 27, 2014

### 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

2. Feb 27, 2014

### Carnot

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

3. Feb 27, 2014

### 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|Hint|g> = - e E·<e|r|g>

Last edited: Feb 27, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook