Model Atom

$\begin{displaymath}H_{\rm atom} = \frac{\hbar\omega_0}{2}\sigma_z,\quad \sigma_z... ... \vert e\rangle \langle e\vert - \vert g\rangle \langle g\vert.\end{displaymath}$

(112)

$\displaystyle \sigma_x$	$\displaystyle \equiv$	$\displaystyle \left( \begin{array}[h]{cc} 0 & 1\\ 1 & 0 \end{array}\right),\qu... ...d \sigma_z\equiv \left( \begin{array}[h]{cc} 1 & 0\\ 0 & -1 \end{array}\right)$
$\displaystyle \sigma_-$	$\displaystyle \equiv$	$\begin{displaymath}\left( \begin{array}[h]{cc} 0& 0\\ 1 & 0 \end{array}\right),... ...iv \left( \begin{array}[h]{cc} 0& 1\\ 0 & 0 \end{array}\right)\end{displaymath}$
$\displaystyle \sigma_{\pm}$	$\displaystyle =$	$\displaystyle \frac{1}{2}(\sigma_x\pm i\sigma_y),\quad \sigma_x=\sigma_++\sigma_-,\quad \sigma_y=-i(\sigma_+-\sigma_-)$
$\displaystyle \left[\sigma_+,\sigma_-\right]$	$\displaystyle =$	$\displaystyle \sigma_z,\quad [\sigma_z,\sigma_{\pm}]=\pm 2\sigma_{\pm}.$	(113)