Awaiting Activation edited 2QEnergies.tex  over 8 years ago

Commit id: a01768f6e4c673928da3a124f071669a67d95e62

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(I will not use the "hat" ($\hat{}$) for the operators unless it is strictly necessary)  The Rabi Hamiltonian for 2 qubit is  \begin{equation} \begin{equation}\label{eqn:H2R}  H_{2q}=\hbar \omega_0\adag a + \hbar \frac{\omega_1}{2}\sigma^{(1)}_z + \hbar \frac{\omega_2}{2}\sigma^{(2)}_z + \hbar(\Gamma_1\sigma^{(1)}_x + \Gamma_2\sigma^{(2)}_x)(\adag + a)  \end{equation}.   

  Taking $\Gamma_i\in\mathbb{R}$ and remembering $\sigma_x^{\dagger}=\sigma_x$ one has $\hat{\gamma}^{\dagger}=\hat{\gamma}$.  The eigenstates of Hamiltonian \ref{eqn:H2R} are the displaced Fock states:  \begin{equation}  |N_{nm}nm>=\ddag{\omega^{-1}\gamma_{nm}}|N>|n>|m>  \end{equation}  \end{document}