this is for holding javascript data
Awaiting Activation edited 2QEnergies.tex
over 8 years ago
Commit id: a01768f6e4c673928da3a124f071669a67d95e62
deletions | additions
diff --git a/2QEnergies.tex b/2QEnergies.tex
index 326ef40..8d23f46 100644
--- a/2QEnergies.tex
+++ b/2QEnergies.tex
...
(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}