Capacitively Coupled Charge Qubits: Difference between revisions

[[Image:Detuning graph.png|thumb|Energy levels of the 2 qubit system as a function of both detunings.|300px]]

For a single charge qubit, the Hamiltonian is

H_i = \left( \begin{matrix}

\epsilon_i/2 & \Delta_i \\

\Delta_i & -\epsilon_i/2

\end{matrix}\right)

We will refer to $\epsilon_i$ and $\Delta_i$ as the \emph{detuning} and \emph{tunnel coupling} of qubit $i$, respectively.

 

We can further write down the full Hamiltonian explicitly:

 

H = \left( \begin{matrix}

\frac{1}{2}(\epsilon_1+\epsilon_2) + g & \Delta_2 & \Delta_1 & 0 \\

0 & \Delta_1 & \Delta_2 & \frac{1}{2}(-\epsilon_1-\epsilon_2) + g

\end{matrix}\right)