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Capacitively Coupled Charge Qubits: Difference between revisions
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Capacitively Coupled Charge Qubits (view source)
Revision as of 17:27, 3 November 2014
, 3 November 2014→Rotations
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-B\frac{g}{\lambda_1}& 0 & 0 &B\frac{\Delta_1+\Delta_2}{\lambda_1}
\end{matrix}\right)\cos{(\omega_{AC}t)}</math>
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{| border="1" cellpadding="2"
! colspan="2" width="100"|AC Pulse
!width="225"|Rotating Frame (<math>\Delta_1>\Delta_2</math>)
!width="225"|Rotating Frame (<math>\Delta_1<\Delta_2</math>)
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|rowspan="2"|<math>\epsilon_1</math> || <math>\omega_{AC} = (\lambda_1-\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & A_1 & 0 & 0 \\
A_1 & 0 & 0 & 0 \\
0 & 0 & 0 & -A_1 \\
0 & 0 & -A_1 & 0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & -A_1 & 0 & 0 \\
-A_1 & 0 & 0 & 0 \\
0 & 0 & 0 & -A_1 \\
0 & 0 & -A_1 & 0
\end{matrix}\right)</math>
|-
|<math>\omega_{AC} = (\lambda_1+\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & -A_2 & 0 \\
0 & 0 & 0 & -A_2 \\
-A_2 & 0 & 0 & 0 \\
0 & -A_2 & 0 & 0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & -A_2 & 0 \\
0 & 0 & 0 & A_2 \\
-A_2 & 0 & 0 & 0 \\
0 & A_2 & 0 & 0
\end{matrix}\right)</math>
|-
|rowspan="2"|<math>\epsilon_2</math> || <math>\omega_{AC} = (\lambda_1-\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & -C_1 & 0 & 0 \\
-C_1 & 0 & 0 & 0 \\
0 & 0 & 0 & -C_1 \\
0 & 0 & -C_1 & 0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & C_1 & 0 & 0 \\
C_1 & 0 & 0 & 0 \\
0 & 0 & 0 & -C_1 \\
0 & 0 & -C_1 & 0
\end{matrix}\right)</math>
|-
| <math>\omega_{AC} = (\lambda_1+\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & -C_2 & 0 \\
0 & 0 & 0 & C_2 \\
-C_2 & 0 & 0 & 0 \\
0 & C_2 & 0 & 0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & -C_2 & 0 \\
0 & 0 & 0 & -C_2 \\
-C_2 & 0 & 0 & 0 \\
0 & -C_2 & 0 & 0
\end{matrix}\right)</math>
|-
|rowspan="2"|<math>\Delta_1</math> || <math>\omega_{AC} = 2(\lambda_1)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & -B\frac{g}{\lambda_1} \\
0 & 0 & 0 & 0 \\
0& 0 & 0 & 0\\
-B\frac{g}{\lambda_1}& 0 & 0 &0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & -B\frac{g}{\lambda_1} \\
0 & 0 & 0 & 0 \\
0& 0 & 0 & 0\\
-B\frac{g}{\lambda_1}& 0 & 0 &0
\end{matrix}\right)</math>
|-
| <math>\omega_{AC} = 2(\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & 0 \\
0 & 0 & -B\frac{g}{\lambda_2} & 0 \\
0& -B\frac{g}{\lambda_2} & 0 & 0\\
0& 0 & 0 &0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 &0 \\
0 & 0 & B\frac{g}{\lambda_2} & 0 \\
0& B\frac{g}{\lambda_2} & 0 & 0\\
0& 0 & 0 &0
\end{matrix}\right)</math>
|-
|rowspan="2"|<math>\Delta_2</math> || <math>\omega_{AC} = 2(\lambda_1)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & -B\frac{g}{\lambda_1} \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
-B\frac{g}{\lambda_1}& 0 & 0 &0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & -B\frac{g}{\lambda_1} \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
-B\frac{g}{\lambda_1}& 0 & 0 &0
\end{matrix}\right)</math>
|-
| <math>\omega_{AC} = 2(\lambda_2)/\hbar</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & 0 \\
0 & 0 & B\frac{g}{\lambda_2} & 0 \\
0 & B\frac{g}{\lambda_2} & 0 & 0 \\
0& 0 & 0 &0
\end{matrix}\right)</math> || <math>\frac{1}{4}\left( \begin{matrix}
0 & 0 & 0 & 0 \\
0 & 0 & -B\frac{g}{\lambda_2} & 0 \\
0 & -B\frac{g}{\lambda_2} & 0 & 0 \\
0& 0 & 0 &0
\end{matrix}\right)</math>
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