58
edits
Capacitively Coupled Charge Qubits: Difference between revisions
Jump to navigation
Jump to search
Capacitively Coupled Charge Qubits (view source)
Revision as of 19:44, 25 October 2014
, 25 October 2014no edit summary
No edit summary |
No edit summary |
||
|
==Rotations==
After bringing the system adiabatically to the sweet spot <math>\epsilon_1=\epsilon_2=0</math>, we can apply an AC pulse to some of our parameters to induce a rotation within the system.
{| border="1" cellpadding="2"
!width="100"|AC Pulse
!width="225"|Resulting Matrix (Lab Basis)
!width="225"|Resulting Matrix (Energy Basis)
|-
|<math>\epsilon_1</math> || <math>\frac{1}{2}\left( \begin{matrix}
B & 0 & 0 & 0 \\
0 & B & 0 & 0 \\
0 & 0 & -B & 0 \\
0 & 0 & 0 & -B
\end{matrix}\right)\cos{(\omega_{AC}t)}</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & 0 & B & 0 \\
0 & 0 & 0 &B \\
B & 0 & 0 & 0 \\
0 & B & 0 & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math>
|-
|<math>\epsilon_2</math> || <math>\frac{1}{2}\left( \begin{matrix}
B & 0 & 0 & 0 \\
0 & -B & 0 & 0 \\
0 & 0 & B & 0 \\
0 & 0 & 0 & -B
\end{matrix}\right)\cos{(\omega_{AC}t)}</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & 0 & B & 0 \\
0 & 0 & 0 &B \\
B & 0 & 0 & 0 \\
0 & B & 0 & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math>
|-
|<math>\Delta_1</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & 0 & B & 0 \\
0 & 0 & 0 &B \\
B & 0 & 0 & 0 \\
0 & B & 0 & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & 0 & B & 0 \\
0 & 0 & 0 &B \\
B & 0 & 0 & 0 \\
0 & B & 0 & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math>
|-
|<math>\Delta_2</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & B & 0 & 0 \\
B & 0 & 0 & 0 \\
0 & 0 & 0 & B \\
0 & 0 & B & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math> || <math>\frac{1}{2}\left( \begin{matrix}
0 & 0 & B & 0 \\
0 & 0 & 0 &B \\
B & 0 & 0 & 0 \\
0 & B & 0 & 0
\end{matrix}\right)\cos{(\omega_{AC}t)}</math>
|}
| |||