Capacitively Coupled Charge Qubits: Difference between revisions

\lambda_1 = -\sqrt{\Delta_1^2+\Delta_2^2+\frac{\epsilon_1^2}{4}+g^2+\sqrt{4\Delta_1^2\Delta_2^2+\epsilon_1^2(\Delta_2^2+g^2)}}

\lambda_2 = -\sqrt{\Delta_1^2+\Delta_2^2+\frac{\epsilon_1^2}{4}+g^2-\sqrt{4\Delta_1^2\Delta_2^2+\epsilon_1^2(\Delta_2^2+g^2)}}

\lambda_3 = \sqrt{\Delta_1^2+\Delta_2^2+\frac{\epsilon_1^2}{4}+g^2-\sqrt{4\Delta_1^2\Delta_2^2+\epsilon_1^2(\Delta_2^2+g^2)}}

\lambda_4 = \sqrt{\Delta_1^2+\Delta_2^2+\frac{\epsilon_1^2}{4}+g^2+\sqrt{4\Delta_1^2\Delta_2^2+\epsilon_1^2(\Delta_2^2+g^2)}}

\lambda_2 \approx \lambda_2^0 + \frac{\Delta_2(\Delta_1+-\Delta_2)-g^2}{8\Delta_1\Delta_2\lambda_2^0}\epsilon_1^2

\lambda_3 \approx \lambda_3^0 + \frac{\Delta_2(\Delta_1+-\Delta_2)-g^2}{8\Delta_1\Delta_2\lambda_3^0}\epsilon_1^2

SimilarlyUnfortunately, tonone makeof the other transitions betweencan <math>|00\rangle</math>be andmade <math>|01\rangle</math>to andbe betweeninvariant <math>|10\rangle</math>to andsecond order fluctuations in <math>|11\rangleepsilon_1</math>. flatIf we wish to make this transition invariant to all second order indetuning fluctuations, we must set <math>\epsilon_1Delta_1 = \Delta_2</math>, weand can<math>g set= \sqrt{2}\Delta_1</math>.