Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 6) : Part2

6.10 (1) Define as: Then, So, the interaction Hamiltonian is: Since: We have: By dropping the non-RWA terms such as , we have: (2) By dropping the third state, we have: For Hence, from the Schroedinger equation: , we have: --- (1) --- (2)By combining them, we have: , where From the initial conditio…