Question

2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi- where ω1 parameterizes the strength of the oscillating transverse field and where in general ω U0. a. Construct the 2 × 2 Hamiltonian matrix. b. Use the time-dependent unitary transformation U = e(-iwt/2)oz to transform to a reference frame rotating with the oscillating transverse field. Recall that a state |) in the laboratory frame is transformed to the state ψ-υψ in the rotating frame. Evaluate the time derivative dv/dt to derive the Schrödinger equation in the rotating frame. What is the effective Hamiltonian in the rotating frame?

Answer 1

ven 2ee Pobi o Cas (us hus ut

91 e 2- ko。