The Jaynes-Cummings model (sometimes abbreviated JCM) is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity (or a bosonic field).
Two-Level Atom Interacting with a Quantum Field
The Hamiltonian of Jaynes–Cummings model is
Only pairs of eigenstates ∣g,n+1⟩↔∣e,n⟩ are coupled, and thus the Hamiltonian is block diagonal, in 2×2 blocks, making it simple to diagonalize analytically
For large detuning∣ω−ω0∣≫g⟨a†a⟩ , the generalized Rabi frequency is approximately
Therefore, when ω≪ω0 (blue detune), we have Eg≈E−<0 and Ee≈E+>0. While when ω≫ω0 (red detune), we have Ee≈E−<0 and Eg≈E+>0. Now, to perform adiabatic population transfer, we adjust the laser gradually and slowly from blue detune to red detune. Assume the atom was initially at ∣g⟩, and the laser is blued detuned, thus ∣g⟩∼∣−⟩. In the process of adjusting ω0, due to the adiabatic theorem, the atom will remain in the state ∣−⟩. However, when the adjustment ended, we find that ∣−⟩ sims ∣e⟩ now! The population transfers from ∣g⟩ to ∣e⟩.
Collapse and Revival
When an atom was initially at ∣g,α⟩, where ∣α⟩ is the coherent state, the phenomenon of collapse and revival occurs.
In large detuning limit, the effective Hamiltonian is
where χ=g2/Δ and Δ=ω0−ω.
Gerry, C., & Knight, P. (2004). Introductory Quantum Optics. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511791239 ↩︎