2023/01/28 by Prosenjit Maity, Maity, Prosenjit · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2301.12275
openalex publication_date 2023/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Various approaches have been used in the literature for eliminating nonresonant levels in atomic systems and deriving effective Hamiltonians. Important among these are elimination techniques at the level of probability amplitudes, operator techniques to project the dynamics on to the subspace of resonant levels, Green's function techniques, the James' effective Hamiltonian approach, etc. None of the previous approaches is suitable for deriving effective Hamiltonians in intracavity situations. However, the James' approach does work in the case of only two-photon transitions in a cavity. A generalization of the James' approach works in the case of three-photon transitions in a cavity, but only under Raman-like resonant conditions. Another important approach for adiabatic elimination is based on an adaptation of the Markov approximation well-known in the theory of system-bath interactions. However, this approach has not been shown to work in intracavity situations. In this paper, we present a method of adiabatic elimination for atoms inside cavities in the presence of multiphoton transitions. We work in the Heisenberg picture, and our approach has the advantage that it allows one to derive effective Hamiltonians even when Raman-like resonance conditions do not hold.