2011/06/30 by Victor V. Albert, Gregory D. Scholes, Paul Brumer
Computer Science · Mathematics · Physics and Astronomy · #Approximation error #Born approximation #Born–Huang approximation #Boson #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian (control theory) #Mathematical analysis #Mathematics #Operator (biology) #Parity (physics) #Photon #Physics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum optics and atomic interactions #Rotating wave approximation #Scattering #cond-mat.mes-hall #physics.chem-ph #quant-ph
paper · pdf · doi:10.1103/physreva.84.042110
published as Phys. Rev. A 84, 042110 (2011) · 11 pages, 5 figures
arxiv created 2011/09/07 · openalex publication_date 2011/10/11 · arxiv updated 2012/03/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra- and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime. Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.