Adiabatic theorem without a gap condition: Two-level system coupled to quantized radiation field

1998/03/31 by J. E. Avron, Alexander Elgart, A. Elgart · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #Quantum and electron transport phenomena #math-ph #math.FA #math.MP #math.SP #physics.atom-ph #quant-ph

paper · pdf · doi:10.1103/physreva.58.4300

published as Phys. Rev. A, 58, 4300-4306, (1998) · Revised version, 15 pages

arxiv created 1998/08/20 · openalex publication_date 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an adiabatic theorem for the ground state of the Dicke model [Phys. Rev. 93, 99 (1954)] in a slowly rotating magnetic field and show that for weak electron-photon coupling, the adiabatic time scale is close to the time scale of the corresponding two-level system without the quantized radiation field. There is a correction to this time scale, which is the Lamb shift of the model. The photon field affects the rate of approach to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of QED.

Citations

• Quantal phase factors accompanying adiabatic changes

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