Solution to the Landau–Zener problem via Susskind–Glogower operators

• Published in: Physics letters. A Vol. 375; no. 43; pp. 3770 - 3774
• Main Authors: Rodríguez-Lara, B.M., Rodríguez-Méndez, D., Moya-Cessa, H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 17-10-2011
• Subjects: Approximation; Coherent control of atomic interactions with photons; Mathematical analysis; Mathematical models; Operators; Photons; Quantum optics; Solid state physics; Transformations; Quantum optics; Coherent control of atomic interactions with photons
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2011.08.051

We show that, by means of a right-unitary transformation, the fully quantized Landau–Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau–Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau–Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.
► We study a full quantum Landau–Zener model derived from the Jaynes–Cummings model. ► The model within the rotating wave appoximation is diagonalized in the field basis. ► Solutions to the quantum model are presented in terms of well-know solutions to the classical Landau–Zener problem. ► The model without the rotating wave appoximation is diagonalized in the qubit basis.