2016/02/14 by Zhiguo Lü, Yiying Yan, Hsi‐Sheng Goan +2 · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Quantum optics and atomic interactions #Quantum tunnelling #Rabi frequency #Rotating wave approximation #Statistical physics #Unitary transformation #quant-ph
paper · pdf · doi:10.1103/physreva.93.033803
15pages,7figures, Phys. Rev. A accepted
arxiv created 2016/02/14 · openalex publication_date 2016/03/02 · arxiv updated 2016/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We investigate the bias-modulated dynamics of a strongly driven two-level system using the counterrotating-hybridized rotating-wave (CHRW) method. This CHRW method treats the driving field and the bias on equal footing by a unitary transformation with two parameters \ensuremathξ and \ensuremathζ, and is nonperturbative in driving strength, tunneling amplitude, or bias. In addition, this CHRW method is beyond the traditional rotating-wave approximation (Rabi-RWA) and yet by properly choosing the two parameters \ensuremathξ and \ensuremathζ, the transformed Hamiltonian takes the RWA form with a renormalized energy splitting and a renormalized driving strength. The reformulated CHRW method possesses the same mathematical simplicity as the Rabi-RWA approach and thus allows us to calculate analytically the dynamics and explore explicitly the effect of the bias. We show that the CHRW method gives the accurate driven dynamics for a wide range of parameters as compared to the numerically exact results. When energy scales of the driving are comparable to the intrinsic energy scale of the two-level systems, the counterrotating interactions and static bias profoundly influence the generalized Rabi frequency. In this regime, where ordinary perturbation approaches fail, the CHRW works very well and efficiently. We also demonstrate the dynamics of the system in the strong-driving and off-resonance cases for which the Rabi-RWA method breaks down but the CHRW method remains valid. We obtain analytical expressions for the generalized Rabi frequency and bias-modulated Bloch-Siegert shift as functions of the bias, tunneling, and driving field parameters. The CHRW approach is a mathematically simple and physically clear method. It can be applied to treat some complicated problems for which a numerical study is difficult to perform.