2007/11/27 by Svetoslav S. Ivanov, S. S. Ivanov, Nikolay V. Vitanov +1 · 4 citations
Computer Science · Physics and Astronomy · #Adiabatic process #Cold Atom Physics and Bose-Einstein Condensates #Gaussian #Hilbert space #Laser-Matter Interactions and Applications #Physics #Propagator #Quantum #Quantum Information and Cryptography #Quantum electrodynamics #Quantum entanglement #Quantum mechanics #Quantum state #Spin (aerodynamics) #Statistical physics #Superposition principle #quant-ph
paper · pdf · doi:10.1103/physreva.77.023406
10 pages, 6 figures
arxiv created 2007/11/27 · openalex publication_date 2008/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a J=1 level in a magnetic field, and in control of entanglement of a pair of spin-1∕2 particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.