Exact results for survival probability in the multistate Landau–Zener model

Volkov, Mikhail V.; Ostrovsky, V N

doi:10.1088/0953-4075/37/20/003

Cited by 54 publications

(76 citation statements)

References 23 publications

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“…The survival probabilities P 1→1 and P 3→3 coincide with the exact expressions conjectured [7] and derived exactly for constant couplings [17,19] earlier.…”

Section: Evolution Matrix In the Adiabatic Basissupporting

confidence: 77%

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Steering quantum transitions between three crossing energy levels

Ivanov

Vitanov

2008

Phys. Rev. A

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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 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.

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“…The survival probabilities P 1→1 and P 3→3 coincide with the exact expressions conjectured [7] and derived exactly for constant couplings [17,19] earlier.…”

Section: Evolution Matrix In the Adiabatic Basissupporting

confidence: 77%

“…The cases of one [15] or two [16] degenerate levels have also been solved. In the most general case of linear energies of arbitrary slopes, the general solution is not known, but exact results for some survival probabilities have been derived [17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Steering quantum transitions between three crossing energy levels

Ivanov

Vitanov

2008

Phys. Rev. A

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“…Result (4.5) does not depend on ε j . Formula (4.5) was conjectured by Brundobler and Elser (1993) and recently proved using two different methods by Shytov (2004) and Volkov and Ostrovsky (2004). Again we consider the case q = 0, when the maximum slope corresponds to k = ±(n−1).…”

Section: Exact Results For Survival Probabilitymentioning

confidence: 92%

Thermal Stability and Scalability of Mictamict Ti–Si–N Metal–Oxide–Semiconductor Gate Electrodes

Kondo

Furumai

Sakashita

et al. 2009

jjap

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Degeneracy of energy levels of excited hydrogen atoms is not fully lifted by external perpendicular electric and magnetic fields in the first order of perturbation theory. Within the submanifold of residual degeneracy the levels splitting is governed by the second-order effects. The related classical electron trajectories exhibit instabilities characterized by the Lyapunov exponent. The present study establishes quantum mechanical implications of these instabilities. In particular, we derive from a quantum framework a simple analytical approximation for the Lyapunov exponent. The classical instabilities are linked to the presence of a diabatic quasistationary state in the quantum mechanical problem. Its meaning is elucidated by considering a related non-stationary quantum system with time-dependent field parameter. Some of the state-to-state transition probabilities are approximately expressed via Lyapunov exponents. Exact formulae for these probabilities are derived in the framework of multistate generalization of the Landau-Zener model. Nonadiabatic transitions are interpreted in terms of analytical properties of adiabatic potential curves.

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“…Extensions of the original LZ model have been studied in the past few years to account for the effects of nonlinearities [92], finite-coupling duration effects [93], multistate dynamics [94,95], or decoherence, noise and dissipation [96][97][98].…”

Section: Photonic Landau-zener Tunnelingmentioning

confidence: 99%

Dynamical Tunneling from the Edge of Vibrational State Space of Large Molecules

2011

Dynamical Tunneling

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Exact results for survival probability in the multistate Landau–Zener model

Cited by 54 publications

References 23 publications

Steering quantum transitions between three crossing energy levels

Steering quantum transitions between three crossing energy levels

Thermal Stability and Scalability of Mictamict Ti–Si–N Metal–Oxide–Semiconductor Gate Electrodes

Dynamical Tunneling from the Edge of Vibrational State Space of Large Molecules

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