Evolution of superpositions of quantum states through a level crossing
Abstract
The Landau-Zener-Stueckelberg-Majorana (LZSM) model is widely used for estimating transition probabilities in the presence of crossing energy levels in quantum physics. This model, however, makes the unphysical assumption of an infinitely long constant interaction, which introduces a divergent phase in the propagator. This divergence remains hidden when estimating output probabilities for a single input state insofar as the divergent phase cancels out. In this paper we show that, because of this divergent phase, the LZSM model is inadequate to describe the evolution of pure or mixed superposition states across a level crossing. The LZSM model can be used only if the system is initially in a single state or in a completely mixed superposition state. To this end, we show that the more realistic Demkov-Kunike model, which assumes a hyperbolic-tangent level crossing and a hyperbolic-secant interaction envelope, is free of divergences and is a much more adequate tool for describing the evolution through a level crossing for an arbitrary input state. For multiple crossing energies which are reducible to one or more effective two-state systems (e.g., by the Majorana and Morris-Shore decompositions), similar conclusions apply: the LZSM model does not produce definite values of the populations and the coherences, andmore »
- Authors:
-
- Department of Physics, Sofia University, James Bourchier 5 Blvd., 1164 Sofia (Bulgaria)
- Publication Date:
- OSTI Identifier:
- 22095637
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. A
- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 6; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ENERGY LEVELS; ENERGY-LEVEL TRANSITIONS; LANDAU-ZENER FORMULA; MIXED STATE; PROBABILITY; PROPAGATOR; QUANTUM MECHANICS; QUANTUM STATES
Citation Formats
Torosov, B. T., Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradso Shose Blvd., 1784 Sofia, and Vitanov, N. V. Evolution of superpositions of quantum states through a level crossing. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.063411.
Torosov, B. T., Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradso Shose Blvd., 1784 Sofia, & Vitanov, N. V. Evolution of superpositions of quantum states through a level crossing. United States. https://doi.org/10.1103/PHYSREVA.84.063411
Torosov, B. T., Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradso Shose Blvd., 1784 Sofia, and Vitanov, N. V. 2011.
"Evolution of superpositions of quantum states through a level crossing". United States. https://doi.org/10.1103/PHYSREVA.84.063411.
@article{osti_22095637,
title = {Evolution of superpositions of quantum states through a level crossing},
author = {Torosov, B. T. and Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradso Shose Blvd., 1784 Sofia and Vitanov, N. V.},
abstractNote = {The Landau-Zener-Stueckelberg-Majorana (LZSM) model is widely used for estimating transition probabilities in the presence of crossing energy levels in quantum physics. This model, however, makes the unphysical assumption of an infinitely long constant interaction, which introduces a divergent phase in the propagator. This divergence remains hidden when estimating output probabilities for a single input state insofar as the divergent phase cancels out. In this paper we show that, because of this divergent phase, the LZSM model is inadequate to describe the evolution of pure or mixed superposition states across a level crossing. The LZSM model can be used only if the system is initially in a single state or in a completely mixed superposition state. To this end, we show that the more realistic Demkov-Kunike model, which assumes a hyperbolic-tangent level crossing and a hyperbolic-secant interaction envelope, is free of divergences and is a much more adequate tool for describing the evolution through a level crossing for an arbitrary input state. For multiple crossing energies which are reducible to one or more effective two-state systems (e.g., by the Majorana and Morris-Shore decompositions), similar conclusions apply: the LZSM model does not produce definite values of the populations and the coherences, and one should use the Demkov-Kunike model instead.},
doi = {10.1103/PHYSREVA.84.063411},
url = {https://www.osti.gov/biblio/22095637},
journal = {Physical Review. A},
issn = {1050-2947},
number = 6,
volume = 84,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2011},
month = {Thu Dec 15 00:00:00 EST 2011}
}