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Title: Solvable multistate model of Landau-Zener transitions in cavity QED

Abstract

We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

Authors:
 [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1338764
Report Number(s):
LA-UR-16-20731
Journal ID: ISSN 2469-9926; TRN: US1701815
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 93; Journal Issue: 6; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Atomic and Nuclear Physics; Material Science; quantum integrability; cavity-QED; Landau-Zener

Citation Formats

Sinitsyn, Nikolai, and Li, Fuxiang. Solvable multistate model of Landau-Zener transitions in cavity QED. United States: N. p., 2016. Web. doi:10.1103/PhysRevA.93.063859.
Sinitsyn, Nikolai, & Li, Fuxiang. Solvable multistate model of Landau-Zener transitions in cavity QED. United States. doi:10.1103/PhysRevA.93.063859.
Sinitsyn, Nikolai, and Li, Fuxiang. 2016. "Solvable multistate model of Landau-Zener transitions in cavity QED". United States. doi:10.1103/PhysRevA.93.063859. https://www.osti.gov/servlets/purl/1338764.
@article{osti_1338764,
title = {Solvable multistate model of Landau-Zener transitions in cavity QED},
author = {Sinitsyn, Nikolai and Li, Fuxiang},
abstractNote = {We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.},
doi = {10.1103/PhysRevA.93.063859},
journal = {Physical Review A},
number = 6,
volume = 93,
place = {United States},
year = 2016,
month = 6
}

Journal Article:
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  • Cited by 3
  • Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.
  • Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.
  • In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less