Solvable fourstate LandauZener model of two interacting qubits with path interference
In this paper, I identify a nontrivial fourstate LandauZener 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 timedependent 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 of integrability in the multistate LandauZener 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 sixstate generalization as an example.
 Authors:

^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
 Publication Date:
 Report Number(s):
 LAUR1528160
Journal ID: ISSN 10980121
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. B, Condensed Matter and Materials Physics
 Additional Journal Information:
 Journal Volume: 92; Journal Issue: 20; Journal ID: ISSN 10980121
 Publisher:
 American Physical Society (APS)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Mathematics; Material Science; quantum dots
 OSTI Identifier:
 1335604
 Alternate Identifier(s):
 OSTI ID: 1227519
Sinitsyn, Nikolai A. Solvable fourstate LandauZener model of two interacting qubits with path interference. United States: N. p.,
Web. doi:10.1103/PhysRevB.92.205431.
Sinitsyn, Nikolai A. Solvable fourstate LandauZener model of two interacting qubits with path interference. United States. doi:10.1103/PhysRevB.92.205431.
Sinitsyn, Nikolai A. 2015.
"Solvable fourstate LandauZener model of two interacting qubits with path interference". United States.
doi:10.1103/PhysRevB.92.205431. https://www.osti.gov/servlets/purl/1335604.
@article{osti_1335604,
title = {Solvable fourstate LandauZener model of two interacting qubits with path interference},
author = {Sinitsyn, Nikolai A.},
abstractNote = {In this paper, I identify a nontrivial fourstate LandauZener 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 timedependent 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 of integrability in the multistate LandauZener 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 sixstate generalization as an example.},
doi = {10.1103/PhysRevB.92.205431},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 20,
volume = 92,
place = {United States},
year = {2015},
month = {11}
}