Solvable 4-state Landau-Zener model of two interacting qubits with path interference

Abstract

We identify a nontrivial 4-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. We argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows us to derive explicit exact analytical expressions for the transition probability matrix. We also argue that this model is likely a special case of a larger class of solvable systems, and present a 6-state generalization as an example.

7 pages, 5 figures

References in corpus (7)

• Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum Dots
• Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots
• Exact results for models of multichannel quantum nonadiabatic transitions
• Quantum integrability in the multistate Landau-Zener problem
• Exact transition probabilities in a six-state Landau-Zener system with path interference
• Comment on "Exact results for survival probability in the multistate Landau-Zener model"
• Counterintuitive transitions between crossing energy levels

Cited by in corpus (24)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Electrically Protected Valley-Orbit Qubits in Silicon
• Integrable time-dependent quantum Hamiltonians
• Solvable multistate model of Landau-Zener transitions in cavity QED
• Landau-Zener extension of the Tavis-Cummings model: structure of the solution
• The Quest for Solvable Multistate Landau-Zener Models
• Constraints on scattering amplitudes in multistate Landau-Zener theory
• Landau-Zener transitions in an open multilevel quantum system
• Multistate Landau-Zener models with all levels crossing at one point
• Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory
• A large class of solvable multistate Landau-Zener models and quantum integrability
• Dynamic spin localization and gamma-magnets
• Loss of adiabaticity with increasing tunneling gap in non-integrable multistate Landau-Zener models
• Nonadiabatic Phase Transition with Broken Chiral Symmetry
• Defect production and quench dynamics in the three-dimensional Kitaev model
• Single spin Landau-Zener-Stückelberg-Majorana interferometry of Zeeman-split states with strong spin-orbit interaction in a double quantum dot
• Generic theory of characterizing topological phases under quantum slow dynamics
• SU(3) Landau-Zener interferometry with a transverse periodic drive
• Dynamic Symmetries and Quantum Nonadiabatic Transitions
• Solution to a class of multistate Landau-Zener model beyond integrability conditions
• Nonadiabatic dissociation of molecular Bose-Einstein condensates: competition between chemical reactions
• Derivation of the Landau-Zener formula via functional equations
• Landau-Zener transition between two quantum dots coupled by resonant tunneling
• Graph-theoretical search for integrable multistate Landau-Zener models