Geometric phase in Stückelberg interferometry

Abstract

We study the time evolution of a two-dimensional quantum particle exhibiting an energy spectrum, made of two bands, with two Dirac cones, as e.g. in the band structure of a honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated to each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wavefunctions.

20 pages, 12 figures

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Cited by in corpus (7)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Bloch state tomography using Wilson lines
• Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
• Geometry of Bloch states probed by Stückelberg interferometry
• Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models
• Stückelberg interferometry using spin-orbit-coupled cold atoms in an optical lattice
• High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts