Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models

Abstract

We systematically investigate the non-Hermitian generalisations of the Landau-Zener (LZ) transition and the Landau-Zener-Stückelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behaviour analysed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulae for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasised. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time $(\mathcal{P}\mathcal{T})$ reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualised through the beam intensity profile and the transition probabilitiess measured by the centre of mass of the profile.

arXiv comment10 pages, 6 figures. Comments are welcome

References in corpus (33)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Edge states and topological invariants of non-Hermitian systems
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Symmetry and Topology in Non-Hermitian Physics
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Hermitian Chern bands
• Landau-Zener-Stuckelberg interferometry
• AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Non-Hermitian Delocalization and Eigenfunctions
• Robust light transport in non-Hermitian photonic lattices
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Transition times in the Landau-Zener model
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Hall Conductance of a Non-Hermitian Chern Insulator
• Time-resolved measurement of Landau-Zener tunneling in periodic potentials
• Nuclear spin driven resonant tunnelling of magnetisation in Mn12 acetate
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Topology and Observables of the Non-Hermitian Chern Insulator
• Geometry of Bloch states probed by Stückelberg interferometry
• Solvable multistate model of Landau-Zener transitions in cavity QED
• Landau-Zener extension of the Tavis-Cummings model: structure of the solution
• Coulomb blockade in superconducting quantum point contacts
• Enhancement of Macroscopic Quantum Tunneling by Landau-Zener Transitions
• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Tight-binding lattices with an oscillating imaginary gauge field
• Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Non-equilibrium dynamics in Bose-Hubbard ladders
• Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids
• Geometric phase in Stückelberg interferometry
• Non-adiabatic transitions in a non-symmetric optical lattice

Cited by in corpus (15)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Stückelberg interferometry using spin-orbit-coupled cold atoms in an optical lattice
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Nonadiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level systems
• The global phase diagram of the cluster-XY spin chain with dissipation
• Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Landau-Zener transitions through a pair of higher order exceptional points