Non-Hermitian quantum rings

Abstract

We investigate the spectral and dynamical properties of a quantum particle constrained on a ring threaded by a magnetic flux in presence of a complex (non-Hermitian) potential. For a static magnetic flux, the quantum states of the particle on the ring can be mapped into the Bloch states of a complex crystal, and magnetic flux tuning enables to probe the spectral features of the complex crystal, including the appearance of exceptional points. For a time-varying (linearly-ramped) magnetic flux, Zener tunneling among energy states is realized owing to the induced electromotive force. As compared to the Hermitian case, striking effects are observed in the non-Hermitian case, such as a highly asymmetric behavior of particle motion when reversing the direction of the magnetic flux and field-induced delayed transparency.

9 pages, 5 figures; to appear in the Phys. Rev. A

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Invisibility and PT-symmetry
• Towards a Landau-Zener formula for an interacting Bose-Einstein condensate
• Rotational Fluxons of Bose-Einstein Condensates in Coplanar Double-Ring Traps
• SUSY transformations with complex factorization constants. Application to spectral singularities

Cited by in corpus (6)

• Parity-time symmetry under magnetic flux
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field
• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics