Bloch oscillations in non-Hermitian lattices with trajectories in complex plane

Abstract

Bloch oscillations (BOs), i.e. the oscillatory motion of a quantum particle in a periodic potential, are one of the most striking effects of coherent quantum transport in the matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called 'acceleration' theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e. not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only {\it on average}, and that the periodic wave packet motion of the particle in the real space is described by a trajectory in {\it complex} plane, i.e. it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.

9 pages, 6 figures, to appear in Phys. Rev. A

References in corpus (12)

• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Fractional Bloch oscillations in photonic lattices
• Acoustic Analogue of Bloch Oscillations and Resonant Zener Tunneling in Ultrasonic Superlattices
• Bloch oscillations of Path-Entangled Photons
• Coherent control of interacting particles using dynamical and Aharonov-Bohm phases
• Stopping and Time Reversal of Light in Dynamic Photonic Structures via Bloch Oscillations
• Bloch dynamics in lattices with long range hoppings
• Dynamics of Bloch Oscillations in Disordered Lattice Potentials
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Talbot self-imaging in $\mathcal{P}\mathcal{T}$-symmetric complex crystals
• Wannier-Stark ladder in the linear absorption of a random system with scale-free disorder

Cited by in corpus (20)

• Topological phases of non-Hermitian systems
• Non-Bloch band collapse and chiral Zener tunneling
• Non-Hermitian bidirectional robust transport
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Non-Hermitian tight-binding network engineering
• Tight-binding lattices with an oscillating imaginary gauge field
• Loschmidt echo and fidelity decay near an exceptional point
• Kinked linear response from non-Hermitian cold-atom pumping
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• PT-symmetric quantum oscillator in an optical cavity
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Super Bloch Oscillation in a PT symmetric system
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Scattering of accelerated wave packets
• Dynamics of non-Hermitian Floquet Wannier-Stark system
• Real-time edge dynamics of non-Hermitian lattices
• Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• Non-Hermitian interaction of a discrete state with a continuum
• Noisy Stark probes as quantum-enhanced sensors
• Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices