Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2211.08003 · Optics Letters

Non-Hermitian Bloch–Zener phase transition

Stefano Longhi

Published Nov 14, 2022• 7 citations
arXivHTMLPDF

Abstract

Bloch-Zener oscillations (BZO), i.e., the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external direct current (DC) force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian systems such oscillations are rather generally aperiodic and only accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition from aperiodic to periodic as a NH parameter in the system is varied. Remarkably, the phase transition can be either smooth or sharp, contrary to other types of NH phase transitions which are universally sharp. A discrete-time photonic quantum walk on a synthetic lattice is suggested for an experimental observation of smooth BZO phase transitions.

DOI
10.1364/ol.478059

Related papers

Nonsmooth Bloch Oscillations in Non-Hermitian Systems

Yanyan He, Tomoki Ozawa

Bloch oscillations (BOs) represent a paradigmatic manifestation of force-driven band dynamics in lattices, conventionally characterized by continuous quasimomentum evolution and smooth periodic trajectories. Here we show that non-Hermiticity qualitatively changes this paradigm, introducing nonsmooth BOs characterized by cusp-like real-space trajectories and abrupt momentum jumps. Reversing the force switches the dynamics between smooth and nonsmooth BOs, enabling strongly nonreciprocal dynamics. We derive a universal relation for the critical force that governs the nonsmooth-to-smooth dynamical transition in general one-dimensional lattices, which is induced by a pitchfork bifurcation in momentum space. Our work establishes a unified framework for non-Hermitian BOs and uncovers a fundamental bifurcation mechanism that can generate nonsmooth wave transport in entirely linear systems.

quant-pharXiv:2606.26480•Jun 26, 2026

Bloch-Zener oscillations of strongly correlated electrons

Stefano Longhi

It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.

Physical Review B•Aug 23, 2012•23 citations

Non-Bloch parity-time-symmetric phase transition in quantum walks

Bingzi Huo, Quan Lin, Lei Xiao +3 more

Parity-time ($\mathcal{P}\mathcal{T}$) symmetry is extensively studied within non-Hermitian physical systems as it has the capability to ensure the presence of real eigenenergies of the systems characterized by non-Hermitian Hamiltonians. Previous studies have been mostly based on the Bloch band theory. Recent developments have unveiled intriguing phenomena which can only be explained by non-Bloch band theory. In this paper, we observe the $\mathcal{P}\mathcal{T}$ phase transition in photonic quantum walks, which can only be explained by the non-Bloch band theory, which relies on the open boundary condition. Furthermore, we explore the impact of disorder on $\mathcal{P}\mathcal{T}$ symmetry and demonstrate disorder-induced $\mathcal{P}\mathcal{T}$ phase transitions. Our work provides a valuable perspective for further explorations on non-Hermitian physics.

Physical Review A•Nov 6, 2024•4 citations

Real-time measurement of non-Hermitian Landau–Zener tunneling near band crossings

Lange Zhao, Shulin Wang, Chengzhi Qin +5 more

Landau–Zener (LZ) tunneling, i.e., the nonadiabatic level transition under strong parameter driving, is a fundamental concept in modern quantum mechanics. With the advent of non-Hermitian physics, research interest has been paid to the LZ tunneling involving level dissipations. However, experimental demonstrations of such an interesting non-Hermitian LZ problem remain yet elusive. By harnessing a synthetic temporal lattice using a fiber-loop circuit, we report on the first real-time measurement of non-Hermitian LZ tunneling in a dissipative two-band lattice model. An innovative approach based on mode interference is developed to measure the transient band occupancies, providing a powerful tool to explore the non-Hermitian LZ tunneling dynamics in non-orthogonal eigenmodes. We find that the loss does not change the final LZ tunneling probability but can highly affect the tunneling process by modifying the typical band occupancies oscillation behaviors. We initiate exploring intriguing LZ physics and measurements beyond the standard Hermitian paradigm, with potential applications in coherent quantum control and quantum technologies.

Advanced Photonics•Apr 11, 2025•2 citations

Zitterbewegung, Bloch Oscillations and Landau-Zener Tunneling in a Quantum Walk

Alois Regensburger, Christoph Bersch, Hinrichs, Benjamin +4 more

We experimentally investigate a discrete time quantum walk in a system of coupled fiber loops and observe typical phenomena known from the wave propagation in periodic structures as ballistic spreading or an oscillation between two internal quantum states similar to Zitterbewegung (trembling motion). If a position-dependent phase gradient is applied we find localization and Bloch oscillations of the field for moderate as well as Landau-Zener tunneling for strong phase gradients.

arXiv:1104.0105•Apr 1, 2011•5 citations

Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

Xin Shen, Fudong Wang, Zhi Li +1 more

We systematically investigate the non-Hermitian generalizations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"uckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behavior is analyzed. 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 formulas for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasized. 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 $(\mathcal{PT})$ 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 visualized through the beam intensity profile and the transition probabilities measured by the center of mass of the profile.

arXiv:1909.05001•Physical Review A•Dec 23, 2019•31 citations
Bloch-Zener oscillations (BZO), i.e., the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external direct current (DC) force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian systems such oscillations are rather generally aperiodic and only accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition from aperiodic to periodic as a NH parameter in the system is varied. Remarkably, the phase transition can be either smooth or sharp, contrary to other types of NH phase transitions which are universally sharp. A discrete-time photonic quantum walk on a synthetic lattice is suggested for an experimental observation of smooth BZO phase transitions.
Bloch oscillations (BOs) represent a paradigmatic manifestation of force-driven band dynamics in lattices, conventionally characterized by continuous quasimomentum evolution and smooth periodic trajectories. Here we show that non-Hermiticity qualitatively changes this paradigm, introducing nonsmooth BOs characterized by cusp-like real-space trajectories and abrupt momentum jumps. Reversing the force switches the dynamics between smooth and nonsmooth BOs, enabling strongly nonreciprocal dynamics. We derive a universal relation for the critical force that governs the nonsmooth-to-smooth dynamical transition in general one-dimensional lattices, which is induced by a pitchfork bifurcation in momentum space. Our work establishes a unified framework for non-Hermitian BOs and uncovers a fundamental bifurcation mechanism that can generate nonsmooth wave transport in entirely linear systems.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
Parity-time (PT\mathcal{P}\mathcal{T}PT) symmetry is extensively studied within non-Hermitian physical systems as it has the capability to ensure the presence of real eigenenergies of the systems characterized by non-Hermitian Hamiltonians. Previous studies have been mostly based on the Bloch band theory. Recent developments have unveiled intriguing phenomena which can only be explained by non-Bloch band theory. In this paper, we observe the PT\mathcal{P}\mathcal{T}PT phase transition in photonic quantum walks, which can only be explained by the non-Bloch band theory, which relies on the open boundary condition. Furthermore, we explore the impact of disorder on PT\mathcal{P}\mathcal{T}PT symmetry and demonstrate disorder-induced PT\mathcal{P}\mathcal{T}PT phase transitions. Our work provides a valuable perspective for further explorations on non-Hermitian physics.
Landau–Zener (LZ) tunneling, i.e., the nonadiabatic level transition under strong parameter driving, is a fundamental concept in modern quantum mechanics. With the advent of non-Hermitian physics, research interest has been paid to the LZ tunneling involving level dissipations. However, experimental demonstrations of such an interesting non-Hermitian LZ problem remain yet elusive. By harnessing a synthetic temporal lattice using a fiber-loop circuit, we report on the first real-time measurement of non-Hermitian LZ tunneling in a dissipative two-band lattice model. An innovative approach based on mode interference is developed to measure the transient band occupancies, providing a powerful tool to explore the non-Hermitian LZ tunneling dynamics in non-orthogonal eigenmodes. We find that the loss does not change the final LZ tunneling probability but can highly affect the tunneling process by modifying the typical band occupancies oscillation behaviors. We initiate exploring intriguing LZ physics and measurements beyond the standard Hermitian paradigm, with potential applications in coherent quantum control and quantum technologies.
We systematically investigate the non-Hermitian generalizations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"uckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behavior is analyzed. 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 formulas for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasized. 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 (PT)(\mathcal{PT})(PT) 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 visualized through the beam intensity profile and the transition probabilities measured by the center of mass of the profile.