[Paper Review] Controlled transport based on multiorbital Aharonov-Bohm photonic caging

Gabriel Cáceres-Aravena, Diego Guzmán-Silva+2 more|arXiv (Cornell University)|May 25, 2022

Nonlinear Photonic Systems48 references52 citations

TL;DR

This paper proposes a multiorbital photonic lattice using femtosecond laser-written waveguides to induce a synthetic π-flux via S-P orbital coupling, enabling controlled Aharonov-Bohm caging and directional transport. By engineering positive and negative couplings in a diamond lattice, the authors experimentally demonstrate flat band formation with three degenerate flat bands, achieving perfect linear control of energy transport by tuning input phase or position.

ABSTRACT

The induction of synthetic magnetic fields on lattice structures allows to effectively control their localization and transport properties. In this work, we generate effective $\pi$ magnetic fluxes on a multi-orbital diamond lattice, where first ($S$) and second ($P$) order modes effectively interact. We implement a $z$-scan method on femtosecond laser written photonic lattices and experimentally observe Aharonov-Bohm caging for $S$ and $P$ modes, as a consequence of a band transformation and the emergence of a spectrum composed of three degenerated flat bands. As an application, we demonstrate a perfect control of the dynamics, where we translate an input excitation across the lattice in a completely linear and controlled way. Our model, based on a flat band spectrum, allows us to choose the direction of transport depending on the excitation site or input phase.

Motivation & Objective

• To realize synthetic magnetic flux in a photonic lattice without complex geometries, using interorbital coupling between S and P modes.
• To demonstrate Aharonov-Bohm caging in a multi-orbital system, leading to extreme localization and flat band formation.
• To achieve controllable, linear, and directional energy transport in a compact lattice structure using input phase and excitation site selection.
• To provide a stable, nonlinearity-free method for steering light in photonic integrated circuits.
• To establish a platform for future integration of non-Hermitian and nonlinear effects in a flexible, on-demand photonic architecture.

Proposed method

• Utilized femtosecond laser writing to fabricate a multi-orbital diamond lattice with S and P waveguides, enabling controlled coupling between fundamental and second-order modes.
• Engineered positive and negative coupling constants via waveguide orientation and mode symmetry, inducing an effective π-flux per plaquette.
• Applied a z-scan method to measure intensity evolution along the propagation direction, observing caging and transport dynamics.
• Used a tight-binding model with Hamiltonian $-irac{ ext{d}oldsymbol{ ho}}{ ext{d}z} = oldsymbol{V}oldsymbol{ ho}$, where $oldsymbol{V}$ includes site-dependent couplings to simulate the system.
• Implemented a Bloch ansatz to compute the band structure, revealing three degenerate flat bands at $E = 0, /pm 2V$ under π-flux conditions.
• Explored input-dependent transport by varying excitation site (central vs. edge) and phase (in-phase vs. out-of-phase), enabling directional control.

Experimental results

Research questions

• RQ1 Can synthetic magnetic flux with φ = π be induced in a photonic lattice using only interorbital coupling between S and P modes?
• RQ2 Does the induced π-flux lead to the formation of degenerate flat bands and Aharonov-Bohm caging for both S and P modes?
• RQ3 Can the direction of energy transport be controlled linearly by adjusting input phase or excitation site in the absence of nonlinearity?
• RQ4 Is the flat band spectrum robust enough to support perfect, localized, and directional transport in a real experimental setup?
• RQ5 Can this system serve as a stable, on-demand platform for photonic logic operations without requiring nonlinearities?

Key findings

• The authors experimentally observed Aharonov-Bohm caging for both S and P modes in a multi-orbital diamond lattice under π-flux conditions, confirmed by intensity evolution measurements.
• The system exhibits a flat band spectrum with three degenerate eigenvalues ($E = 0, /pm 2V$), each with two-fold degeneracy, due to the induced π-flux.
• Single-site excitation at the central row leads to complete localization (caging), while in-phase or out-of-phase excitation at edge sites enables perfect directional transport over 50 mm.
• Directional transport was reversed by changing the input phase: in-phase profiles moved left in {Bn, Cn} sites and right in {En±1, Fn±1} sites, demonstrating full control.
• The transport mechanism is purely linear and stable, with no need for nonlinearity, offering a robust solution for photonic logic and integrated optical circuits.
• The z-scan method successfully mapped the propagation dynamics, showing that energy is confined to a few unit cells under caging and fully translated under controlled excitation.