Deep-Learning-Empowered Programmable Topolectrical Circuits

TL;DR

A deep learning empowered programmable topolectrical circuits (DLPTCs) platform for physical modeling and analysis by integrating fully independent, continuous tuning of both on site and off site terms of the lattice Hamiltonian, physics graph informed inverse state design, and immediate hardware verification is presented.

Abstract

Topolectrical circuits provide a versatile platform for exploring and simulating modern physical models. However, existing approaches suffer from incomplete programmability and ineffective feature prediction and control mechanisms, hindering the investigation of physical phenomena on an integrated platform and limiting their translation into practical applications. Here, we present a deep learning empowered programmable topolectrical circuits (DLPTCs) platform for physical modeling and analysis. By integrating fully independent, continuous tuning of both on site and off site terms of the lattice Hamiltonian, physics graph informed inverse state design, and immediate hardware verification, our system bridges the gap between theoretical modeling and practical realization. Through flexible control and adiabatic path engineering, we experimentally observe the boundary states without global symmetry in higher order topological systems, their adiabatic phase transitions, and the flat band like characteristic corresponding to Landau levels in the circuit. Incorporating a physics graph informed mechanism with a generative AI model for physics exploration, we realize arbitrary, position controllable on board Anderson localization, surpassing conventional random localization. Utilizing this unique capability with high fidelity hardware implementation, we further demonstrate a compelling cryptographic application: hash based probabilistic information encryption by leveraging Anderson localization with extensive disorder configurations, enabling secure delivery of full ASCII messages.

Figures (9)

• Figure 1: The conception of DLPTCs ‘HeTu’. a, The schematic of DLPTC and integration with different components. Physics-graph information is embedded into the deep learning framework for physics phenomenon prediction and generation. The generated parameters are loaded into the driving controller and used to drive the DLPTC. b, By controlling the onsite and offsite terms, this setup facilitates various complex systems, including higher-order topological lattices, flat-band systems for Landau levels, and Anderson localizations, with further potential for exploration beyond these areas. c, The on-site and off-site terms, corresponding to the vortex and edge values of the graph, are fully programmable through voltage control. d, With the DLPTC, we demonstrate an ASCII-based message encryption system for practical application.
• Figure 1: Experiment observation of phase transition in HOTI without global symmetry. By adiabatically and continuously tuning the off-site capacitance, we can experimentally observe the phase transition process. The coupling coefficient $t_1$ linearly varies from 0.25 to 0.75, while $t_2$ transitions from 0.75 to 0.25, resulting in $\gamma= t_1/(t_1+t_2)$ changing from 0.25 to 0.75. The seven-mode distribution in the figure illustrates the variation of $\gamma$ from 0.25 to 0.75. We selected two representative nodes, $A_{009}$ and $A_{018}$, to demonstrate the continuous variation of their normalized impedance, as depicted by the blue and red curves.
• Figure 2: Higher-order topological insulator without global symmetry.a, Schematic of the lattice model when $t_1<t_2$. b, The energy spectrum for a function of $t_1/(t_1+t_2)$. c, Schematic of the lattice model when $t_1>t_2$. d, The calculated and measured impedance spectra on characteristic points of model a. e, The calculated and measured impedance spectra on characteristic points of model b. f, The impedance distribution of edge, bulk, and BCIEC modes in model a. g, The impedance distribution of bulk and edge modes in model b.
• Figure 2: Circuit implementation of Landau levels and the "breathing" mode observation.a, Schematic of the flat-band lattice and representative sites at the corner, edge, and bulk position. b, The simulated impedance curve summation of all sites with minor parasite parameters, all 19 impedance bands can be observed, corresponding to the peaks of TBM DOS. c, The simulated impedance curve summation of all sites with actual parasite parameters, the lower half of the bands is compressed and closely packed. d, The experimental data of modes $M=1$ to $M=9$. The mode spreads from the center to the edges when mode order increases, and then shrinks to the center when continuously increasing to $M=9$. During this "breathing" process, their spatial distributions remain $C_3$ symmetry with respect to the center of the lattice.
• Figure 3: Two-dimensional Fock-state lattice with an effective pseudomagnetic field and Landau levels.a, Schematic of the flat-band lattice. b, The eigenenergy spectrum and corresponding DOS calculated by TBM. c, Circuit simulation and experiment result of DOS.