Time Reversal Invariant Topologically Insulating Circuits (1309.0878v2)

Abstract: From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed matter frontier and the landscape of modern materials science. Accordingly, there is a broad effort to realize topologically non-trivial electronic and photonic materials for fundamental science as well as practical applications. In this work, we demonstrate the first simultaneous site- and time- resolved measurements of a time reversal invariant topological band-structure, which we realize in a radio frequency (RF) photonic circuit. We control band-structure topology via local permutation of a traveling wave capacitor-inductor network, increasing robustness by going beyond the tight-binding limit. We observe a gapped density of states consistent with a modified Hofstadter spectrum at a flux per plaquette of $\phi=\pi/2$. In-situ probes of the band-gaps reveal spatially-localized bulk-states and de-localized edge-states. Time-resolved measurements reveal dynamical separation of localized edge-excitations into spin-polarized currents. The RF circuit paradigm is naturally compatible with non-local coupling schemes, allowing us to implement a M\"{o}bius strip topology inaccessible in conventional systems. This room-temperature experiment illuminates the origins of topology in band-structure, and when combined with circuit quantum electrodynamics (QED) techniques, provides a direct path to topologically-ordered quantum matter.

• The paper develops a time- and site-resolved RF circuit method to emulate a topologically invariant band structure with robust edge states.
• It employs a capacitive and inductive network to simulate the Hofstadter model with π/2 flux, uncovering a gapped density of states and spin-polarized currents.
• The findings highlight the potential for integrating topological order into quantum systems through resilient circuit designs that mitigate environmental noise.

Time- and Site-Resolved Dynamics in a Topological Circuit

The paper presented by Ningyuan et al. investigates the dynamics of topological photonic materials specifically tailored for radio frequency (RF) photonic circuits. This research is a significant exploration within condensed matter physics and material science realms, focusing on unveiling topological properties in designed materials. By employing a site- and time-resolved measurement technique, the authors achieve a controlled manipulation of a topological band structure in a novel type of RF circuit. This work elucidates the underpinnings of topological invariants and offers insights into potential applications in spintronics and quantum information processing.

Theoretical and Experimental Framework

Topological insulators (TIs), which are materials that behave as insulators in their bulk while having conductive surface states, form the theoretical foundation of this paper. TIs are characterized by their robustness against perturbations, leveraging topological invariants like the Chern number. In this paper, the researchers generate a time-reversal invariant topological band structure through engineered RF photonic circuits. Utilizing a network of capacitors and inductors, the authors control the band topology by permuting the local connections, which allows the emulation of the Hofstadter model with a flux per plaquette of $\phi = \pi/2$.

The RF photonic circuit demonstrates topologically protected phenomena such as edge states and spin-polarized currents. Through this RF circuit, a M\"{o}bius strip topology is realized—a feature not feasible in conventional systems. This topology facilitates the simulation of complex boundary conditions which are theoretically intriguing.

Results and Observations

The structural arrangement led to significant results, revealing the presence of a gapped density of states analogous to known topological phases. The experiment’s design enabled in-situ probing of spatially-resolved characteristics of both bulk and edge states. Bulk states exhibited localization, while edge states were characterized by spatial delocalization with spin-polarization—a haLLMark of topological protection.

Time-resolved measurements captured the evolution of edge modes and the separation of spin-directed dynamics, indicating spin-orbit coupling's influence. The observed band structure, with topologically protected modes residing between bulk bands, points toward practical measurement of intrinsic topological properties. They confirmed the presence of protected states through temporal and spatial separation of spins, supplemented by spin-orbit locked dynamics.

Implications and Future Directions

The experimental demonstration of these principles in RF circuits opens pathways to simulate and understand more complex topological phases in engineered systems. The presented approach provides a solid experimental foundation for integrating topological order with circuit quantum electrodynamics (QED). Practically, the resilience of such topologically derived states lends itself to potential applications in robust quantum information systems, enabling devices less susceptible to environmental noise.

Future developments might focus on extending these techniques to more sophisticated configurations that include interactions and non-linearities, enabling exploration into fractional topological phases and completely new forms of quantum matter. The presented circuit design could also serve as a prototype for more advanced photonic and electronic devices operating under similar topological protection principles.

In summary, this paper contributes a comprehensive investigation into topologically non-trivial structures within a controllable RF photonic circuit environment. It demonstrates site- and time-resolved dynamic behavior within a structured quantum system, paving the way for further exploration into topological materials and their potential applications in emerging quantum technologies.