Session: 

Paper Number: 173542

Experimental Realization of a Temporal Topological Interface State in a Single Parametrically-Driven Oscillator 

Topological concepts have revolutionized phononics, enabling robust wave transport in spatially structured media [1]. Recently, attention has shifted to phononic time crystals, where material properties are modulated in time, unlocking new possibilities for wave control. These temporally driven systems support exotic phenomena such as momentum bandgaps, nonreciprocal dynamics, and time-localized excitations—extending the reach of topological mechanics into the time domain. A key challenge, however, remains the experimental realization of topological phenomena in these time-varying systems, which often rely on complex lattice structures and carefully synchronized modulation protocols. Reducing this complexity without compromising topological behavior remains an important goal.

In this work, we demonstrate the direct observation of a Temporal Topological Interface State [2] within a highly compact, single-degree-of-freedom magneto-mechanical system. This state is an excitation localized sharply in time, emerging at the boundary between two distinct temporal modulation sequences. It represents a topologically protected response associated with the mismatch in the modulation phase profiles. Our approach circumvents the need for a physical lattice, instead showing how topological features can be encoded entirely within the time evolution of a single oscillator. This realization illustrates that temporal topology can be compressed into a minimal system governed purely by time-domain dynamics.

Our experimental platform is a custom-designed magneto-mechanical oscillator: a pendulum whose stiffness is parametrically controlled via non-contact magnetic forces. These forces are generated by synchronized, motor-driven arrays of permanent magnets, allowing for precise, programmable modulation of the oscillator’s dynamics in real time. The magnet arrays are mounted on stationary structures positioned symmetrically on either side of the pendulum to ensure spatial balance and effective coupling. To create the topological interface, we apply two sequential harmonic modulation protocols, engineered to possess different topological invariants (Zak phases), thereby constructing a temporal boundary in the system’s modulation history. The resulting discontinuity in topology between the two sequences is responsible for the emergence of a localized state.

At the precise moment the system switches from the first protocol to the second—the temporal interface—we observe the dramatic appearance of a localized resonance, which is both temporally confined and spectrally distinguishable. This finding provides unambiguous experimental evidence of a Temporal Topological Interface State. It confirms that temporal topological modes can be realized in a system with no spatial periodicity, using only a single parametrically modulated oscillator. By realizing this phenomenon in a tunable magneto-mechanical system, our work opens a direct path to developing compact, time-programmable phononic devices for advanced vibration control, energy localization, and temporal wave steering. This platform offers an accessible route to study bulk-boundary correspondence in time and may inspire future temporal metamaterial designs.

References:

1. Mousavi, S. Hossein, Alexander B. Khanikaev, and Zheng Wang. "Topologically protected elastic waves in phononic metamaterials." Nature communications 6.1 (2015): 8682.

2. Lustig, Eran, Yonatan Sharabi, and Mordechai Segev. "Topological aspects of photonic time crystals." Optica 5.11 (2018): 1390-1395.

Presenting Author: Harshit Kumar Sandhu Indian Institute of Science, Bengaluru

Presenting Author Biography: Harshit Kumar Sandhu is a Ph.D. student in the Department of Aerospace Engineering at the Indian Institute of Science (IISc), Bangalore. He works under the guidance of Dr. Rajesh Chaunsali at the Laboratory for Engineered Materials & Structures (LEMS). His research focuses on wave propagation in time-modulated mechanical systems, with emphasis on phononic time crystals, non-Hermitian dynamics, and temporal topological interface states. He secured an All-India Rank of 53 in GATE 2019 Engineering Sciences (XE), and is a recipient of the GATE Fellowship (MoE, Govt. of India) and the Metamaterials 2025 Travel Grant. His work integrates analytical modeling with time-periodic modulation and magneto-mechanical experiments to realize compact phononic systems exhibiting temporal topological phenomena.

Authors:

Harshit Kumar Sandhu Indian Institute of Science, Bengaluru
Avinash Umashankar Indian Institute of Science, Bengaluru, India
Rajesh Chaunsali Indian Institute of Science, Bengaluru, India