Application Cases

Experiment Name: Non-Hermitian Tight-Binding Model Experiment

Experiment Content: This experiment constructs a simple non-Hermitian tight-binding model to explore the topological weaving and phase transitions of acoustic complex energy bands. To achieve acoustic non-Hermiticity, we introduce non-reciprocal coupling in a dual-cavity-tube structure, which is modulated by a power amplifier and a phase shifter. The former controls the strength of one-way coupling, while the latter simulates lattice momentum, thereby generating a series of topological complex energy band links and knots in the synthetic dimension space, including single links, single knots, Hopf links, and trefoil knots.

Research Direction: Acoustic Metamaterials

Testing Equipment: ATA-2022H high-voltage amplifier, sound source, phase shifter, microphone, etc.

Figure 1: Schematic diagram of the non-Hermitian tight-binding model experimental setup

Experiment Process: We use an external circuit to generate non-reciprocal complex coupling with adjustable amplitude and phase. The principle is as follows: The sound field in cavity 1 is picked up by microphone D2, amplified by the power amplifier, and phase-shifted by the phase shifter, then output to cavity 2 by speaker S2. Due to the simplex characteristics of the microphone and speaker, the sound field in cavity 2 cannot be coupled back to cavity 1 through the external circuit. The amplitude and phase of the non-reciprocal coupling can be adjusted by the gain of the power amplifier and the phase of the phase shifter, respectively.

Experiment Results:

Figure 2: Experimental results of the non-Hermitian tight-binding model

With the gain G of the power amplifier fixed at 5.5 and the phase of the phase shifter adjusted point by point, the variation of non-reciprocal coupling in the complex space is obtained by fitting the sound pressure transmission response data. The fitted parameters are substituted into the Hamiltonian to solve for the eigenvalues, yielding two acoustic complex energy band structures. At this time, the two bands do not interfere with each other, corresponding to a trivial link. When the gain G of the power amplifier is increased to 8.5 and the phase changes by one cycle, correspondingly, the two complex energy bands interweave once within the momentum interval, achieving a trivial knot.

Power Amplifier Recommendation: ATA-2022B High-Voltage Amplifier

Figure: Specifications of the ATA-2022B High-Voltage Amplifier