Fig. 3: Measuring entanglement entropy in 2D phononic systems.
From: Measuring entanglement entropy and its topological signature for phononic systems
a Schematic of the unit-cell structure of the 2D honeycomb phononic crystals. Geometry parameters: a = 40mm, d = 16mm, r = 4mm, h1 = 24mm, and h2 = 24mm (28 mm) for the gapless (gapped) phase. b Photograph of a phononic crystal sample. The speaker and microphone used in pump-probe measurement are shown in the zoom-in image. From the same procedure as in Fig. 2, after measuring the pump-probe response, we perform the spectral decomposition, construct the correlation matrix of subsystem A, and obtain the entanglement entropy. c Measured phonon equifrequency contours. Cyan curves represent the results from the full-wave simulation. d, e Measured entanglement entropy versus the “Fermi energy” ωF for the gapless (d) and gapped (e) phases. f, g Measured entanglement entropy versus the subsystem’s size L for the gapless (f) and gapped (g) phases. Points represent the experimental data, while the lines give the scaling relations according to the Gioev-Klich-Widom law or the area law. The numerical prefactors in the scaling relations are calculated according to Eq. (2).
