Acoustic anti-parity-time symmetric structure enabling equivalent lasing and coherent perfect absorption

Non-Hermitian systems with parity-time $(\mathcal{P}\mathcal{T})$ symmetry have attracted increasing interest due to their intriguing properties and associated applications. Inspired by that, we propose here an acoustic anti-parity-time $(\mathrm{A}\text{\ensuremath{-}}\mathcal{P}\mathcal{T})$ symmetric structure with metamaterials featuring balanced positive and negative indices, together with equal gain/loss. According to the derived scattering matrix, we demonstrate its extraordinary scattering properties. For example, the spontaneous phase transition of the scattering matrix is observed, by simply modulating the frequency, gain/loss, or geometric width. In the absence of gain/loss, the $\mathrm{A}\text{\ensuremath{-}}\mathcal{P}\mathcal{T}$ symmetric structure degrades into a pair of complementary media, resulting in bidirectional total transmission. At the zero and pole of the scattering matrix, the structure behaves as an acoustic coherent perfect absorber and equivalent laser, respectively, which can perfectly absorb two-port coherent incident waves and radiate two coherent output waves with extensive and equal amplitudes. Different from that in the $\mathcal{P}\mathcal{T}$ symmetric structure, these three effects based on the $\mathrm{A}\text{\ensuremath{-}}\mathcal{P}\mathcal{T}$ symmetric structure are all achieved in the symmetric phase of the scattering matrix, resulting in the symmetric intensity distributions. Besides, the coherent perfect absorption and lasing modes of the $\mathrm{A}\text{\ensuremath{-}}\mathcal{P}\mathcal{T}$ symmetric structure are continuous and symmetric in the parameter space, which may facilitate further experimental realizations. The proposed $\mathrm{A}\text{\ensuremath{-}}\mathcal{P}\mathcal{T}$ symmetric structure provides an alternative method to demonstrate the physics of the non-Hermitian Hamiltonian, and may offer an alternative approach to design acoustic functional devices such as absorbers, sensors, and amplifiers.