Chaotic Time-Reversed Acoustics: Sensitivity of the Loschmidt Echo to Perturbations

We experimentally demonstrate a new acoustic sensor based on the concept of quantum mechanical scattering fidelity and the Loschmidt echo applied to classical acoustic waves in air. The sensor employs a one-recording--channel time-reversal mirror that exploits spatial reciprocity to sensitively measure the classical analog of the scattering fidelity of an enclosed region. The experiments are carried out in a stairwell using a simple speaker and microphone. The input is a 7.0 kHz signal that is amplitude modulated with a 1 ms long pulse. We examine the sensitivity of the time-reversed reconstructed pulse to phase noise, long term drift, and to typical perturbations caused by the rotation of an object in the scattering environment. PACS numbers: 03.55.Kk, 05.45.Mt, 43.58.+z, 43.60.+d 1