Chaotic Time Reversed Acoustics: Sensitivity οf the Loschmidt Echo to Perturbations

B.T. Taddesea,b,c, M.D. Johnsond, J.A. Hartb,e, T.M. Antonsen, Jr.b,c,e, E. Ottb,c,e and S.M. Anlagea,b,c a Center for Nanophysics and Advanced Materials, Physics Department, University of Maryland, College Park, MD 20742-4111, USA b Physics Department, University of Maryland, College Park, MD 20742-4111, USA c Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA d Department of Physics, University of California, Santa Barbara, CA 93106, USA e Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742-3511, USA

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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.

DOI: 10.12693/APhysPolA.116.729 PACS numbers: 03.55.Kk, 05.45.Mt, 43.58.+z, 43.60.+d