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

Abstract

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.

Sensing small changes in a wave chaotic scattering system

“…Under these conditions a single-channel time-reversal mirror can very effectively approximate the conditions required to measure the LE using classical waves [17,18]. The experimental set up for the measurement of the LE can be further simplified by exploiting the spatial reciprocity of the wave equation [9,19]. Time-reversal mirrors have found a wide range of practical applications such as crack imaging in solids [20], and improved acoustic communication in air [21], among other things.…”

Nonlinear time reversal of classical waves: Experiment and model

“…This newly transmitted set of signals essentially undoes the time-forward propagation, producing waves which converge on the original localized source, reconstructing a time-reversed version of the original signal at the localized source. Although real situations deviate from the above described ideal, time-reversal in this manner has been effectively realized in acoustic [2-9, 12, 13] and electromagnetic waves [6,8,14,15], and applications such as lithotripsy [2,4], underwater communication [2,16,17], sensing small perturbations [12,13], and achieving subwavelength imaging [6][7][8]18] have been developed.…”

Nonlinear Time Reversal in a Wave Chaotic System

“…This can be realized by transmitting a waveform at a particular source location and recording the reverberating waveforms (sona) with an array of receivers; the recorded waveforms are reversed in time and retransmitted back from the receivers, propagating to and reconstructing a time-reversed version of the original waveform at the source [3]. Time-reversal mirrors have been demonstrated for both acoustic [2-9, 11, 12] and electromagnetic waves [6,8,13], and exploited for applications such as lithotripsy [2,4], underwater communication [2,14,15], sensing perturbations [11,12], and achieving sub-wavelength imaging [6][7][8]16]. An ideal time-reversal mirror in an open environment would collect the forward-propagating wave at every point on a closed surface enclosing the transmitter, re-quiring a very large number of receivers.…”

“…An ideal time-reversal mirror in an open environment would collect the forward-propagating wave at every point on a closed surface enclosing the transmitter, re-quiring a very large number of receivers. The receiving array can be simplified, without significant loss of fidelity of the reconstruction, if there is a closed, ray-chaotic environment where a propagating wave (with wavelength much smaller than the size of the enclosure) will eventually reach every point in the environment, allowing the use of a single receiver to capture the signal to be timereversed [9,11]. Reconstruction is possible even when only a small fraction of the transmitted energy is collected by the receiver.…”