Sensor based on extending the concept of fidelity to classical waves

Abstract

We propose and demonstrate a remote sensor scheme by applying the quantum mechanical concept of fidelity loss to classical waves. The sensor makes explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to sensitively and remotely measure the presence of small perturbations. The loss of fidelity is measured through a classical wave-analog of the Loschmidt echo by employing a single-channel time-reversal mirror to rebroadcast a probe signal into the perturbed system. We also introduce the use of exponential amplification of the probe signal to partially overcome the effects of propagation losses and to vary the sensitivity.

Controlling waves in space and time for imaging and focusing in complex media

“…Indeed, as was shown by Moustakas and colleagues 107 , the information capacity of a medium can be significantly improved by scattering. Researchers recently proposed the use of time reversal for developing new sensors, by applying the quantum concept of fidelity to classical waves 108 .…”

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

“…On the other hand, the normalized cross correlation of the pulses before and after perturbation is 93%. From this and many other measurements [18] it is clear that monitoring the decrease in the peak-to-peak amplitude of the reconstructed time-reversed pulse is not only computationally simpler but it is also a statistically more reliable mechanism to detect perturbations.…”

“…The disadvantage is that the sensor cannot easily identify the location and size of the perturbation. Further work is needed to refine the sensor to reveal more detailed information about the location and nature of the perturbation giving rise to the signal [18].…”

“…A Loschmidt echo scattering fidelity experiment is demonstrated using acoustic waves in a 2-story-tall enclosed stairwell, roughly 6 m deep ×2.5 m wide ×6.5 m tall [18]. A desktop speaker and microphone (Samson C01U) inside the stairwell are connected to a controlling computer stationed outside the enclosure (see Fig.…”

Focusing waves at arbitrary locations in a ray-chaotic enclosure using time-reversed synthetic sonas

“…A sweep of carrier frequency from 1 GHz to 20 GHz takes hours, during which the cavity state may change due to temperature fluctuations or other time-dependant perturbations [32][33][34]49]. This problem can be addressed by switching to frequency domain measurements where the scattering parameter (S-matrix) of the system is measured only once and is then used to calculate the timedomain responses.…”