Exact time-reversal focusing of acoustic and quantum excitations in open cavities: The perfect inverse filter

TL;DR

This paper introduces a simplified perfect inverse filter (PIF) method for exact time-reversal focusing of acoustic and quantum excitations in open cavities, improving resolution and correction of signal distortions.

Contribution

It derives a simple form of PIF applicable when the initial excitation is inside the cavity, enhancing time-reversal techniques for acoustics and quantum systems.

Findings

PIF corrects and improves time-reversal focusing in open cavities.

PIF achieves subwavelength resolution in localized excitations.

Application to chaotic and resonator models demonstrates effectiveness.

Abstract

The time-reversal mirror (TRM) prescribes the reverse playback of a signal to focalize an acoustic excitation as a Loschmidt echo. In the quantum domain, the perfect inverse filter (PIF) processes this signal to ensure an exact reversion provided that the excitation originated outside the cavity delimited by the transducers. We show that PIF takes a simple form when the initial excitation is created inside this cavity. This also applies to the acoustical case, where it corrects the TRM and improves the design of an acoustic bazooka. We solve an open chaotic cavity modeling a quantum bazooka and a simple model for a Helmholtz resonator, showing that the PIF becomes decisive to compensate the group velocities involved in a highly localized excitation and to achieve subwavelength resolution.