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The time-reversal mirror (TRM) prescribes the reverse playback of a signal tofocalize an acoustic excitation as a Loschmidt echo. In the quantum domain, theperfect inverse filter (PIF) processes this signal to ensure an exact reversionprovided that the excitation originated outside the cavity delimited by thetransducers. We show that PIF takes a simple form when the initial excitationis created inside this cavity. This also applies to the acoustical case, whereit corrects the TRM and improves the design of an acoustic bazooka. We solve anopen chaotic cavity modeling a quantum bazooka and a simple model for aHelmholtz resonator, showing that the PIF becomes decisive to compensate thegroup velocities involved in a highly localized excitation and to achievesubwavelength resolution.

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