# Nonperiodic echoes from quantum mushroom billiard hats

## TL;DR

This paper reports the observation of nonperiodic, tunable quantum echoes in an open microwave billiard with Fibonacci-like delay sequences, enabling quantum pulse shaping through classical and wave effects.

## Contribution

It demonstrates how Fibonacci-like delay sequences in an integrable scattering system can produce tunable quantum echoes for pulse shaping.

## Key findings

- Observation of nonperiodic quantum echoes in microwave billiards
- Fibonacci-like sequences influence delay times
- Quantum pulses can be shaped by system geometry and wave effects

## Abstract

Nonperiodic tunable quantum echoes have been observed in experiments with an open microwave billiard whose geometry under certain conditions provides Fibonacci like sequences of classical delay times. These sequences combined with the reflection at the opening induced by the wave character of the experiment and the size of the opening allow to shape quantum pulses. The pulses are obtained by response of an integrable scattering system.