# Quantum resonances of kicked rotor in the position representation

## TL;DR

This paper demonstrates that quantum resonances in the kicked rotor system can be more accurately measured via position space density, offering a feasible alternative to momentum-based methods and avoiding phase reversal issues.

## Contribution

It introduces a theoretical approach to measure quantum resonances through position space density, eliminating the need for phase-reversed kicks and improving measurement accuracy.

## Key findings

- Position space density measurement is feasible and accurate.
- Quantum resonances can be observed without phase-reversed kicks.
- The method enhances the precision of Talbot time measurement.

## Abstract

The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays ballistic mean energy growth due to coherent momentum transfer. Secondly, the sharp quantum resonance peaks are useful in the context of measurement of Talbot time, one of the parameter that helps in precise measurement of fine structure constant. Most of the earlier works rely on fidelity based approach and have proposed Talbot time measurement through experimental determination of the momentum space probability density of the periodically kicked atomic cloud. Fidelity approach has the disadvantage that phase reversed kicks need to be imparted as well which potentially leads to dephasing. In contrast to this, in this work, it is theoretically shown that, without manipulating the kick sequences, the quantum resonances through position space density can be measured more accurately and is experimentally feasible as well.