Phonon Number Measurement Using Optimal Composite Pulses

TL;DR

This paper introduces a quantum control-based composite pulse method for direct, high-accuracy measurement of phonon number states in laser-cooled ions, surpassing traditional techniques in efficiency and precision.

Contribution

It proposes a novel composite pulse technique combined with quantum optimal control to directly measure Fock state populations without fitting, improving accuracy for high phonon states.

Findings

Enhanced measurement fidelity with quantum optimal control

Direct measurement of higher Fock states

Improved accuracy over existing methods

Abstract

Measuring the phonon number of the laser-cooled ions is an indispensable step in evaluating whether an ion is in ground state. At present, commonly used methods in the experiments are red-to-blue sideband ratios and adiabatic evolution red-sideband methods. We theoretically propose a method using composite pulses which does not need a fit of state evolution and can directly measure the population of the selected Fock state. It can measure higher Fock state population more directly comparing with the adiabatic evolution red-sideband method. We use quantum optimal control method to improve the fidelity of unitary operation of the composite pulses. With quantum optimal control technology, we can discuss the situation where the laser strength is strong, and many approximations will not be necessary, where the gate fidelity can be further improved. Then we give a method to modify the measurement result for a higher accuracy which has a good performance, and we give an example to illustrate its application on high Fock state measurement.