Control of inhomogeneous atomic ensembles of hyperfine qudits

TL;DR

This paper develops a semi-analytic method for controlling inhomogeneous hyperfine qudit ensembles in alkali-metal atoms, enabling robust state preparation and addressing despite experimental uncertainties.

Contribution

It introduces a semi-analytic protocol for inhomogeneous control of qudit ensembles using SU(2) rotations, outperforming brute force methods in certain regimes.

Findings

High fidelity (>0.99) control achieved for <1% inhomogeneities

Semi-analytic protocol is effective and faster than brute force search

Method enables tomographic addressing of different states in ensemble

Abstract

We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semi-analytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semi-analytic protocol is compared to a brute force, full numerical search. For small inhomogeneities, < 1%, both approaches achieve average fidelities greater than 0.99, but the brute force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.