Complete unitary qutrit control in ultracold atoms

TL;DR

This paper demonstrates complete control over a three-level quantum system (qutrit) in ultracold atoms, enabling arbitrary SU(3) gates with high fidelity, advancing the potential for high-dimensional quantum information processing.

Contribution

It introduces a method to implement arbitrary single-qutrit SU(3) gates in ultracold neutral atoms using only two microwave tones, including direct coupling between disconnected levels.

Findings

Achieved high-fidelity arbitrary SU(3) gates on ultracold atom qutrits.

Demonstrated the implementation of the Walsh-Hadamard Fourier transform for qutrits.

Validated two different gate sets with similar state fidelity and purity.

Abstract

Physical quantum systems are commonly composed of more than two levels and offer the capacity to encode information in higher-dimensional spaces beyond the qubit, starting with the three-level qutrit. Here, we encode neutral-atom qutrits in an ensemble of ultracold $^{87}$Rb and demonstrate arbitrary single-qutrit SU(3) gates. We generate a full set of gates using only two resonant microwave tones, including synthesizing a gate that effects a direct coupling between the two disconnected levels in the three-level $\Lambda$-scheme. Using two different gate sets, we implement and characterize the Walsh-Hadamard Fourier transform, and find similar final-state fidelity and purity from both approaches. This work establishes the ultracold neutral-atom qutrit as a promising platform for qutrit-based quantum information processing, extensions to $d$-dimensional qudits, and explorations in multilevel quantum state manipulations with nontrivial geometric phases.