Generalized Ramsey Interferometry Explored with a Single Nuclear Spin Qudit

TL;DR

This paper experimentally explores generalized Ramsey interferometry with a single nuclear spin qudit (d=4), demonstrating new protocols for measuring geometric phases, quantum gate phases, and coherence times in multilevel quantum systems.

Contribution

It introduces and experimentally implements three generalized Ramsey protocols for a nuclear spin qudit, extending quantum interferometry techniques beyond qubits.

Findings

Successfully measured geometric phases using Ramsey interference.

Determined the phase of an iSWAP quantum gate in a nuclear spin system.

Measured the coherence time of a three-state superposition.

Abstract

Qudits, with their state space of dimension d > 2, open fascinating experimental prospects. The quantum properties of their states provide new potentialities for quantum information, quantum contextuality, expressions of geometric phases, facets of quantum entanglement and many other foundational aspects of the quantum world, which are unapproachable with qubits. We here experimentally investigate the quantum dynamics of a qudit (d = 4) that consists of a single 3/2 nuclear spin embedded in a molecular magnet transistor geometry, coherently driven by a microwave electric field. We propose and implement three protocols based on a generalization of the Ramsey interferometry to a multilevel system. First, the standard Ramsey interference is used to measure the accumulation of geometric phases. Then, two distinct transitions of the nuclear spin are addressed to measure the phase of an iSWAP quantum gate. Finally, through a succession of two Hadamard gates, the coherence time of a 3-state superposition is measured.