Ramsey Interferometry in Wigner-Majorana Qudits

Abstract

Ramsey interferometry estimates a detuning from the phase accumulated between two interaction zones, with a resolution set by the interrogation time $τ$. We propose a single-qudit extension based on Wigner-Majorana (WM) spin-$j$ dynamics, whose internal levels form a multipath interferometer. The enhancement is not generic: ideal $\mathrm{QFT}_D$ and $\sqrt{X_D}$ sequences do not densify the central fringe under the population readouts considered. Instead, in manifolds that realize the WM coupling, it arises from coherences between separated ladder states created and recombined by a single near-resonant drive per Ramsey zone. For the qutrit, preparing the central state of a spin-1 WM manifold and measuring its return probability gives $P_3(Δ)=\cos^2(Δτ)$, versus the qubit $P_2(Δ)=\cos^2(Δτ/2)$. The central fringe is thus compressed twofold at fixed $τ$ and the maximal slope doubled in the ideal limit, with contrast ideally unity. For higher-dimensional WM manifolds (odd and even $D$) the central response sharpens with dimension, but the signal spreads over several channels; we introduce a scalar readout from nearest-neighbor shoulder populations and quantify the resolution-contrast trade-off via the slope $S_D$ and contrast $C_D$. We also study robustness to diagonal phase noise from probe-shift fluctuations: under projector-type common-mode dephasing, the WM readouts are less contrast-sensitive than the qubit readout. The robustness is symmetry-selective, not universal: for linear Zeeman dephasing ($L=J_z$), the large $m$-separation that compresses the fringe also enhances dephasing, so higher-dimensional readouts become more sensitive, not protected. The WM qutrit is thus a practical operating point for enhanced Ramsey spectroscopy at fixed $τ$; higher qudits trade extra slope for reduced contrast.