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arXiv:2509.06290

Ramsey Interferometry in Wigner-Majorana Qudits

Branislav Ilikj, T. Zanon-Willette, Nikolay V. Vitanov

Published Sep 8, 2025• 0 citations
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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.

DOI
10.48550/arxiv.2509.06290

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Ramsey interferometry estimates a detuning from the phase accumulated between two interaction zones, with a resolution set by the interrogation time τττ. We propose a single-qudit extension based on Wigner-Majorana (WM) spin-jjj dynamics, whose internal levels form a multipath interferometer. The enhancement is not generic: ideal QFTD\mathrm{QFT}_DQFTD​ and XD\sqrt{X_D}XD​​ 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 P3(Δ)=cos⁡2(Δτ)P_3(Δ)=\cos^2(Δτ)P3​(Δ)=cos2(Δτ), versus the qubit P2(Δ)=cos⁡2(Δτ/2)P_2(Δ)=\cos^2(Δτ/2)P2​(Δ)=cos2(Δτ/2). The central fringe is thus compressed twofold at fixed τττ and the maximal slope doubled in the ideal limit, with contrast ideally unity. For higher-dimensional WM manifolds (odd and even DDD) 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 SDS_DSD​ and contrast CDC_DCD​. 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=JzL=J_zL=Jz​), the large mmm-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 τττ; higher qudits trade extra slope for reduced contrast.
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Quantum entanglement is a powerful quantum resource for enhancing measurement precision beyond classical limit. % Here we propose an entanglement-enhanced symmetry-protected destructive many-body Ramsey interferometry for precise parameter estimation. % Through matching the symmetry of input states and Hamiltonian, the spectral shift of Ramsey spectroscopy caused by interparticle interaction, noise, decoherence and experimental imperfection can be mitigated for both time-independent and time-dependent signals, as explored in the companion Letter [S. Chen, et al., Ramsey Spectroscopy via Symmetry-Protected Destructive Many-Body Interferometry (submitted)]. % In this work, we show that symmetric entangled input states can further improve the measurement precision of symmetry-protected Ramsey spectroscopy without affecting the measurement accuracy. % Through inputting spin cat states and applying suitable interaction-based readout operations, the measurement precisions of time-independent and time-dependent signals can both approach the Heisenberg limit. % In particular, we systematically analyze how precision scaling and robustness depend on the input states, parameters, experimental imperfection and decoherence. % This work establishes a practical pathway to Heisenberg-limited quantum metrology with many-body Ramsey interferometry, offering resilience against realistic noise and imperfections.
In a standard two-level Ramsey interferometer, the accumulated signal phase is linearly mapped to the readout phase. Here, we introduce three-level Ramsey interferometry, in which projected interference between internal paths reshapes this mapping through a noncyclic geometric phase response. Near a geodesic-closure transition, a small accumulated signal phase produces a sharply amplified readout-phase shift. We quantify the accompanying gain--visibility tradeoff and identify a finite operating window in which the amplified response can yield a net signal-to-noise-ratio gain in the presence of additional technical phase noise. A controllable Ramsey phase offset further positions this high-slope response at a chosen operating point, making the local enhancement accessible without requiring a large signal-induced phase. More broadly, these results establish a multilevel Ramsey route to enhanced phase sensitivity in quantum platforms, in which two signal-collecting internal paths interfere to produce a controllable noncyclic geometric response.
We present a theoretical study of the Rabi and Ramsey coherence time of Majorana-based qubits formed by double NNN-site quantum-dot artificial Kitaev chains, following the recent experimental realization arXiv:2607.09511. We generalize the qubit to two chains of arbitrary length and compare the Rabi and Ramsey oscillations of the four-dot and six-dot qubits, simulated with realistic disorder for three sets of parameters: small and large superconducting gaps, and the experimental parameters. We find that, in the pristine limit, the Rabi oscillation is independent of the chain length, whereas the Ramsey oscillation of the six-dot qubit suffers from larger leakage, because the third site suppresses the unwanted energy splitting away from the sweet spot but at the same time makes the deliberate splitting difficult to achieve, which requires a larger detuning that could excite the bulk. In reality with disorder, neither coherence time improves universally with the chain length. The Rabi coherence is set by the competition of three dephasing channels, and the additional dots pay off only if the fluctuation of the interchain tunneling is suppressed; the Ramsey coherence is set by the fluctuation of the energy splitting during the σzσ_zσz​ rotation, which for the four-dot qubit is fixed by the sweet-spot disorder alone and does not depend on the mean splitting, whereas for the six-dot qubit the detuning that generates the splitting adds a fluctuation growing with the splitting itself, so the additional dots pay off only for small splittings. This implies that a longer chain is thus a better quantum memory but not necessarily a better qubit under manipulation. Although topological protection is expected in a longer Kitaev chain qubit, observing it in the current Rabi and Ramsey measurement protocols remains an experimental challenge.
The use of entanglement in sensing is often motivated by improved sensitivity arising from non-classical correlations among probes. For static signals, however, this quantum advantage in Ramsey spectroscopy with NNN probes is known to be highly susceptible to dephasing, which severely limits the possible gain from entanglement. In contrast, we consider sensing of signals that vary in time. Considering the simplest example of dephasing by classical white noise, we show that entanglement allows a large increase in bandwidth when estimating the frequency components of a time-dependent signal. Without sacrificing any sensitivity, entanglement allows for an increase in bandwidth by a factor of NNN. Alternatively, when interrogation times are limited by the signal bandwidth rather than by dephasing, the average estimation uncertainty over a fixed bandwidth is reduced by a factor of N\sqrt{N}N​ compared with separable states.
Nitrogen-vacancy (NV) centers in diamond offer a promising solid-state platform for rotation sensing, operating across diverse environmental conditions. Our previous work demonstrated a rotation sensor utilizing 14N nuclear spins, detecting rotation via precession rate shifts [1]. This sensor employs direct optical polarization/readout and radio-frequency double-quantum Ramsey interferometry, eliminating microwave pulses. However, magnetic field, temperature, and RF pulse variations limit long-term stability. To enhance robustness, we developed two generalized Ramsey schemes: one utilizing stimulated Raman adiabatic passage (STIRAP) for pulse-area resilience [2], and a dynamical elimination protocol using modulated zero-pulse-area fields to control two-photon transitions and suppress single-photon excitations [3]. Experimental results demonstrate enhanced robustness against pulse parameter variations, yielding improved quantum state generation fidelities and robust Ramsey fringes insensitive to single-photon detuning. Our results pave the way for enhanced long-term stability in diamond-based sensors (clocks, gyroscopes, magnetometers), advancing quantum metrology and spectroscopy. Furthermore, we anticipate that the developed two-photon spectroscopy techniques will find widespread application in atomic, molecular, and spin systems, enabling robust control methods for quantum technology, including high-fidelity quantum gates, Ramsey spectroscopy, atom interferometry, and quantum sensing. [1] A. Jarmola, S. Lourette, V. M. Acosta, A. G. Birdwell, P. Blümler, D. Budker, T. Ivanov, V. S. Malinovsky, Sci. Adv. 7, eabl3840 (2021). [2] S. Lourette, A. Jarmola, J. Chathanathil, S. C. Carrasco, D. Budker, S. A. Malinovskaya, A. G. Birdwell, T. G. Ivanov, and V. S. Malinovsky, arXiv:2407.16057 (2024). [3] S. C. Carrasco, S. Lourette, I. Sola, V. S. Malinovsky, arXiv:2411.05670 (2024).