Beyond Qubits: Multilevel Quantum Sensing for Dark Matter

Abstract

Quantum sensing with qubits has advanced fundamental physics searches, but higher dimensional systems offer untapped potential. We present a universal qutrit framework that yields a sequence-independent fourfold increase in quantum Fisher information and a twofold gain in sensitivity. In ultralight dark matter searches, spin-1 NV-center qutrits can enhance the axion-electron coupling reach by an order of magnitude beyond qubits. This principle applies broadly to multilevel quantum systems including superconducting, neutral atom and trapped-ion qutrits, establishing higher dimensional sensing as a powerful tool for probing new physics.

Figures (3)

• Figure 1: Schematic illustration of qutrit DM sensing proposed in this work. A wave-like DM field couples a spin triplet, driving simultaneous transitions between the $\ket{0}$ and $\ket{\pm 1}$ states with Rabi frequency $\Omega_{\mathrm{SQ}}$ and frequencies $\nu_{\pm}$. By coherently exciting both $\ket{\pm 1}$ levels, a spin-1 qutrit superposition is prepared that enhances the phase accumulation and sensitivity to the oscillating DM field compared to a conventional qubit configuration.
• Figure 2: Pulse sequence protocols for DC and AC magnetometry using NV center electron spins as qutrits. Top: For DC magnetometry, a Ramsey sequence is applied. A $\pi/2$ rotation about the $y$-axis ($R_y^{\pi/2}$) prepares a coherent superposition, which freely evolves under $R_z^{\theta_p}(\tau)$ to accumulate a magnetic field-dependent phase, followed by a second $\pi/2$ pulse with phase $\theta = \pi/4$ and optical readout. Bottom: In AC magnetometry a Hahn-echo sequence is applied and suppresses low-frequency noise. After the initial $\pi/2$ pulse, free evolution for $\tau/2$ is interrupted by a refocusing $\pi$ pulse and followed by another $\tau/2$ evolution and final $\pi/2$ pulse. The acquired phase encodes the oscillating magnetic-field component resonant with the sequence.
• Figure 3: Left panel: The projected $95\%$ confidence level sensitivity to the axion-electron coupling ($g_{aee}$) for NV qutrit (solid line) compared with qubit results of Ref. Chigusa:2023roq (dashed line) using DC magnetometry Ramsey sequences. The DC magnetometry has a broadband sensitivity for the low frequency region of DM. For frequencies smaller than the Nyquist frequency $f_a\leq 1/\tau$, owing to improved signal strength and the longer dephasing time of qutrits, they have about an order of magnitude improvement. Right panel: As the left panel, but for AC magnetometry with the Hahn-echo sequence. AC magnetometry is highly sensitive to the higher frequency range of $f_a\sim 1/\tau$, while quickly losing sensitivity for both lower and higher frequencies. For the frequency $f_a\leq 1/\tau$, the qutrit shows an improvement of around an order of magnitude. For each system and sequence we considered the value $\tau=T_2^{(*)}/2$, with the dephasing time (transverse relaxation time) $T_2^{(*)}$ given in main text. The terrestrial laboratory limits include comagnetometers Bloch:2019lcy, torsion pendulum experiments Terrano:2015snaTerrano:2019clh and fermionic axion interferometer Crescini:2023zyl, with underground detector limits from XENONnT XENON:2022ltv considering solar axions and red giants Capozzi:2020cbu also shown.