Dissipation-Based Quantum Sensing of Magnons with a Superconducting Qubit

Hybrid quantum devices expand the tools and techniques available for quantum sensing in various fields. Here, we experimentally demonstrate quantum sensing of a steady-state magnon population in a magnetostatic mode of a ferrimagnetic crystal. Dispersively coupling the magnetostatic mode to a superconducting qubit allows for the detection of magnons using Ramsey interferometry with a sensitivity on the order of ${10}^{-3}\mathrm{magnons}/\sqrt{\mathrm{Hz}}$. The protocol is based on dissipation as dephasing via fluctuations in the magnetostatic mode reduces the qubit coherence proportionally to the number of magnons.

Figure 1

(a) Photographs and schematics of a 0.5-mm-diameter single-crystal yttrium-iron-garnet (YIG) sphere and a superconducting transmon qubit. A static magnetic field ${\mathbf{B}}_0$ magnetizes the YIG sphere to saturation. The Kittel mode couples dispersively to the qubit with a dispersive shift ${\chi }_{q-m}$. The Kittel mode and qubit have linewidths ${\gamma }_m$ and ${\gamma }_q$, respectively. (b) Pulse sequence used for the quantum sensing of magnons. Two ${\widehat{X}}_{\pi /2}$ pulses with frequency ${\omega }_s$, separated by the sensing time $\tau$, are applied to the qubit as in conventional Ramsey interferometry, followed by a readout of the qubit state. A continuous drive close to resonance with the Kittel mode creates a coherent state of magnons with population ${\overline{n}}_m$. (c) Qubit spectra obtained from Ramsey interferometry with a steady-state magnon population ${\overline{n}}_m=0$ (blue circles) and 0.61 (red dots). The detuning $|\omega -{\omega }_s|/2\pi$ is relative to the qubit control frequency ${\omega }_s/2\pi$, which is itself detuned from the qubit frequency by $-4\mathrm{MHz}$ to induce Ramsey oscillations (shown in the inset up to $\tau =1\mu \mathrm{s}$) from which the spectra are obtained. Solid black lines show fits to a model. The spectra are normalized to the maximal value of the fit for ${\overline{n}}_m=0$. (d) Magnon detection sensitivity $\mathcal{S}$ calculated as a function of the Kittel mode linewidth ${\gamma }_m/2\pi$, for amplitudes of the qubit–magnon dispersive shift $|{\chi }_{q-m}|/2\pi =2\mathrm{MHz}$ (solid line) and 10 MHz (dashed line). The sensing time $\tau =0.89\mu \mathrm{s}$ is fixed to be equal to the qubit coherence time $T_2^{*}=2/{\gamma }_q$ measured in the experiment with no magnons present.

Figure 2

(a) Qubit excited-state probability $p_e$ as a function of the magnon population ${\overline{n}}_m$. Equation (1) is fitted to the data to yield the magnon detection efficiency $\eta =0.70$. (b) Demodulated signal $\mathrm{\Delta }V$ for a subset of single-shot qubit measurements. Horizontal dashed lines indicate the demodulated signal corresponding to the qubit in the ground state $|g⟩$ and excited state $|e⟩$. (c) Magnon population Allan deviation ${\mathrm{\Xi }}_m$ as a function of measurement time $T$. The solid line indicates a fit to Eq. (2). The horizontal dashed line indicates the value of ${\mathrm{\Xi }}_m$ for $T=1\mathrm{s}$ (vertical dashed line), corresponding to the magnon detection sensitivity $\mathcal{S}=1.55\times {10}^{-3}\text{magnons}/\sqrt{\mathrm{Hz}}$.

Figure 3

(a) Magnon detection efficiency $\eta$, (b) noise of single-shot qubit readout for one-second measurement time, ${\mathrm{\Xi }}_q(1\mathrm{s})$, and (c) magnon detection sensitivity $\mathcal{S}$ as a function of sensing time $\tau$. In (a) and (c), solid black lines are results from numerical simulations. In (b), the solid black line is the shot noise calculated from Eq. (3).

Figure 4

(a) Qubit excited-state probability $p_e$ and (b) magnon detection sensitivity $\mathcal{S}$ as a function of Ramsey detuning ${\mathrm{\Delta }}_s/2\pi$. The probability $p_e$ is shown for the cases of sensing different steady-state magnon populations ${\overline{n}}_m=0$ (blue circles) and ${\overline{n}}_m=0.05$ (red dots), with the shaded region indicating the difference. Dashed vertical lines correspond to nodes of the Ramsey fringes. Solid black lines are results from numerical simulations.