<p>By sequentially recording the phase of an AC signal relative to an external clock, quantum heterodyne schemes have recorded MHz and GHz signals with Fourier-limited precision. However, in systems with large inhomogeneous broadening, existing heterodyne protocols provide limited protection of the spin coherence, impacting amplitude sensitivity. Here, we use a continuous microwave scheme that extends spin coherence towards the effective <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_59148_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">${T}_{2}\approx \frac{1}{2}{T}_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>≈</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> limit and resolves the frequency, amplitude and phase of MHz to GHz magnetic fields. In an ensemble of boron vacancies in hexagonal boron nitride the scheme achieves an amplitude sensitivity of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_59148_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="138" /> </InlineMediaObject> <EquationSource Format="TEX">$\eta \approx 3-5\,\mu {{{\rm{T}}}}/\sqrt{{{{\rm{Hz}}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> <mo>≈</mo> <mn>3</mn> <mo>−</mo> <mn>5</mn> <mspace width="0.25em" /> <mi>μ</mi> <mi mathvariant="normal">T</mi> <mo>/</mo> <msqrt> <mrow> <mi mathvariant="normal">Hz</mi> </mrow> </msqrt> </math></EquationSource> </InlineEquation> and phase sensitivity of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_59148_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="151" /> </InlineMediaObject> <EquationSource Format="TEX">${\eta }_{\phi }\approx 0.076\,{{{\rm{rads}}}}/\sqrt{{{{\rm{Hz}}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>ϕ</mi> </mrow> </msub> <mo>≈</mo> <mn>0.076</mn> <mspace width="0.25em" /> <mi mathvariant="normal">rads</mi> <mo>/</mo> <msqrt> <mrow> <mi mathvariant="normal">Hz</mi> </mrow> </msqrt> </math></EquationSource> </InlineEquation>. We demonstrate that the scheme is compatible with quantum heterodyne detection, recording a GHz signal with a resolution  < 1 Hz and SNR of 235 over a 10 s measurement. Achieving this performance in a two-dimensional material platform could have broad applications in probing nanoscale condensed matter systems.</p>

Microwave quantum heterodyne sensing using a continuous concatenated dynamical decoupling protocol

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2025年5月12日

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Charlie J. Patrickson,
Valentin Haemmerli,
Shi Guo,
Andrew J. Ramsay,
Isaac J. Luxmoore

摘要

By sequentially recording the phase of an AC signal relative to an external clock, quantum heterodyne schemes have recorded MHz and GHz signals with Fourier-limited precision. However, in systems with large inhomogeneous broadening, existing heterodyne protocols provide limited protection of the spin coherence, impacting amplitude sensitivity. Here, we use a continuous microwave scheme that extends spin coherence towards the effective ${T}_{2}\approx \frac{1}{2}{T}_{1}$ $T_{2} \approx \frac{1}{2} T_{1}$ limit and resolves the frequency, amplitude and phase of MHz to GHz magnetic fields. In an ensemble of boron vacancies in hexagonal boron nitride the scheme achieves an amplitude sensitivity of $\eta \approx 3-5\,\mu {{{\rm{T}}}}/\sqrt{{{{\rm{Hz}}}}}$ $η \approx 3 - 5 μ T / \sqrt{Hz}$ and phase sensitivity of ${\eta }_{\phi }\approx 0.076\,{{{\rm{rads}}}}/\sqrt{{{{\rm{Hz}}}}}$ $η_{ϕ} \approx 0.076 rads / \sqrt{Hz}$ . We demonstrate that the scheme is compatible with quantum heterodyne detection, recording a GHz signal with a resolution < 1 Hz and SNR of 235 over a 10 s measurement. Achieving this performance in a two-dimensional material platform could have broad applications in probing nanoscale condensed matter systems.