Microwave quantum heterodyne sensing using a continuous concatenated dynamical decoupling protocol.

Abstract

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 <math xmlns="http://www.w3.org/1998/Math/MathML"> <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> 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi> <mo>≈</mo> <mn>3</mn> <mo>-</mo> <mn>5</mn> <mspace></mspace> <mi>μ</mi> <mi>T</mi> <mo>/</mo> <msqrt><mrow><mi>Hz</mi></mrow> </msqrt> </math> and phase sensitivity of <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>η</mi></mrow> <mrow><mi>ϕ</mi></mrow> </msub> <mo>≈</mo> <mn>0.076</mn> <mspace></mspace> <mi>rads</mi> <mo>/</mo> <msqrt><mrow><mi>Hz</mi></mrow> </msqrt> </math> . 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.