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arXiv:1702.06710 · Nature Communications

Quantum sensing of weak radio-frequency signals by pulsed Mollow absorption spectroscopy

Timo Joas, A. M. Waeber, Georg Braunbeck, Friedemann Reinhard

Published Oct 11, 2017• 68 citations
arXivHTMLPDF

Abstract

Abstract Quantum sensors—qubits sensitive to external fields—have become powerful detectors for various small acoustic and electromagnetic fields. A major key to their success have been dynamical decoupling protocols which enhance sensitivity to weak oscillating (AC) signals. Currently, those methods are limited to signal frequencies below a few MHz. Here we harness a quantum-optical effect, the Mollow triplet splitting of a strongly driven two-level system, to overcome this limitation. We microscopically understand this effect as a pulsed dynamical decoupling protocol and find that it enables sensitive detection of fields close to the driven transition. Employing a nitrogen-vacancy center, we detect GHz microwave fields with a signal strength (Rabi frequency) below the current detection limit, which is set by the center’s spectral linewidth $$1{\rm{/}}T_2^*$$ 1 ∕ T 2 * . Pushing detection sensitivity to the much lower 1/ T 2 limit, this scheme could enable various applications, most prominently coherent coupling to single phonons and microwave photons.

DOI
10.1038/s41467-017-01158-3

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Abstract Quantum sensors—qubits sensitive to external fields—have become powerful detectors for various small acoustic and electromagnetic fields. A major key to their success have been dynamical decoupling protocols which enhance sensitivity to weak oscillating (AC) signals. Currently, those methods are limited to signal frequencies below a few MHz. Here we harness a quantum-optical effect, the Mollow triplet splitting of a strongly driven two-level system, to overcome this limitation. We microscopically understand this effect as a pulsed dynamical decoupling protocol and find that it enables sensitive detection of fields close to the driven transition. Employing a nitrogen-vacancy center, we detect GHz microwave fields with a signal strength (Rabi frequency) below the current detection limit, which is set by the center’s spectral linewidth 1/T2∗1{\rm{/}}T_2^*1/T2∗​ 1 ∕ T 2 * . Pushing detection sensitivity to the much lower 1/ T 2 limit, this scheme could enable various applications, most prominently coherent coupling to single phonons and microwave photons.
Abstract Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system’s resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.
Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system's resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.
Quantum sensors using solid-state spin defects excel in the detection of radiofrequency (RF) fields, serving various applications in communication, ranging, and sensing. For this purpose, pulsed dynamical decoupling (PDD) protocols are typically applied, which enhance sensitivity to RF signals. However, these methods are limited to frequencies of a few megahertz, which poses a challenge for sensing higher frequencies. We introduce an alternative approach based on a continuous dynamical decoupling (CDD) scheme involving dressed states of nitrogen vacancy (NV) ensemble spins driven within a microwave resonator. We compare the CDD methods to established PDD protocols and demonstrate the detection of RF signals up to ~85 MHz, about ten times the current limit imposed by the PDD approach under identical conditions. Implementing the CDD method in a heterodyne/synchronized protocol combines the high-frequency detection with high spectral resolution. This advancement extends to various domains requiring detection in the high frequency (HF) and very high frequency (VHF) ranges of the RF spectrum, including spin sensor-based magnetic resonance spectroscopy at high magnetic fields.
Color centers in diamond and silicon carbide, and molecular spins through a host matrix control are promising for nanoscale quantum sensing because they can be optically addressable, coherently controllable, and placed proximate to the targets. However, large transverse zero-field splitting (ZFS) is often inevitable due to their intrinsic symmetry and/or the high local strains of the host matrix. Although spin coherence can be extended due to magnetic noise-insensitive clock transitions at a vanishing magnetic field, the eigenstates of these sensors are not sensitive to weak magnetic signals in the linear order. We address this challenge by employing a combination of radio-frequency (rf) field driving along the NV orientation and microwave dynamic decoupling pulse sequences. Radio-frequency driving can effectively mitigate the transverse ZFS effect and enhance the NV center's sensitivity to ac magnetic field signals. This combination not only suppresses environmental noise but also enables quantum frequency mixing between the transverse ZFS and the signal. It also offers the potential to detect weak ac signals at intermediate and high frequencies with high resolution, a task difficult to achieve using conventional methods.
Abstract State-of-the-art methods for sensing weak AC fields are only efficient in the low frequency domain (<10 MHz). The inefficiency of sensing high-frequency signals is due to the lack of ability to use dynamical decoupling. In this paper we show that dynamical decoupling can be incorporated into high-frequency sensing schemes and by this we demonstrate that the high sensitivity achieved for low frequency can be extended to the whole spectrum. While our scheme is general and suitable to a variety of atomic and solid-state systems, we experimentally demonstrate it with the nitrogen-vacancy center in diamond. For a diamond with natural abundance of 13 C, we achieve coherence times up to 1.43 ms resulting in a smallest detectable magnetic field strength of 4 nT at 1.6 GHz. Attributed to the inherent nature of our scheme, we observe an additional increase in coherence time due to the signal itself.
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 T2≈12T1{T}_{2}\approx \frac{1}{2}{T}_{1}T2​≈21​T1​ T 2 ≈ 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 η≈3−5 μT/Hz\eta \approx 3-5\,\mu {{{\rm{T}}}}/\sqrt{{{{\rm{Hz}}}}}η≈3−5μT/Hz​ η ≈ 3 − 5 μ T / Hz and phase sensitivity of ηϕ≈0.076 rads/Hz{\eta }_{\phi }\approx 0.076\,{{{\rm{rads}}}}/\sqrt{{{{\rm{Hz}}}}}ηϕ​≈0.076rads/Hz​ η ϕ ≈ 0.076 rads / 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.