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Heterodyne Sensing of Microwaves with a Quantum Sensor

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Heterodyne Sensing of Microwaves with a Quantum Sensor ARTICLE https://doi.org/10.1038/s41467-021-22714-y OPEN Heterodyne sensing of microwaves with a quantum sensor ✉ ✉ Jonas Meinel 1,2 , Vadim Vorobyov 1 , Boris Yavkin1, Durga Dasari 1,2, Hitoshi Sumiya3, ✉ Shinobu Onoda 4, Junichi Isoya 5 & Jörg Wrachtrup1,2 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 1234567890():,; 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. 1 3rd Institute of Physics, University of Stuttgart Institute for Quantum Science and Technology IQST, Stuttgart, Germany. 2 Max Planck Institute for Solid State Research, Stuttgart, Germany. 3 Advanced Materials Laboratory, Sumitomo Electric Industries Ltd., Itami, Japan. 4 Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology, Takasaki, Japan. 5 Faculty of Pure and Applied Sciences, ✉ University of Tsukuba, Tsukuba, Japan. email: [email protected]; [email protected]; [email protected] NATURE COMMUNICATIONS | (2021) 12:2737 | https://doi.org/10.1038/s41467-021-22714-y | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-22714-y recise detection of microwave frequency fields is of impor- This is achieved by creating the initial state of the sensor, using tance for a wide range of applications in cosmology1,radar2,3, the above-mentioned coherent external reference MW source. P 4–6 quantum optics with quantum circuit systems and electron This state evolves under the signal field, and is sensitive to the spin signals or coupling to phonons7. Oscillating magnetic fields, relative phase between reference and signal. We further show that described by their amplitude and frequency, require a sensor with the interaction with the signal field can be controlled with dres- high sensitivity and high spectral resolution over a wide range of sing fields while preserving the phase sensitivity. First, we study frequencies. pulsed Mollow absorption, a dynamical decoupling sequence Atomic systems, such as nitrogen vacancy (NV) centers in applied to sense MW-fields, making our protocol compliant with diamond, offer a microwave (MW) sensing platform through the high sensitivity detection schemes and still achieving sensor- electron spin transition8–10. Furthermore, the spin state can be unlimited spectral resolution. Second, we study Floquet dressed optically pumped, leading to an effective sensor temperature of states under strong longitudinal radio frequency (RF) drive, about 10 mK (99% polarization)8, hence in principle being able to allowing to create detection sidebands independent from the resolve single photon level signals11. However, for any quantum resonance frequency of the quantum system and allowing to sensors, the spectral resolution and sensitivity are linked through control the interaction strength. the lifetime of the system12–14. Advancements in experimental control of dynamical decoupling sequences allowed to separate Results sensitivity from spectral resolution15,16, widely applied in nuclear Theory. In the following, we theoretically describe how one magnetic resonance (NMR) detection using NV-centers, e.g.,17,18. achieves heterodyne sensing using a quantum sensor, here with While with these techniques, radio frequency signals can be NV center electron spin. The task at hand is to sense an oscil- detected with a spectral resolution below 1 Hz, they fail for fre- lating microwave field with frequency ω, given by: quencies beyond 10 MHz. Thus, MW detection protocols based on Ωðt; ϕ Þ¼Ω ðωt þ ϕ Þ: ð Þ the absorption in the electron spin transition19, though they could 0 0 cos 0 1 potentially reach high sensitivity8,10 and large spectral range9, are Ω = γB fi γ Tà T Where 0 signal is the amplitude of the eld with being the limited in spectral resolution with 2 and 1ρ times of the electron ϕ electron gyromagnetic ratio, and 0 is the initial phase of the spin. In our work, we aim to overcome the resolution limitations fi fi signal. The coupling of such a eld to the electronÀÁ spin of the NV and bene t from state-of-art sensing protocols for MW detection. H ¼ ΩðtÞ θ Á ^ ^ Conceptually, we extend heterodyne detection15,16 to the micro- center, is given by the Hamiltonian S , where S is wave regime. Furthermore, we apply the sensitivity advancements the vector of spin operators for the triplet ground-state spin fi θ brought by dynamical decoupling8–10 for MW sensing to het- con guration of the NV center and is the direction of the fi erodyne MW sensing. Finally, we profit from the robustness of microwave eld relative to the NV axis (see Supplementary fi Floquet dynamics for MW sensing20–22 and implement them as Fig. 3). The NV energy eigenstates with aligned magnetic eld are fi ji; ji jiÀ control fields for our protocols. This leads to a heterodyne MW de ned as 1 0 and 1 . The contribution of longitudinal Ω t ϕ sensor scheme, shown in Fig. 1a. We mix an external reference components of ( , 0) can be neglected for small amplitudes ω ≫ Ω Ω t ϕ with the MW signal and detect a demodulated signal in the ( 0), hence we assume ( , 0) to be along the x-axis. In fluorescence of the NV-center. secular approximation, the overall Hamiltonian becomes: H ¼ ω S^ þ Ω ðωt þ ϕ ÞS^ ; ð Þ s z 0 cos 0 x 2 where ωs is the transition frequency in the two-levelp subspaceffiffiffi of ^ ^ the NV-spin triplet, Sz ¼ðσz À 1Þ=2 and Sx ¼ σx= 2, where σ are the Pauli matrices and 1 is the identity. After transformation into the rotating frame, we get: Δω Ω Ω 0 0 0 H ðϕ Þ¼ σ^z þ pffiffiffi cosðϕ Þσ^x þ pffiffiffi sinðϕ Þσ^y; ð3Þ 0 2 2 2 0 2 2 0 where Δω = ωs − ω, depicted as orange arrow in Fig. 1b. For heterodyne sensing, we have to add a second microwave field Ω t ϕ ref( , ref) acting as a reference. In our concept, the reference source recreates the initial state with a π/2 pulse: pffiffiffi iϕ ψ ðϕ Þ ¼ðjiþ e ref jiÞÀ = ; ð Þ init ref 0 1 2 4 which evolves under the Hamiltonian in Eq. (3) for the time τ: ψðτÞ ¼ U^ ðH0ðϕ Þ; τÞ ψ ðϕ Þ : ð5Þ Fig. 1 Microwave heterodyne detection principle and its realization with a 0 init ref quantum sensor. a Heterodyne detection of a multimode microwave ^ After evolution, we measure the expectation value hSzi: frequency field relative to an external frequency reference using the NV hS ðτ; ϕ ; ϕ Þi Ω τ ðϕ À ϕ ÞðÞ center sensor as a mixer. The interaction with the signal is controlled by z ref 0 0 sin 0 ref 6 application of dressing fields. We benchmark two techniques: (1) pulsed pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω0τ; Δω Ω0 ¼ Δω2 þ Ω2 Mollow absorption using dynamical decoupling sequence and (2) Floquet for Ω0 1 with . We thus achieve a het- dynamics under strong RF-driving. The demodulated signal leads to high erodyne response as we compare the phases of two microwave ^ spectral resolution. b Heterodyne detection by creating the same initial fields through the measurement of the Sz expectation value. We ψ t = t + T state init (blue) from a coherent external MW-source between now perform a series of measurements at times n+1 n sequential measurements. A long coherent signal Ω(t) (orange) is (sampling interval T), where the initial phases for each mea- ϕ = ϕ + ωT ϕ = ϕ + ω T stroboscopically observed in the rotating frames. Finally, the z-projection surement are 0,n+1 0,n and ref,n+1 ref,n ref . (green) of ψ0 , the final state after evolution under Ω, is measured, Experimentally and theoretically, it is instructive to analyze the allowing to reconstruct the relative microwave phase. autocorrelation C(n) between the single measurement outcomes 2 NATURE COMMUNICATIONS | (2021) 12:2737 | https://doi.org/10.1038/s41467-021-22714-y | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-22714-y ARTICLE S = S t ω − ω = π ⋅ n z ( n) given by: the frequency difference of ( 1 2 2 482 Hz). The narrow linewidth of just 1 Hz and the measured frequency difference of 500 CðnÞ¼ hS S i n0 n0þn Hz demonstrate the spectral resolution beyond the coherence time M of the sensor, which is typically in the range of 1/T >kHz. ¼ ∑ Ω2τ2 ðδωTn0 þ δϕÞ ðδωTðn0 þ nÞþδϕÞ 2 sin sin ð Þ Furthermore, we analyze the peak width in Fig. 2ebycomputing n0¼1 7 the correlation function up to the correlation length N and extract 1 MΩ2τ2 cosðδωTnÞ; the linewidth of its spectral peak with a Lorentzian fit. For 2 measurement of Δω = 2π ⋅ 75 kHz, τ = 1.824 μs, T = 4.505 μsand Ω = π ⋅ where δω = ωref − ω is the demodulated frequency, M is the 0 2 111 kHz, we extract a 300 mHz linewidth for a correlation δϕ = ϕ − ϕ fi number of measurements and ref 0 is the initial phase length of 3 seconds.
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