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Physical Review Applied

Steady-State Microwave Mode Cooling with a Diamond N- V Ensemble

Donald P. Fahey, Kurt A. Jacobs, Matthew J. Turner, Hyeongrak Choi, J. E. Hoffman, Dirk Englund, Matthew E. Trusheim

Published Jul 17, 2023• 20 citations
Publisher

Abstract

All electronics are subject to thermal noise, which sets a minimum power to distinguish a signal from ambient background. Here quantum systems---in particular the nitrogen-vacancy center in diamond---show a path forward, as they can be laser-cooled to a quantum mechanical ground state while a device remains at ambient conditions. By placing an ensemble of N-$V$ centers inside a low-loss microwave cavity in which their spins strongly interact with gigahertz magnetic fields, the cold spins extract more energy than can leak in from the hot environment. The output voltage shows vastly reduced fluctuations at the cavity frequency; the effective temperature is lowered by 150 K.

DOI
10.1103/physrevapplied.20.014033

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•Oct 23, 2021•0 citations
All electronics are subject to thermal noise, which sets a minimum power to distinguish a signal from ambient background. Here quantum systems---in particular the nitrogen-vacancy center in diamond---show a path forward, as they can be laser-cooled to a quantum mechanical ground state while a device remains at ambient conditions. By placing an ensemble of N-VVV centers inside a low-loss microwave cavity in which their spins strongly interact with gigahertz magnetic fields, the cold spins extract more energy than can leak in from the hot environment. The output voltage shows vastly reduced fluctuations at the cavity frequency; the effective temperature is lowered by 150 K.
A fundamental result of quantum mechanics is that the fluctuations of a bosonic field are given by its temperature TTT. An electromagnetic mode with frequency ωωω in the microwave band has a significant thermal photon occupation at room temperature according to the Bose-Einstein distribution nˉ=kBT/ℏω\bar{n} = k_BT / \hbarωnˉ=kB​T/ℏω. The room temperature thermal state of a 3 GHz mode, for example, is characterized by a mean photon number nˉ∼2000\bar{n} \sim 2000nˉ∼2000 and variance Δn2≈nˉ2Δn^2 \approx \bar{n}^2Δn2≈nˉ2. This thermal variance sets the measurement noise floor in applications ranging from wireless communications to positioning, navigation, and timing to magnetic resonance imaging. We overcome this barrier in continuously cooling a ∼3{\sim} 3∼3 GHz cavity mode by coupling it to an ensemble of optically spin-polarized nitrogen-vacancy (NV) centers in a room-temperature diamond. The NV spins are pumped into a low entropy state via a green laser and act as a heat sink to the microwave mode through their collective interaction with microwave photons. Using a simple detection circuit we report a peak noise reduction of −2.3±0.1 dB-2.3 \pm 0.1 \, \textrm{dB}−2.3±0.1dB and minimum cavity mode temperature of 150±5K150 \pm 5 \textrm{K}150±5K. We present also a linearized model to identify the important features of the cooling, and demonstrate its validity through magnetically tuned, spectrally resolved measurements. The realization of efficient mode cooling at ambient temperature opens the door to applications in precision measurement and communication, with the potential to scale towards fundamental quantum limits.
Recent experiments demonstrated the cooling of a microwave mode of a high-quality dielectric resonator coupled to optically cooled nitrogen-vacancy (NV) spins in diamond. Our recent theoretical study [arXiv:2110.10950] pointed out the cooled NV spins can be used to realize cavity quantum electrodynamics effects (C-QED) at room temperature. In this article, we propose to modify the setup used in a recent diamond maser experiment [Nature 55, 493-496 (2018)], which features a higher spin transition frequency, a lower spin-dephasing rate and a stronger NV spins-resonator coupling, to realize better microwave mode cooling and the room-temperature CQED effects. To describe more precisely the optical spin cooling and the collective spin-resonator coupling, we extend the standard Jaynes-Cumming model to account for the rich electronic and spin levels of the NV centers. Our calculations show that for the proposed setup it is possible to cool the microwave mode from 293293293 K (room temperature) to 116116116 K, which is about 727272 K lower than the previous records, and to study the intriguing dynamics of the CQED effects under the weak-to-strong coupling transition by varying the laser power. With simple modifications, our model can be applied to, e.g., other solid-state spins or triplet spins of pentacene molecules, and to investigate other effects, such as the operations of pulsed and continuous-wave masing.
Abstract Recent experimental and theoretical studies demonstrated microwave mode cooling and cavity quantum electrodynamics (C-QED) effects at room temperature by using optically cooled nitrogen-vacancy (NV) spins. In this article, we consider improvements of these effects by exploring parameters in recent diamond maser experiments with a high frequency microwave resonator. By accounting for the rich electronic and spin levels, we provide a more complete treatment of optical pumping and dissipation in NV centers, and study the dependence of system performance on laser power. We predict the reduction of microwave photon number down to 261 (equivalent to a temperature of 116 K), about five times lower than the values reported recently. We also predict the laser-power controlled C-QED effects across weak-to-strong coupling regimes, and observe saturation of these effects under strong laser pumping. Our model can be modified straightforwardly to investigate similar effects with other solid-state spins and possible C-QED effects in maser operation.
We propose a method to create a room-temperature maser operating at approximately 2.9~GHz frequency using an ensemble of negatively charged nitrogen-vacancy electronic spins (NV) in diamond, without requiring population inversion. Our method considers a DC magnetic field of a few milli-Tesla (mT) applied along the perpendicular direction of an ensemble of NV spins aligned along a common axis. This perpendicular magnetic-field creates superposition states of ∣ms=−1⟩|m_{\mathrm{s}}=-1\rangle∣ms​=−1⟩ and ∣ms=+1⟩|m_{\mathrm{s}}=+1\rangle∣ms​=+1⟩ of the NV spin's ground state triplet levels and thereby makes it possible to drive all three transitions in the NV spin ground state. We model the system by including optical pumping of the NV spins, near-resonant driving of two transitions, and coupling the third transition to a near-resonant microwave resonator. Numerical estimates using experimentally realizable parameters show that inversionless masing can be achieved inside the microwave resonator using our method. As an application, we show that the output intensity of an inversionless maser (1.1×10141.1\times10^{14}1.1×1014 spins) can be used for magnetic field sensing with a DC sensitivity on the order of a hundred pT/Hz\sqrt{\mathrm{Hz}}Hz​. Our study opens a new direction in room-temperature diamond NV maser devices for quantum technological applications without the requirement of a strong bias magnetic field, as in conventional NV diamond masers.
Abstract Quantum sensors based on solid-state defects, in particular nitrogen-vacancy (NV) centers in diamond, enable precise measurement of magnetic fields, temperature, rotation, and electric fields. Cavity quantum electrodynamic (cQED) readout, in which an NV ensemble is hybridized with a microwave mode, can overcome limitations in optical spin detection and has resulted in leading magnetic sensitivities at the pT-level. This approach, however, remains far from the intrinsic spin-projection noise limit due to thermal Johnson-Nyquist noise and spin saturation effects. Here we tackle these challenges by combining recently demonstrated spin refrigeration techniques with comprehensive nonlinear modeling of the cQED sensor operation. We demonstrate that the optically-polarized NV ensemble simultaneously provides magnetic sensitivity and acts as a heat sink for the deleterious thermal microwave noise background, even when actively probed by a microwave field. Optimizing the NV-cQED system, we demonstrate a broadband sensitivity of 576 ± 6 fT/ Hz\sqrt{{{{\rm{Hz}}}}}Hz​ Hz around 15 kHz in ambient conditions. We then discuss the implications of this approach for the design of future magnetometers, including near-projection-limited devices approaching 3 fT/ Hz\sqrt{{{{\rm{Hz}}}}}Hz​ Hz sensitivity enabled by spin refrigeration.
Continuous Cooling of a Microwave Mode on a Benchtop using Hyperpolarized NV−^-− Diamond.
We demonstrate the cooling of a microwave mode at 2872 MHz through its interaction with optically spin-polarized NV−^-− centers in diamond at zero applied magnetic field, removing thermal photons from the mode. By photo-exciting (pumping) a brilliant-cut red diamond jewel with a continuous-wave 532-nm laser, outputting 2 W, the microwave mode is cooled down to a noise temperature of 188 K. This noise temperature can be preserved continuously for as long as the diamond is optically excited and kept cool. The latter requirement restricted operation out to 10 ms in our preliminary setup. The mode-cooling performance of NV−^-− diamond is directly compared against that of pentacene-doped para-terphenyl, where we find that the former affords the advantages of cooling immediately upon light excitation without needing to mase beforehand (or at all) and being able to cool continuously at substantially lower optical pump power.