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arXiv:2203.04102

Cavity Quantum Electrodynamics Effects of Optically Cooled Nitrogen-Vacancy Centers Coupled to a High Frequency Microwave Resonator

Yuan Zhang, Qilong Wu, Wu, Hao, Yang, Xun, Shi‐Lei Su, Chongxin Shan, Klaus Mølmer

Published Mar 8, 2022• 0 citations
arXivHTMLPDF

Abstract

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 $293$ K (room temperature) to $116$ K, which is about $72$ 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.

DOI
10.48550/arxiv.2203.04102

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•Oct 23, 2021•0 citations
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.
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.
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.
We present a quantum theory of diamond masers operating at any temperature using a cavity quantum electrodynamical framework. Special attention is paid to the recently demonstrated room-temperature solid-state masers based on nitrogen-vacancy (NV) defect centers in diamond, but the model can easily be modified for other photoexcited chromophores such as pentacene-doped paraterphenyl, vacancies in silicon-carbide or boron nitride. We show that the eight energy levels involved in the optically pumped NV center polarization process can be mapped to a simple pumped two-level-system. We then derive simple analytical expressions for the optical pump threshold condition for masing as well as the steady-state microwave output power which can be used to design and predict maser performance. Finally, we investigate second-order correlations and find that typical diamond masers operate in an intermediate regime between the good and bad cavity limits where photon emission is driven by both stimulated and superradiant processes.
Magnetic resonance can be used as a testbed for observing, demonstrating, and studying fundamental concepts of quantum cavity interaction with a two-level system at the microwave regime. Such experiments are mostly carried out at low cryogenic temperatures with spin systems that are embedded in a high-quality (Q-factor) superconducting cavity. For example, recent work has shown that under such conditions, and in a regime of high cooperativity and strong collective coupling between an electron spin system and a microwave cavity, multiple spin echoes are observed. These echoes have been analysed as signatures of coherent quantum effects; namely, the photons in the cavity can excite the spin system, which in turn can excite the cavity itself and so on. In this work we show that the use of a unique tailor-made moderate Q cavity in conjunction with diamond crystals having large concentrations of nitrogen vacancy (NV) centers makes it possible to observe such non-linear quantum phenomenon, even at room temperature. A key requirement of our experiments is that the spin system’s thermodynamic (rather than the physical) temperature is cooled to a few K, while high cooperativity and/or strong coupling are not a necessary prerequisite for such observations. The observation of meaningful microwave cavity quantum effects even at room temperature could lead to applications such as quantum memories and quantum sensing.
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.