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arXiv:1112.4767 · Physical Review A

Strong magnetic coupling of an inhomogeneous nitrogen-vacancy ensemble to a cavity

K. Sandner, Helmut Ritsch, Robert Amsüss, Christian Koller, Tobias Nöbauer, Stefan Putz, Jörg Schmiedmayer, Johannes Majer

Published May 7, 2012• 75 citations
arXivHTMLPDF

Abstract

We study experimentally and theoretically a dense ensemble of negatively charged nitrogen-vacancy centers in diamond coupled to a high-$Q$ superconducting coplanar waveguide cavity mode at low temperature. The nitrogen-vacancy centers are modeled as effective spin-one defects with inhomogeneous frequency distribution. For a large enough ensemble the effective magnetic coupling of the collective spin dominates the mode losses and inhomogeneous broadening of the ensemble and the system exhibits well-resolved normal-mode splitting in probe transmission spectra. We use several theoretical approaches to model the probe spectra and the number and frequency distribution of the spins. This analysis reveals an only slowly temperature-dependent $q$-Gaussian energy distribution of the defects with a yet unexplained decrease of effectively coupled spins at very low temperatures below $100\phantom{\rule{0.28em}{0ex}}\mathrm{m}\mathrm{K}$. Based on the system parameters we predict the possibility to implement an extremely stable maser by adding an external pump to the system.

DOI
10.1103/physreva.85.053806

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We study experimentally and theoretically a dense ensemble of negatively charged nitrogen-vacancy centers in diamond coupled to a high-QQQ superconducting coplanar waveguide cavity mode at low temperature. The nitrogen-vacancy centers are modeled as effective spin-one defects with inhomogeneous frequency distribution. For a large enough ensemble the effective magnetic coupling of the collective spin dominates the mode losses and inhomogeneous broadening of the ensemble and the system exhibits well-resolved normal-mode splitting in probe transmission spectra. We use several theoretical approaches to model the probe spectra and the number and frequency distribution of the spins. This analysis reveals an only slowly temperature-dependent qqq-Gaussian energy distribution of the defects with a yet unexplained decrease of effectively coupled spins at very low temperatures below 100mK100\phantom{\rule{0.28em}{0ex}}\mathrm{m}\mathrm{K}100mK. Based on the system parameters we predict the possibility to implement an extremely stable maser by adding an external pump to the system.
We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a superconducting coplanar single-mode waveguide resonator.
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 report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to (13)C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time of the NV center at millikelvin temperatures in a nondestructive way.
Hybrid quantum systems, which combines the advantages of different quantum systems, play an essential role in the realisation of quantum computation, especially as quantum memory. This thesis discusses the very promising hybrid quantum system based on the ensemble of negatively charged nitrogen-vacancy centers (NV-centers) in diamond and superconducting microwave cavities. The decoherence of this system, due to the inhomogeneous spin broadening, seems to be the major obstacle of utilising the NV-centers as a quantum information storage. This works focuses on the study of the dynamics of our NV-center spin ensemble strongly coupled to a superconducting resonator driven by pulse sequences with a carrier frequency equaling the cavity frequency. A precise knowledge of the spin broadening, which has a non-Lorentzian distribution, led to the observation of the so called 'cavity protection effect'. Furthermore this work demonstrates the enhancement of the damped Rabi oscillations between the spin ensemble and the cavity mode through appropriate chosing of the microwave pulses, which could change in the order of two magnitudes. Last we also confirmed the theoretical analysis of the crossover from markovian to non-markovian dynamics for our system, which is achieved for increasing coupling strength.
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.
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.