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arXiv:1103.1045 · Physical Review Letters

Cavity QED with Magnetically Coupled Collective Spin States

Robert Amsüss, Christian Koller, Tobias Nöbauer, Stefan Putz, Stefan Rotter, K. Sandner, Stephan Schneider, Matthias Schramboeck, Georg Steinhäuser, Helmut Ritsch, Jörg Schmiedmayer, Johannes Majer

Published Aug 3, 2011• 330 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.107.060502

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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.
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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.
Circuit-QED has demonstrated very strong coupling between light and matter, and has the potential to engineer large quantum devices. Hybrid designs have been proposed which couple large ensembles of atomic and molecular systems to the superconducting resonator. We show that one can achieve an effective strong coupling between light and matter for much smaller ensembles (and even a single electronic spin), through the use of an interconnecting quantum system: in our case a persistent current qubit. Using this interconnect we show that one can effectively magnify the coupling strength between the light and matter by over five orders of magnitude $g\ensuremath{\sim}7\text{ }\text{Hz}\ensuremath{\rightarrow}100\text{ }\text{kHz}$ and enter a regime where a single nitrogen-vacancy (NV) electronic spin can shift the cavity resonance line by over $\ensuremath{\sim}20$ linewidths. With such strong coupling between an individual electronic spin in an NV and the light in the resonator, one has the potential build devices where the associated NV nuclear spins can be strongly coupled over centimeters via the superconducting bus.
We demonstrate strong coupling in a solid-state hybrid quantum system comprising a fixed-frequency coplanar-waveguide resonator, a superconducting transmon qubit, and an ensemble of nitrogen-vacancy centers in diamond. Frequency-domain spectroscopy reveals a characteristic three-mode avoided crossing, consistent with excitations being distributed across all three subsystems through hybridized eigenmodes. At higher probe powers, we observe nonlinear features and signatures of transmon- N 14 nuclear-spin interactions, highlighting the accessibility of higher-excitation manifolds in this architecture. These results establish an experimentally accessible regime of hybrid cavity QED that integrates superconducting and spin degrees of freedom, providing a platform for exploring complex multicomponent dynamics and developing hybrid quantum interfaces.
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 show that a hybrid quantum device consisting of three ensembles of nitrogen-vacancy (NV) centers whose spins are collectively coupled to a superconducting coplanar waveguide resonator enables the generation of controllable macroscopic tripartite entangled states. At the instants of time when the waveguide resonator is completely depleted of photons and is thus disentangled from the NV-center ensembles, macroscopic Greenberger–Horne–Zeilinger-type states are generated in NV-diamond memories.