We report strong coupling between an ensemble of N impurity
(P1) centers in diamond and microwave photons using a unique double-post reentrant cavity. The cavity is designed so that the magnetic component of the cavity field is spatially separated from the electric component and focused into the small volume in which the diamond sample is mounted. The novelty of the structure simultaneously allows the high magnetic filling factor (38.4%) and low frequencies necessary to interact, at low magnetic field, with transitions in diamond such as those in negatively charged nitrogen-vacancy and
P1 centers. Coupling strength (or normal-mode splitting) of 51.42 MHz was achieved with
P1 centers at 6.18 GHz and 220 mT in a centimeter-scale cavity, with a corresponding cooperativity factor of 4.7. This technique offers an alternative way, with some significant advantages, to couple 3D cavities to transitions in diamond and achieve the strong coupling necessary for applications to quantum information processing.
Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful platforms for high-precision metrology. Coupling the NV ensemble to a microwave cavity mode in a cavity quantum electrodynamics (cQED) configuration enables spin readout that surpasses the limitations of conventional optical detection, achieving sub-picotesla magnetic sensitivities. However, existing continuous-wave cQED approaches remain far from the intrinsic spin-projection-noise limit due to spin saturation and power broadening. Here, we introduce a dispersive cQED readout technique to overcome these fundamental limitations in NV ensemble sensing. We develop a comprehensive theoretical framework describing the dispersive interaction and analyze the time-domain dynamics of a strongly-coupled NV-cavity system. Our results indicate near-unity inverse readout fidelity and femtotesla-level sensitivity using a commercially available diamond NV ensemble. Importantly, the dispersive readout exhibits a distinct sensitivity scaling that improves as 1/N with increasing number of spins N, providing a practical pathway toward approaching the standard quantum limit for solid-state spin-ensemble sensors.
We engineer lumped-element superconducting resonators that maximize magnetic coupling to molecular spin qubits, achieving record single-spin couplings up to
100 kHz and collective couplings exceeding
10 MHz. The resonators interact with PTMr organic free radicals, model spin systems with
S=1/2 and a quasi-isotropic
g≃2, dispersed in polymer matrices. The highest collective spin-photon coupling strengths are attained with resonators having large inductors, which therefore interact with most spins in the molecular ensemble. By contrast, the coupling of each individual spin
G1 is maximized in resonators having a minimum size inductor, made of a single wire. The same platform has been used to study spin relaxation and spin coherent dynamics in the dispersive regime, when spins are energetically detuned from the resonator. We find evidences for the Purcell effect, i.e. the photon induced relaxation of those spins that are most strongly coupled to the circuit. The rate of this process gives access to the distribution of single spin photon couplings in a given device. For resonators with a
50 nm wide constriction at the inductor center, single maximum
G1 values reach
∼100 kHz. Pumping the spins with strong pulses fed through an independent transmission line induces coherent Rabi oscillations. The spin excitation then proceeds via either direct resonant processes induced by the main pulse frequency or, in the case of square-shaped pulses, via the excitation of the cavity by sideband frequency components. The latter process measures the cavity mode hybridization with the spins and can be eliminated by using Gaussian shaped pulses. These results establish a scalable route toward integrated molecular-spin quantum processors.
Abstract We demonstrate dispersive readout of the spin of an ensemble of nitrogen-vacancy centers in a high-quality dielectric microwave resonator at room temperature. The spin state is inferred from the reflection phase of a microwave signal probing the resonator. Time-dependent tracking of the spin state is demonstrated, and is employed to measure the T 1 relaxation time of the spin ensemble. Dispersive readout provides a microwave interface to solid state spins, translating a spin signal into a microwave phase shift. We estimate that its sensitivity can outperform optical readout schemes, owing to the high accuracy achievable in a measurement of phase. The scheme is moreover applicable to optically inactive spin defects and it is non-destructive, which renders it insensitive to several systematic errors of optical readout and enables the use of quantum feedback.
Metamaterial resonant structures made from arrays of superconducting lumped-circuit elements can exhibit microwave-mode spectra with left-handed dispersion for the standing-wave resonances, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this regime for multimode circuit quantum electrodynamics, we perform a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we observe the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we probe the qubit dispersively and characterize the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we investigate the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. Through numerical simulations, we explore designs based on this scheme with enhanced coupling so that the coupling energy between the qubit and the metamaterial modes can exceed the intermode spacing in future devices with achievable circuit parameters. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation with microwave photons and quantum memories.
We study the simultaneous interaction of a sample of organic free radicals, which realize the spin-1/2 model with a quasi-isotropic g factor ≈ 2, with three ≈ 5.5 GHz lumped-element superconducting resonators in a chip. Each resonator consists of a finger capacitor in parallel with a single wire inductor, which maximizes the coupling intensity of the spins to the photon magnetic field. Their frequencies have been detuned relative to one another in order to make them individually addressable. Each resonator within the trio is capacitively coupled to its nearest neighbor and inductively coupled to a common readout transmission line, and only the central one hosts a molecular deposit. The device has been characterized by microwave transmission experiments performed as a function of frequency (between 5.3 and 5.7 GHz) and magnetic field (170–220 mT) at very low temperatures (T ≃ 13 mK). The results evidence a strong local interaction of the spins to the central resonator, which reaches the coherent coupling regime. In addition, they show that the same spins also couple to the modes associated with the distant resonators. These data have been analyzed on the basis of a theoretical model that incorporates the direct spin-photon interactions as well as those mediated by the circuit. The results provide a relatively simple, practical method for investigating spin resonance of a material at multiple frequencies. Besides, this method allows designing each resonator differently, to fulfill a specific role, e.g., for optimized control or readout of the spin states, which can be of relevance for the implementation of hybrid quantum computation schemes based on molecular spin qubits.