Spectral hole burning and its application in microwave photonics

Spectral hole burning, used in inhomogeneously broadened emitters, is a well-established optical1 technique, with applications from spectroscopy to slow light2 and frequency combs3. In microwave photonics4, electron spin ensembles5,6 are candidates for use as quantum memories7 with potentially long storage times8. Here, we demonstrate long-lived collective dark states9 by spectral hole burning in the microwave regime10. The coherence time in our hybrid quantum system (nitrogen–vacancy centres strongly coupled to a superconducting microwave cavity) becomes longer than both the ensemble’s free-induction decay and the bare cavity dissipation rate. The hybrid quantum system thus performs better than its individual subcomponents. This opens theway for long-lived quantummultimodememories, solid-state microwave frequency combs, spin squeezed states11, optical-to-microwave quantum transducers12 and novel metamaterials13. Beyond these, new cavity quantum electrodynamics experiments will be possible where spin–spin interactions and many-body phenomena14 are directly accessible. Quantum information science and metrology rely on the coherent manipulation of two-level systems, which allow the storage of single excitations in high-capacity multimode memories15. The manipulation of information within those memories has proven to be difficult, and so the hybridization of distinct quantum systems to form quantum metamaterials offers a realistic way forward. Such ‘hybrid’ quantum systems have become a key strategy in microwave circuit cavity quantum electrodynamics (cQED)4,16. As an example we discuss the hybridization of superconducting devices with electron spin ensembles5,6,17 and show their potential to bypass individual weaknesses while harnessing their strengths. Electrical circuits offer easy manipulation and processing18,19, yet have limited coherence properties, while single electron spins in semiconductor crystals can have coherence times of up to almost one hour20 but are hard to manipulate. In early experiments, coherent energy exchange on the single-photon level and basic memory operations7 were demonstrated in this context21. An outstanding challenge in solid-state-based hybrid systems is the suppression of spin dephasing induced by the host material5,6,17. However, the realization of true multimode memories is only possible in the presence of inhomogeneous spectral broadening and so their short memory times have to be actively recovered by echo refocusing techniques21 or improved by the cavity protection effect22. In this Letter, we present an alternative approach based on collective dark states9,23 that circumvents the necessity for recovery protocols and substantially improves the coherence times beyond the limit given by the cavity and spin ensemble. Our hybrid system consists of a superconducting resonator with a diamond crystal containing an ensemble of negatively charged nitrogen–vacancy (NV) centre electron spins magnetically coupled to it (Fig. 1a,b). The device was placed in a dilution refrigerator operating at temperatures <25 mK. The resonator was characterized at zero external magnetic field by transmission spectroscopy and was determined to have a fundamental resonance at ωc/2π = 2.691 GHz with a cavity linewidth of κ/2π = 440 ± 10 kHz and quality factor of Q = 3,130. The diamond crystal has a NV concentration of ∼4 × 10 cm, meaning that the macroscopic spin ensemble in the cavity mode volume consists of N ≈ 1 × 10 NV spins thermally polarized (≥99%) at our refrigerator’s base temperature. These electron spins were Zeeman-shifted into resonance with the cavity by applying an external d.c. magnetic field (Fig. 1c). We observed a mode splitting and Rabi oscillations with frequency ΩR/2π = 21.3 ± 0.1 MHz and linewidth/decay rate of Γ/2π = 1.45 ± 0.05 MHz on probing the system with low intensities of <1 × 10 photons per spin in the cavity (Supplementary Fig. 1). Although the single spin–cavity coupling strength, gj, is rather small (≲10 Hz) (ref. 6), the large number N of weakly dipole– dipole interacting spins allows us to deeply enter the strong coupling regime (ΩR≫ Γ≫ κ) with cooperativity C ≈ 26. Such an ensemble of individual two-level systems coupled to a single-mode cavity is described by the Tavis–Cummings model, which in the rotating wave approximation can be written as