Transform-Limited Photons From a Coherent Tin-Vacancy Spin in Diamond

Solid-state quantum emitters that couple coherent optical transitions to long-lived spin qubits are essential for quantum networks. Here we report on the spin and optical properties of individual tin-vacancy (SnV) centers in diamond nanostructures. Through cryogenic magneto-optical and spin spectroscopy, we verify the inversion-symmetric electronic structure of the SnV, identify spin-conserving and spin-flipping transitions, characterize transition linewidths, measure electron spin lifetimes, and evaluate the spin dephasing time. We find that the optical transitions are consistent with the radiative lifetime limit even in nanofabricated structures. The spin lifetime is phonon limited with an exponential temperature scaling leading to $T_1>10\mathrm{ms}$, and the coherence time, $T_2^{*}$ reaches the nuclear spin-bath limit upon cooling to 2.9 K. These spin properties exceed those of other inversion-symmetric color centers for which similar values require millikelvin temperatures. With a combination of coherent optical transitions and long spin coherence without dilution refrigeration, the SnV is a promising candidate for feasable and scalable quantum networking applications.

Figure 1

SnV center electronic structure. (a) The SnV energy levels, in the absence of magnetic field, are composed of doubly split ground and excited states with respective splittings ${\mathrm{\Delta }}_g$ and ${\mathrm{\Delta }}_e$, resulting in four optical transitions (red arrows) labeled from $\alpha$ to $\delta$. A magnetic field splits each level into two. The spin state expected from the SnV model (see main text) is indicated for each level with up and down gray arrows. The tilted arrows in the excited state represent the difference in spin quantization axis compared to the ground state. (b) Fluorescence spectrum of a single SnV center at 4 K without magnetic field. (c) Left panel: Magnetic field-dependent fluorescence spectrum of a single unstrained SnV center. Right panel: simulated magnetic field dependence based on the model developed for the SiV center [13]. The transitions are labeled according to the participating states. The simulated transition intensities were obtained from Fermi’s golden rule for dipolar electric transitions and thus depend on the orbital and spin components of the initial and final states. (d) Magnetic field dependence of the fluorescence spectrum of a strained SnV center, both experimental (left panel) and simulated using the strain simulation developed for SiV in previous work [30, 31] (right panel).

Figure 2

SnV center optical coherence. (a) Confocal microscope image of SnV centers in nanopillars with radius $r=150\mathrm{nm}$ (inset, scanning electron micrograph). Scale bars are $1\mu \mathrm{m}$. (b) Resonant PLE spectrum of a single SnV optical transition. Each point was integrated for 0.6 seconds. Blue line: Lorentzian fit with FHWM of $30\pm 2\mathrm{MHz}$. (c) Second-order correlation function under resonant driving. (d) Fluorescence decay after nonresonant pulsed excitation at $t=0$. The gray shaded area between 0 and 0.5 ns indicates the instrument response.

Figure 3

Spin-selective transitions. (a) SnV energy levels under external magnetic field depicting resonant excitation (upward arrows) and subsequent fluorescence (downward arrows) for transitions A1 (red) and B2 (blue) between levels of nearly overlapping spin states. (b) Experimental spectra at 9 T for nonresonant excitation (light gray curve) and resonant excitation of A1 (red curve) and B2 (blue curve). The excitation wavelengths are indicated by arrows of the corresponding colors. (c) Energy levels of the SnV center illustrating resonant excitation (upward arrows) and subsequent fluorescence (downward arrows) for transitions B1 (blue) and A2 (red) between levels of nearly opposite spin states. (d) Experimental spectra at 9 T for nonresonant excitation (light gray curve) and resonant excitation of B1 (blue curve) and A2 (red). Leakage from the laser is visible in both cases at the excitation wavelength.

Figure 4

Spin properties of a single SnV. (a) Spin polarization under an applied magnetic field of 0.13 T along [001] at a measured temperature of 4 K. The phonon sideband fluorescence decays as a function of time under resonant pumping of the A1 transition as level 2 is populated. (b) Polarization decay. The fluorescence of the A1 transition recovers as a function of time between the excitation and readout pulses, indicating repopulation of the ground spin level 1. Blue curve: fit to an exponential with $T_1=1.26\pm 0.28\mathrm{ms}$. (c) Spin decay time $T_1$ measured as a function of temperature (black dots). The blue solid curve is a exponential fit showing that $\log (T_1)$ varies linearly with $1/T$, as expected for single phonon-induced spin decay [22, 23]. (d) Optically detected magnetic resonance spectra. The frequency of an applied microwave field is scanned across the transition between levels 1 and 2, leading to a repopulation of level 1 at resonance. The data (dots) are fitted with a Lorentzian functions (solid curve) with widths at half-maximum of $2.7\pm 0.4\mathrm{MHz}$ at 6 K (red), and $293\pm 30$ and $356\pm 60\mathrm{kHz}$ at 2.9 K (blue).