Inhibited radiative decay enhances single-photon emitters

TL;DR

This work introduces a broadband strategy to enable scalable spin–photon interfaces by inhibiting undesired spontaneous emission rather than maximizing a single transition. Using erbium dopants in silicon photonic-crystal waveguides, the authors suppress all but one radiative channel through careful LDOS engineering, channeling emission into the Y1→Z1 telecom transition while preserving or extending excited-state lifetimes. They spectrally resolve tens of single Er dopants in a single device, observe average lifetimes around 295 μs, and report a branching fraction into the desired transition of about 72%, far exceeding bulk values and not attributable to spectral filtering alone. The approach offers broadband, multiplexed photon sources at telecom wavelengths with relaxed fabrication constraints on mode volume and resonance tuning, and it can be integrated with Purcell enhancement or adapted to other spin-qubit platforms for robust quantum networks.

Abstract

Quantum networks and the modular scaling of quantum computers require efficient spin-photon interfaces. This can be achieved with optical resonators that increase the local density of states, thereby enhancing the radiative decay of emitters on a specific transition. However, small mode volumes and high quality factors are required in this approach, which restricts the multiplexing capacity and necessitates precise tuning of the resonator frequency. Here, we demonstrate an alternative method that avoids these bottlenecks for up-scaling. Instead of strongly enhancing the emission on a selected transition, we suppress all other radiative decay channels by tailoring the photonic bandgap of a W1 silicon photonic crystal waveguide. In such a device, we can spectrally resolve and individually address tens of erbium dopants. We find that their emission is channeled to the desired transition, ensuring efficient collection. At the same time, their lifetimes are preserved or even extended compared to the bulk in a broad spectral range. Furthermore, the extended mode volume facilitates a low dopant concentration and thus a large spatial separation between the emitters, avoiding unwanted interactions that would limit their coherence. The demonstrated approach of inhibiting unwanted spontaneous emission can be combined with Purcell enhancement and applied to other leading spin-qubit platforms. It thus opens intriguing perspectives for photonic quantum technologies.

Figures (11)

• Figure 1: Different approaches to interfacing single-photon emitters.a, An emitter (red filled circle) in a homogeneous medium (grey) emits photons (colored wave packets) in many directions and on desired (light red) and undesired (dark red) optical transitions (arrows in the level scheme on the left). Thus, only a small fraction of the photons is emitted on the desired transition, collected and detected, e.g., with a fiber-coupled single-photon detector (black symbols on the right). This hampers the performance as a single photon source. b, Integrating the emitter into a suited optical resonator (indicated by the two mirrors) can strongly enhance the desired transition (large red wave packet) via the Purcell effect. However, the emission into other spatial modes and on other transitions is largely unaffected. Therefore, such single photon sources require strong Purcell enhancement factors and tight light confinement to be efficient. c, In contrast, the emission into all but one spatial and spectral mode can be strongly suppressed, e.g., by photonic crystal waveguides (grey). Such devices can have an increased bandwidth and do not require precise frequency tuning and stabilization. They are not restricted to small mode volumes and thus their spectral multiplexing capacity is not limited by emitter interactions.
• Figure 2: Photonic crystal waveguide (PCW) for tailoring the radiative decay of individual erbium dopants in silicon.a, Level scheme. The interaction with the host crystal splits the spin-orbit coupled energy levels $^4\text{I}_{15/2}$ and $^4\text{I}_{13/2}$ of erbium's 4f electrons into the crystal field levels $Z_1$ to $Z_8$ and $Y_1$ to $Y_7$, respectively. At cryogenic temperatures, the $Y_1$ and $Z_1$ levels cannot decay via phonon emission and thus exhibit long optical coherence. b, W1 waveguide. The scanning electron microscope image shows a representative PCW terminated by a tapered fiber coupler at the bottom and a photonic crystal mirror at the top. c, Normalized absolute value squared of the strongest electric field components, $E_x$ (left panel) and $E_y$ (right), of the guided eigenmode in a unit cell of the W1 waveguide. d, Simulated photonic band structure (left) and LDOS (right) for a $y$-dipole at the maximum field position of $E_y$. Above the line where $\omega/k_{\parallel}$ equals the speed of light (grey area), the spectrum of states is continuous. Below, a photonic band gap is formed, surrounded by slab modes (light blue) with reduced LDOS. Along the $\Gamma-K$ direction ($k_{\parallel}$), two modes are guided in the W1 waveguide. Below the lower, even mode (red), an approximately 5THz wide band gap (yellow) remains. Thus, the LDOS is significantly reduced for all transitions ($Y_1\rightarrow Z_2...Z_8$, right axis) of embedded erbium dopants, suppressing their spontaneous emission. In contrast, on the $\text{Y}_1\leftrightarrow \text{Z}_1$ transition, the slow light effect leads to an increased LDOS and an enhanced decay into the guided mode.
• Figure 3: Spectral properties of erbium dopants in a silicon photonic-crystal waveguide.a, After pulsed resonant excitation around the $Y_1 \rightarrow Z_1$ transition frequency $\nu_0$ of site "A", the fluorescence spectrum of an inhomogeneously broadened ensemble of erbium dopants in PCW A exhibits distinct peaks. The dashed line indicates the dark count level. b, A measurement of the autocorrelation function $g^{(2)}(\tau)$ on the same emission line results in a zero-delay value of $0.07 \pm 0.01$ when subtracting becher_nonclassical_2001 the contribution of the independently measured detector dark counts (left axis), or $0.25\pm0.03$ without correction (right axis). This proves that the peak originates from a single dopant. c, A Lorentzian (red) fitted to a high-resolution measurement of a single emission line (marked by the red triangle in a) gives a linewidth of 21.5±0.1MHz. Error bars: 1 S.D. d, The spectral diffusion linewidth measured on PCWs A and B (blue and green, respectively) slightly differ between the emitters. It exceeds 13MHz for all dopants. The average linewidth is 27MHz with a standard deviation of 12MHz. The error bars indicate the standard error of the Lorentzian fits.
• Figure 4: Optical lifetimes and $Y_1\rightarrow Z_1$ emission of single dopants.a, Exponential fits are used to extract the lifetimes of all individual emitters in the inhomogeneous ensembles of the PCWs A and B (blue and green, respectively), shown as a function of the detuning from the center of the inhomogeneous line. The solid gray line marks the lifetime in bulk silicon of 142±1µs while the dashed line denotes the value in silicon strip waveguides of 209±1µs gritsch_narrow_2022. The lifetimes of all dopants except one exceed the bulk value, proving the inhibition of spontaneous emission in the PCWs. The fluctuation of the lifetime, further analyzed in the histogram on the right, stems from the random position and orientation of the emitters relative to the guided mode. The average lifetime is 295µs with a standard deviation of 97µs. b, A magnetic field is applied to tune the emission frequency of a single emitter in PCW C via the Zeeman effect. The spectral dependence of the local density of states (LDOS) can then be determined by extracting the lifetime. The gray curves show the expectation based on the LDOS simulation and the measured dispersion in three different PCWs with parameters similar to those of the device hosting the emitters (see \ref{['apxtheory']}) While the slope can be accurately predicted, slight variations across the nanofabricated devices lead to a deviation of the curve offset. c, As an effect of the selective suppression of unwanted optical transitions, the fraction of the photons that are emitted on the $Y_1\rightarrow Z_1$ transition is increased. It can thus exceed the value measured in a silicon strip waveguide of 23±5% (gray line). Inserting a narrowband spectral filter allows determining the fraction of light that is detected at the $Y_1\rightarrow Z_1$ frequency (blue data points). It shows no clear spectral dependence owing to the broadband nature of our approach. It approaches unity for some emitters but exhibits large fluctuations (histogram on the right) because of the random position and orientation of the emitters in the guided mode of the PCW. The average is 72% with a standard deviation of 14%. The measurement was performed on PCW A. All error bars denote 1 S.D.
• Figure 5: Local density of states (LDOS) simulation. a, PCW geometries used for simulating the LDOS spectra for different dipole orientations at the $E_y$ (left) and $E_x$ (right) maximum. The images show a top view of the photonic crystal slab. The black parts are silicon with a refractive index of 3.45 (at $T<10K$), the white parts are air with a refractive index of 1. The dashed green area indicates perfectly matched layers (PML) used to create absorbing boundary conditions. The red dot marks the location of the source in each case. b, LDOS spectra for dipoles oriented in-plane, either parallel to the waveguide axis ($x$), perpendicular to the waveguide axis ($y$), and out-of-plane ($z$). The spectra are simulated at the position of the $E_y$ electric field component maximum or the $E_x$ electric field component maximum of the eigenmode of the W1 waveguide, as indicated in a. The simulated spectra (gray) exhibit fast, high-amplitude oscillations in the band gap, where emission is strongly suppressed. These artifacts originate from the finite run time of the simulation. To remove the fast oscillations, a second-order Butterworth lowpass with a cutoff frequency of 0.2 times the Nyquist frequency filter is applied to the spectra. The filtered spectra are shown in blue. The dashed horizontal line marks $\rho/\rho_{\mathrm{bulk}}=1$, separating the regimes of enhancement (above) and suppression (below) of the emission. The vertical red lines indicate the optical transitions into the different crystal field levels of Er:Si in site "A".