Cavity-coupled telecom atomic source in silicon

Abstract

Novel T centers in silicon hold great promise for quantum networking applications due to their telecom band optical transitions and the long-lived ground state electronic spins. An open challenge for advancing the T center platform is to enhance its weak and slow zero phonon line (ZPL) emission. In this work, by integrating single T centers with a low-loss, small mode-volume silicon photonic crystal cavity, we demonstrate an enhancement of the fluorescence decay rate by a factor of F = 6.89. Efficient photon extraction enables the system to achieve an average ZPL photon outcoupling rate of 73.3 kHz under saturation, which is about two orders of magnitude larger than the previously reported value. The dynamics of the coupled system is well modeled by solving the Lindblad master equation. These results represent a significant step towards building efficient T center spin-photon interfaces for quantum information processing and networking applications.

T centers in silicon are promising candidates for quantum applications yet suffer from weak optical transitions. Here, by integrating with a silicon nanocavity, the authors demonstrate an enhancement of the photon emission rate for a single T center.

Introduction

Optically interfaced atomic defects in solid-state materials are important building blocks for a variety of quantum technologies¹. For example, nitrogen and silicon vacancy centers in diamonds have been used to demonstrate milestone results for fiber-based quantum networks, including spin-photon entanglement², deterministic entanglement generation between remote spins³, quantum state teleportation⁴, and memory-enhanced communication⁵. However, these defects have optical transitions at the visible or near-infrared spectral range resulting in large fiber transmission loss, requiring nonlinear frequency conversion⁶ to extend the network range. Significant progress has been made towards utilizing atomic defects with telecom optical transitions, leading to the discovery of single vanadium ions in silicon carbide⁷, defects in gallium nitride⁸, and single erbium ions in yttrium orthosilicate⁹, as well as a recent demonstration of indistinguishable telecom photon generation from single erbium ions¹⁰.

Early exploration into the scalable fabrication of atomic defects with photonic structures relies on heterogeneous material integration and typically involves pick-and-place type of fabrication procedures^9,11,12. On the other hand, silicon-on-insulator (SOI) is a mature and scalable platform to enable large-scale monolithic photonic and electronic device integration. Telecom-interfaced solid-state spins in silicon can thus benefit from the technological advantages of the SOI platform, and be utilized for realizing large-scale spin-based integrated quantum photonic chips¹³. Moreover, silicon can be isotopically enriched to create a “semiconductor vacuum”¹⁴ for lowering the magnetic noise generated from the ²⁹Si nuclear spin bath.

Beyond efforts towards optical addressing of erbium ions in silicon^15–17, multiple novel atomic defect centers in silicon, including C, G, T, and W centers^18–27, have been experimentally identified recently towards quantum information applications. Among them, T centers are particularly promising due to their telecom O-band optical transitions, doublet ground state spin manifold, and long spin coherence times in an enriched ²⁸Si sample²³. Single T centers have been isolated in micropuck²⁴ and waveguide²⁸ structures. To further advance the single T center platform for quantum networking applications, challenges remain to enhance its weak and slow coherent emission at the zero phonon line (ZPL). The cavity-induced Purcell effect²⁹ has been widely used for enhancing the fluorescence emission of various atomic defects in solids, including G centers^30–32.

In this work, we demonstrate Purcell enhancement of a single T center in a low-loss, small mode-volume silicon photonic crystal (PC) cavity. When the cavity is tuned into resonance with the single T center we observe an enhancement of its fluorescence decay rate by a factor of F = 6.89, shortening the single T center lifetime to 136.4 ± 0.6 ns. Leveraging the nanophotonic circuit and an angle-polished fiber for light coupling³³, the system detection efficiency reaches η_sys = 9.1%, representing the probability of a single photon emitted into the cavity being registered by the detector. This efficiency is 20-fold larger than that achieved in a typical confocal-type measurement system for T centers. We probe single T centers in the device using time-resolved photoluminescence excitation (PLE) spectroscopy. Under the pulsed excitation, the system can detect 0.01 ZPL photon per excitation, reaching an average photon count rate of 73.3 kHz, which is about two orders of magnitude improvement from the previously reported emission rate for single T centers in the waveguide²⁸. By solving the Lindblad master equation, we develop a numerical model to describe the coupling dynamics between the single T center and the cavity, and extract cavity-QED parameters as well as T center pure dephasing rate (Γ_d) and spectral diffusion (Γ_sd). This work represents a key step towards utilizing single T centers in silicon for quantum information applications.

Results

Device integration and PLE spectroscopy

Our experimental configuration is outlined in Fig. 1a. The nanophotonic devices are fabricated on a SOI sample which is situated on the cold finger of a closed-cycle cryostat (T = 3.4 K). Each device consists of a subwavelength grating coupler (GC)³⁴ and a one-dimensional PC cavity, which is connected by a linearly tapered waveguide (Fig. 1b). Optical coupling to the PC cavities is accomplished by using an angle-polished fiber via the GC with a one-way coupling efficiency of η_GC = 46.1% at 1326 nm (Fig. 1c). The fiber is mounted on a three-axis translation stage for optimizing the coupling. The PC cavity used in this work (Fig. 1d) has a quality factor Q = 4.3 × 10⁴. Fluorescence from the T center is detected by a fiber-coupled superconducting nanowire single photon detector (SNSPD) located in a separate cryostat (Fig. 2a). To match the atomic transition, we coarsely red-tune the cavity resonance by condensing nitrogen gas onto the surface of the device; we fine blue-tune the cavity resonance by sending laser pulses with a high optical power into the cavity (Supplementary Section 1.2).

Fig. 1. Efficient optical coupling to single T centers in a silicon photonic cavity.

a Schematic illustration of fiber coupling to the nanophotonic circuits. Each PC cavitiy and subwavelength GC (with a width of 13.1 μm) are connected via a linearly tapered waveguide (200 μm in length). The GC allows efficient light coupling with an angle-polished fiber. (x, y, z) refer to ($\left[0\overline{1}0\right]$, [100], [001]) directions of the silicon crystal. T centers (solid red balls with arrows) are uniformly generated across the whole SOI device layer using the ion implantation method. Inside the dashed square, the simplified electronic level structure of the single T center is shown²³. b Scanning electron microscope image of a block of 10 devices. An individual device (orange-shaded) consists of a PC cavity on the upper left end (inside the orange dashed rectangle) and a GC on the lower right end (inside the blue dashed rectangle). c Measured GC coupling spectrum (blue), with a Gaussian (black) fitted FWHM linewidth of 36.1 nm. The orange dashed box encloses a PC cavity. d Reflection spectrum of the cavity (blue) shown in panel (c), with a Lorentzian (orange) fitted FWHM linewidth of 5.22 ± 0.04 GHz. This cavity is used in later experiments. Results shown in panel (c) and (d) are measured at T = 3.4 K.

Fig. 2. Photoluminescence excitation spectroscopy for T centers.

a Simplified schematic of the experimental setup for performing PLE spectroscopy. Short excitation pulses are generated via a series of acousto-optic modulators (AOMs) and an electro-optic modulator (EOM) from a stabilized laser. The EOM is also used to generate laser sidebands. Fluorescence photons are redirected via an optical circulator to a SNSPD in another cryostat with T = 2.7 K for detection. A small portion of the signal enters a photodiode (PD) for monitoring cavity reflection. FPC: fiber polarization controller. b PLE pulse sequence. The SNSPD is gated to prevent detector latching due to the strong laser excitation pulses. c PLE spectrum for two different implanted SOI samples under similar excitation conditions when the cavity is far-detuned (Δ_ac > 200 GHz). The vertical axis indicates the average number of photons detected in an 5.55 μs integration window after each excitation pulse. Both samples are implanted with 1:1 ratio of ¹²C and ¹H, and the implantation fluences are labeled in the legend. All the frequencies in this paper, if not specified, are offset from a reference f₀ = 226130.674 GHz (1325.749 nm or 935.201 meV). d PLE spectrum for sample B at different excitation powers when the cavity is tuned within the scanning range. Each tuned cavity position is indicated by a green arrow, with the corresponding laser scanning range shaded on the x-axis under the arrow. The spectrum shows a dominant peak, which we interpret as a single T center coupled to the cavity.

T centers are generated in the middle of the device layer (220 nm in thickness) of the SOI samples using the ion implantation method³⁵. Each SOI sample is implanted sequentially with 1:1 ratio of 35 keV ¹²C and 8 keV ¹H ions, with rapid thermal annealing performed in between and after the implantation steps (Supplementary Section 3.1). The two samples shown in this work have an implantation fluence of 5 × 10¹³ cm⁻² (sample A) and 7 × 10¹² cm⁻² (sample B), respectively, which result in different T center densities after the generation process. To search for T centers, we perform time-resolved PLE spectroscopy by scanning the wavemeter-stabilized laser around the reported inhomogeneous center of T centers in silicon^23,24,35, with the pulse sequence shown in Fig. 2b.

First, we measure the spectrum with the cavity far-detuned from the scan range (Fig. 2c). The inhomogeneous distribution linewidth is about Γ_inh ≈ 29 GHz. Isolated peaks can be observed away from the inhomogeneous center, which we interpret as the optical transitions of T centers that are likely located inside the taper waveguide. These peaks have an average full-width half maximum (FWHM) linewidth of 2.40 ± 0.86 GHz, and a fluorescence lifetime of 836.8 ± 57.3 ns (Supplementary Section 4), which is slightly shorter than the bulk T centers’ lifetime of 940 ns²³. The estimated T center densities are ~1 × 10¹² cm⁻³ and ~3 × 10¹¹ cm⁻³ for sample A and B, respectively (Supplementary Section 3.1). To gauge the probability of an excited T center emitting a photon into the waveguide mode, we analyze a typical waveguide-coupled T center (at 46 GHz in sample B); we use the bounded T center quantum efficiency (discussed below) to estimate its emission efficiency to the waveguide mode as 2.6% ≤ η_wg ≤ 10.9% (Supplementary Section 4).

Next, we scan the laser frequency with the cavity tuned in-range to obtain the cavity-coupled PLE spectrum (Fig. 2d). In sample B, a new T center peak at the inhomogeneous center emerges with its fluorescence significantly surpassing all other peaks. This cavity-coupled T center has a FWHM linewidth of Γ = 3.81 ± 0.07 GHz under a low excitation power (Fig. 3a). To verify the peak originates from a single T center, we measure the second-order autocorrelation function g⁽²⁾ using all the detected fluorescence photons after each excitation pulse (Fig. 3b). Photon antibunching is observed with the value g⁽²⁾(0) = 0.024 ± 0.018, which confirms the majority of the detected photons come from a single emitter. This is the lowest g⁽²⁾(0) value ever observed for single T centers, and is comparable or better than other defect-based telecom emitters in solids^{7–10,20,27,36}. Autocorrelation measurements for the single T center can show bunching (g⁽²⁾(n) > 1, when ∣n∣ ≥ 1) under certain excitation conditions, which we speculate to be caused by spectral diffusion (Supplementary Section 5.3).

Fig. 3. Cavity-coupled single T center characterizations.

a PLE spectrum of the cavity-coupled single T center under an excitation power P_in = 0.04 nW. The red line shows the Gaussian fitting. b Second-order autocorrelation measurement for the same T center (P_in = 2.47 nW) shows a strong antibunching. All the photons detected after each excitation pulse are binned into a single-time bin. The horizontal axis shows the autocorrelation offset in units of the pulse repetition period (8 μs). c Gaussian-fitted amplitude (Amp.) and background (Bkgd.) of single T-center PLE spectrum at different P_in. The background has the main contribution from other weakly-coupled T centers beyond the SNSPD dark counts (3 Hz, black dashed line). The saturation behavior is well described by the numerical model (red line). d Spectrum linewidth of the single T center and the g²(0) at different P_in. The blue line shows the numerical calculation results. For results shown in panel (a−d), the cavity is tuned into resonance with the T center transition (Δ_ac = 0). e Spectral diffusion of the single T center (P_in = 8.31 nW). White line shows the center of the spectrum at each iteration (with a duration of 42 seconds) of the experiment. In all plots, error bars denote ± 1σ statistical uncertainty.

The emission amplitude of the cavity-coupled single T center saturates at 0.01 photons per excitation pulse (Fig. 3c). Both the saturation and power-dependent linewidth (Fig. 3d) are well described by the numerical modeling (discussed below). The measured g⁽²⁾(0) at higher powers (Fig. 3d) is limited by the accidental coincidences from background T centers’ emission (Supplementary Section 5.2). To characterize the spectral diffusion, we monitor the spectrum of the cavity-coupled single T center over a few hours time span by taking repetitive PLE scans (Fig. 3e), which reveals a spectrum-center distribution of 11.30 ± 0.13 GHz. A similar level of spectral diffusion is observed for waveguide-coupled T centers (Supplementary Section 4). We note that this method only provides a lower bound of the Γ_sd due to the limited experiment repetition rate. We later turn to the numerical modeling to extract Γ_sd.

We apply a magnetic field (B) up to 300 mT along silicon [100] direction aiming to split the single T center line. We note that we have not been able to observe unambiguous Zeeman splitting using simultaneous two-tone laser sideband excitation, which is likely due to the limited splitting compared with the broad single T center linewidth. When using the single-tone laser excitation, the PLE amplitude decreases at increasing B field due to spin polarization³⁵. We model this behavior (Supplementary Section 5.4) to extract the difference of the excited- and ground-state g-factors ∣Δ_g∣ = 0.55 ± 0.04, which matches with one of the two predicted ∣Δ_g∣ values for T centers under a B field along the silicon [100] direction³⁵.

Purcell enhancement and numerical modeling

Lastly, we study the cavity-QED of the coupled system. When the cavity is tuned into resonance, the single T center’s fluorescence lifetime is shortened to 136.4 ± 0.6 ns (Fig. 4a), which is 6.89 ± 0.03 times faster than the bulk lifetime of 1/Γ₀ = 940 ns²³. Leveraging this enhanced decay, we extract an average ZPL photon outcoupling rate of 73.3 kHz at saturation for the cavity-coupled single T center. To confirm the enhancement originates from the cavity coupling, we measure the fluorescence decay rate Γ_cav at different cavity detunings (Δ_ac) (Fig. 4b), which can be described as ${\mathrm{\Gamma }}_{\mathrm{cav}}/{\mathrm{\Gamma }}_0=P_t/\left[1+{\left(2{\mathrm{\Delta }}_{ac}/\tilde{\kappa }\right)}^2\right]+{\mathrm{\Gamma }}_{\infty }/{\mathrm{\Gamma }}_0$, where P_t = 5.88 ± 0.04 is the Purcell factor describing the fluorescence decay enhancement due to the cavity, Γ_∞ = (1.03 ± 0.02)Γ₀ ≈ Γ₀ is the asymptotic decay rate at large detunings, and $\tilde{\kappa }/2\pi =7.11\pm 0.09$ GHz is the characteristic linewidth. To explain the deviation of $\tilde{\kappa }$ from the cavity linewidth κ/2π = 5.22 GHz, we turn to numerical calculations by solving the Lindblad master equation. Beyond the cavity and atomic loss channels, we also incorporate the pure dephasing and spectral diffusion processes (Supplementary Section 6.1). The dynamics of the coupled system can be described by the Jaynes-Cummings Hamiltonian of the form,

$$H/\hslash ={\mathrm{\Delta }}_a{\sigma }_{+}{\sigma }_{-}+{\mathrm{\Delta }}_c{a}^{†}a+g\left({\sigma }_{+}a+{\sigma }_{-}{a}^{†}\right)+\frac{\mathrm{\Omega }}{2}\left({\sigma }_{+}+{\sigma }_{-}\right),$$ 1

which assumes rotating wave approximation in the rotating frame of the laser field (ω_L). Here Δ_a = ω_a − ω_L and Δ_c = ω_c − ω_L are, respectively, the detunings of the laser from the T center transition ω_a and the cavity resonance ω_c; g is the coupling rate between the single T center and the cavity mode, and Ω is the optical Rabi frequency. The global fitting of the experimental data based on the numerical calculations given the known κ and Γ₀ (Supplementary Section 6.1), reveals the full cavity-QED parameter set (g, κ, Γ₀) = 2π × (42.4 MHz, 5.22 GHz, 169.3 kHz), an excited-state dephasing rate 2Γ_d = 2π × 1.29 GHz, and a spectral diffusion Γ_sd = 2π × 1.69 GHz. The characteristic linewidth $\tilde{\kappa }$ has contributions from the cavity linewidth κ as well as Γ_d and Γ_sd. The model can simultaneously capture the saturation (Fig. 3c), power-dependent linewidth (Fig. 3d), and detuning-dependent fluorescence decay (Fig. 4b) results. Beyond the dephasing and the spectral diffusion, the single T center linewidth also has a minor contribution from the thermal broadening, which we estimate as Γ_th ~ 0.1 GHz from the temperature-dependent linewidth measurements (Supplementary Section 5.5).

Fig. 4. Cavity-enhanced fluorescence emission of the single T center.

a Time-resolved fluorescence for the cavity-coupled single T center under saturation (P_in = 17.01 nW) with different cavity detunings. The exponential fitting (blue and orange lines) reveals decay lifetimes of 136.4 ± 0.6 ns and 835.2 ± 3.1 ns for Δ_ac = 0 GHz and Δ_ac = 24.7 GHz, respectively. b Decay rate enhancement at different cavity detunings with the laser fixed at the T center transition under an excitation power P_in = 1.21 nW. To gain better tuning accuracy, the cavity resonance is first red-tuned to Δ_ac = −20.8 GHz, and subsequently blue-tuned. The blue line shows the numerical calculation results based on solving the Lindblad master equation.

To find out the Purcell enhancement of the single T center ZPL (P_ZPL) and its quantum efficiency (η_QE), we express the total emission rate of a single T center in absence of a cavity as the summation of the emission rates into the ZPL and the phonon sideband (PSB), as well as nonradiative relaxation³⁷, Γ₀ = γ_ZPL + γ_PSB + γ_nr. The Debye-Waller (DW) factor and the quantum efficiency can then be defined as DW = γ_ZPL/(γ_ZPL + γ_PSB) and η_QE = (γ_ZPL + γ_PSB)/Γ₀, respectively. When the cavity is tuned into resonance with the T center ZPL, the cavity-enhanced decay rate is Γ_cav = (P_ZPL + 1)γ_ZPL + γ_PSB + γ_nr, where P_ZPL = P_t/(DWη_QE) is the Purcell factor describing the enhancement of the ZPL. We can thus put a lower bound on the P_ZPL ≥ P_t/DW = 25.6, using the reported DW of 23%²³. For simplicity, we neglect the potential suppression of the γ_PSB due to the cavity³⁷. The ratio of the single T center ZPL emission coupled to the resonant cavity mode can be estimated as $\beta =P_{\mathrm{ZPL}}{\gamma }_{\mathrm{ZPL}}/\left[\left(P_{\mathrm{ZPL}}+1\right){\gamma }_{\mathrm{ZPL}}+{\gamma }_{\mathrm{PSB}}+{\gamma }_{\mathrm{nr}}\right]=P_t/\left(P_t+1\right)=85.5$%. Due to sub-optimal positioning of the single T center inside the cavity and imperfect dipole alignment with the local cavity electrical field polarization, the P_ZPL extracted from measurements should be smaller than the simulated Purcell ($P_{\mathrm{ZPL}}\le P_{\mathrm{ZPL}}^{\mathrm{sim}}$). This enables us to put a lower bound on the quantum efficiency η_QE ≥ 23.4% for the single T center (Supplementary Section 2.1).

Discussion

We now discuss pathways to improve the performance of the cavity-coupled single T center system. We note that the linewidth of the observed single T center is significantly larger than the Purcell enhanced lifetime-limited linewidth (2π × 1.2 MHz). One culprit is the fast dephasing process, which necessitates further investigation to reveal its origin. Significant reduction of Γ_inh down to 33 MHz has been demonstrated for ensemble T centers in enriched ²⁸Si²³. In future work, SOI samples with an enriched silicon device layer can be prepared via molecular beam epitaxy³⁸ to minimize the dephasing. Furthermore, local electrodes can be fabricated on the SOI device layer for implementing electrical field control to minimize the spectral diffusion via in situ tuning³⁹ or depletion of the charge noises⁴⁰. Lastly, focused-ion-beam-based⁴¹ and masked⁴² ion implantation can be leveraged to increase the yield of T center generation at the cavity center.

In summary, we have demonstrated enhanced light-matter interaction for a single T center by integrating it with a silicon nanophotonic cavity. This work opens the door to utilize single T centers in silicon for quantum information processing and networking applications. With realistic improvements in the quality factor of the optical cavity (Q = 5 × 10⁵) and narrower linewidth in an enriched sample (Γ ~ 10 MHz), a large atom-cavity cooperativity C ≥ 29 can be expected, which can lead to applications for high-fidelity dispersive spin readout⁴³ and cavity-mediated spin-spin interactions⁴⁴. Moreover, the current approach can enable parallel control and readout of multiple T centers in the cavity via the frequency domain addressing technique⁴⁵. Finally, leveraging the mature silicon photonics technology, small-footprint and scalable T-center-spin-based silicon quantum photonic chips¹³ may be envisioned.

Note: While finalizing this manuscript, we became aware of a related publication on the detection of a single T center coupled to a cavity using above-band excitation⁴⁶.

Methods

Device nanofabrication

All of the nanophotonic devices are fabricated on SOI samples (WaferPro). The SOI has a 220 ± 10 nm float zone grown P-type device layer with resistivity ≥1000 Ω ⋅ cm. The buried oxide has a customized thickness of 2.3 μm for maximizing the GC coupling efficiency, and the handling layer has a thickness of 725 μm. We spin coat 400 nm electron beam (ebeam) resist ZEP520A (Zeon Specialty Materials Inc.) onto 9 × 9 mm² SOI chips and bake at 170 °C for 5 mins. The sample is exposed using an Elionix ELS-G100 ebeam writer with a dosage of 225 μC/cm², and subsequently developed in o-xylene at room temperature for 90 seconds and rinsed in isopropanol for 20 seconds. The pattern is then defined on the resist layer, which acts as the etching mask. The sample etching is performed using an inductively coupled plasma (ICP) reactive ion etcher (Oxford Plasmalab System 100/ICP 180) with SF₆/C₄F₈ gases. The sample is kept at 0 °C during the etching process. After etching, the sample goes through a series of processes including oxygen plasma descum, dicing (into 4.5 × 4.5 mm²), resist stripping, and piranha cleaning before being transferred into the cryostat for measurements.

T center generation via ion implantation

T centers shown in this work are generated via a uniform ion implantation method following a published procedure³⁵. We use an equal fluence for ¹²C and ¹H during the ion implantation processes (II–VI Coherent Corp). We perform ¹²C ion implantation at 7° direction, 35 keV energy, followed by rapid thermal annealing (RTA) at 1000 °C for 20 s under an Ar background to repair lattice damage and substitute the implanted carbon²⁴. Next, a second round implantation of ¹H at 7° direction, 8 keV energy is performed. After the two implantation steps, we boil the sample for 1 h in DI water, followed by a second RTA process at 420 °C for 3 min with a N₂ background.

Author contributions

A.J., U.F., Y.W. and S.C. contributed to the design and execution of the experiment. Y.W. and S.C. performed numerical modeling of the cavity-QED. A.J., U.F., Y.W. and S.C. analyzed the data and wrote the manuscript. S.C. supervised the whole project.

Peer review

Peer review information

Nature Communications thanks Weibo Gao, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that support the findings of this study are openly available on the Harvard Dataverse at 10.7910/DVN/XCS15A.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-46643-8.