Characterization of the Si:Se+ spin-photon interface

Silicon is the most developed electronic and photonic technological platform and hosts some of the highest-performance spin and photonic qubits developed to date. A hybrid quantum technology harnessing an efficient spin-photon interface in silicon would unlock considerable potential by enabling ultra-long-lived photonic memories, distributed quantum networks, microwave to optical photon converters, and spin-based quantum processors, all linked using integrated silicon photonics. However, the indirect bandgap of silicon makes identification of efficient spin-photon interfaces nontrivial. Here we build upon the recent identification of chalcogen donors as a promising spin-photon interface in silicon. We determined that the spin-dependent optical degree of freedom has a transition dipole moment stronger than previously thought (here 1.96(8) Debye), and the T1 spin lifetime in low magnetic fields is longer than previously thought (>4.6(1.5) hours). We furthermore determined the optical excited state lifetime (7.7(4) ns), and therefore the natural radiative efficiency (0.80(9) %), and by measuring the phonon sideband, determined the zero-phonon emission fraction (16(1) %). Taken together, these parameters indicate that an integrated quantum optoelectronic platform based upon chalcogen donor qubits in silicon is well within reach of current capabilities.

Silicon is the most developed electronic and photonic technological platform and hosts some of the highest-performance spin and photonic qubits developed to date. A hybrid quantum technology harnessing an efficient spin-photon interface in silicon would unlock considerable potential by enabling ultra-long-lived photonic memories, distributed quantum networks, microwave to optical photon converters, and spin-based quantum processors, all linked using integrated silicon photonics. However, the indirect bandgap of silicon makes identification of efficient spin-photon interfaces nontrivial. Here we build upon the recent identification of chalcogen donors as a promising spin-photon interface in silicon. We determined that the spin-dependent optical degree of freedom has a transition dipole moment stronger than previously thought (here 1.96(8) Debye), and the T1 spin lifetime in low magnetic fields is longer than previously thought (> 4.6(1.5) hours). We furthermore determined the optical excited state lifetime (7.7(4) ns), and therefore the natural radiative efficiency (0.80(9) %), and by measuring the phonon sideband, determined the zero-phonon emission fraction (16(1) %). Taken together, these parameters indicate that an integrated quantum optoelectronic platform based upon chalcogen donor qubits in silicon is well within reach of current capabilities.

I. INTRODUCTION
A future quantum technology, wherein stored quantum information is communicated over a quantum network, will necessarily involve both matter-based qubits and optical photons. In pursuit of this aim, many potential spin-photon interfaces are being actively developed [1][2][3]. A wide array of defects in semiconductors and insulators have attracted attention because of their favourable optical and spin characteristics. These include quantum dots in III-V heterostructures [4], nitrogen-vacancy [5] and silicon-vacancy [6] centers in diamond, rare-earth ions in insulators such as Nd:YSO [7] and Er:YSO [8], defects in SiC [9,10], and even recent work on donors in ZnO [11]. Notable in its absence from this list is silicon, which, when isotopically purified to 28 Si, is host to some of the longest-lived and highest-fidelity spin qubits studied to date [12][13][14][15]. Silicon offers high performance integrated single photon detectors [16] in addition to an expansive selection of high quality photonic components [17,18] due to decades of fabrication process development. Furthermore, silicon has a strong χ (3) nonlinearity and large refractive index that enables dense packing of photonic circuitry. Despite the considerable advantages of these two quantum silicon platforms, unifying these technologies through an efficient spin-photon interface has proven elusive.
A few paramagnetic centres in silicon possess spindependent optical transitions, including shallow donorbound excitons [19] and orbital transitions in rare earth ions, such as erbium [20]. However, in the aforementioned * Corresponding author: s.simmons@sfu.ca cases, the defects only weakly couple to light as determined by their small optical transition dipole moments. Although recent work has demonstrated evanescent coupling of defects with strong transition dipole moments in materials placed adjacent to silicon photonic structures [21], the coupling strengths and photon collection efficiencies are inherently limited in such designs.
The ideal silicon spin-photon interface would be a natively-integrated optical center which possess a longlived spin, a high transition dipole moment, and a high radiative efficiency. In this work we demonstrate that singly-ionized deep chalcogen donors in silicon possess a strong light-matter interaction, suitable for strong coupling to silicon photonic cavities at the single-spin level. This offers a clear path towards chalcogen-based integrated silicon quantum optoelectronics.
The optical characteristics of substitutional chalcogen donors (specifically sulfur, selenium, and tellurium) have been studied for decades [22][23][24][25][26]. It was identified that the natural distribution of silicon and chalcogen isotopes act as sources of static inhomogeneity in the bulk. Consequently, ultra-sharp optical linewidths, on the order of µeV can be achieved [26] by working with ensembles of individual chalcogen isotopes in isotopically purified 28 Si. This remarkable uniformity allowed for the hyperfine splitting and the electron spin g-value of the 1s:A ground state of singly-ionized 77 Se to be directly observed through optical excitation into the first excited state, 1s:T 2 :Γ 7 . Following this, initial electron spin characterization at X-band microwave frequencies on 77 Se + demonstrated promising electron spin qubit coherence and lifetime characteristics [27] similar to that of the shallow donors' ultra-long lived electron spins.
The identification of singly-ionized chalcogen donors as a promising spin-photon interface in silicon was only made relatively recently [28], and bounds on some key spin and optical parameters of 77 Se + were determined to support this proposal. Key parameters in Ref. [28] included a lower bound on the spin T 1 lifetime (> 6.2(4) minutes) as well as lower bounds on the optical transition dipole moment (> 0.77 Debye), optical excited state lifetime (> 5.5 ns), as well as an upper bound on the calculated radiative lifetime (< 39 µs). In this work we improve upon the bounds on all of these key parameters, including the spin T 1 time (> 4.6(1.5) hours) and the transition dipole moment (1.96(8) Debye). Furthermore, we offer new insights into the optical transition of interest by reporting the phonon sideband profile and zero phonon line (ZPL) fraction (16(1) %) and a direct measurement of the excited state lifetime (7.7(4) ns), and hence the total radiative efficiency (0.80(9) %). Lastly, we precisely determine the location of the second excited state in the neutral charge state of Se by performing Raman spectroscopy. The experimental results presented in Section II are structured in that order.
A. The 28 Si: 77 Se + spin-photon system Substitutional selenium atoms in silicon are deep double donors. When singly ionized, the unpaired spin-1 2 electron possesses a hydrogenic orbital structure with a 1s ground state. The sixfold degeneracy of the conduction band and the two electron spin states give rise to twelve 1s levels which are split by a combination of central cell, valley-orbit, and spin-orbit effects. The spin and photon degrees of freedom relevant to this work are all contained within these twelve electronic 1s levels.
The ground state, 1s:A, possesses two degenerate electron spin levels and has a binding energy of ∼593 meV [24]. The first orbital excited states, labeled 1s:T 2 , are split into components labeled 1s:T 2 :Γ 7 and 1s:T 2 :Γ 8 , the lower of which, 1s:T 2 :Γ 7 , possesses two spin-orbit levels and has a binding energy of ∼166 meV [24]. The remaining 1s levels, labeled 1s:E, are thought to lie above 1s:T 2 :Γ 8 , as is the case for the neutral charge state Se 0 and the group V shallow donors, but have not been observed in Se + . The optical transitions between 1s:A and 1s:T 2 :Γ 7 are forbidden according to effective mass theory (EMT) but are symmetry-allowed, and approximately 427 meV, or 2.9 µm, [24] which is in the mid-infrared optical band. Further details on the orbital structure of this system are given in Ref. [28] and references therein.
Additionally, the 77 Se + isotope possesses a spin-1 2 nuclear spin and a corresponding A ≈ 1.66 GHz hyperfine [26,28] interaction within the 1s:A electronic manifold. This gives rise to a ground state spin Hamiltonian shared by that of the neutral shallow donor 31 P and given by where A, the hyperfine constant, and g e (2.0057) and g n (1.07), the electron and nuclear g-factors respectively, are specific to 77 Se + . Here µ B and µ N are the Bohr and nuclear magnetons, h is the Planck constant, and S and I are the spin operators of the electron and nucleus. At zero magnetic field, this spin Hamiltonian results in split 1s:A energy levels defined by electron-nuclear spin singlet and triplet states. The 1s:T 2 :Γ 7 state possesses no such splitting and therefore these levels form a lambda transition [24] which can be spectrally resolved in the bulk [26,28]. The allowed magnetic resonance transitions from the singlet state S 0 to the triplet states T − , T 0 , T + support long lived qubits [28], particularly across the S 0 ⇔ T 0 transition which is a 'clock transition' [29] at zero field.

II. EXPERIMENTAL RESULTS
A. Singlet-triplet T1 temperature dependence The spin equilibration time constant, T 1 , of the 77 Se + singlet/triplet qubit in Earth's magnetic field and at low temperatures (1.6 K) was previously found to be approximately 6 minutes [28]. Although already quite long, this T 1 time is shorter than the ∼30 minute electron T 1 of 31 P measured at 1.6 K and 0.35 T, as well as significantly shorter than the projected electron T 1 times available to 31 P at 1.6 K in Earth's magnetic field [30]. Six minutes is substantially longer than previously measured 77 Se + electron T 1 times collected at higher temperatures [27], but shorter than the ∼337 hour projected T 1 time following a T 9 dependence fitted from this higher-temperature data and extrapolated to 1.6 K (See Fig 1). Here we elucidate the decay mechanisms affecting the 77 Se + singlet/triplet qubit and determine an experimental regime which gives rise to a 276(90) minute (4.6(1.5) hour) T 1 time.
The similarities between the 31 P and 77 Se + systems imply that a number of known 31 P electron T 1 decay mechanisms, such as the direct [30], Raman [31], and concentration-dependent decay mechanisms with concentrations above 10 16 cm −3 [30], can apply to 77 Se + . The significantly larger valley-orbit splitting between the ground 1s:A and first excited states 1s:T 2 :Γ 7 of 77 Se +at least seven times greater than the maximum phonon energy -implies that the Orbach [32] decay mechanism known to apply to 31 P is irrelevant to 77 Se + .
An additional decay mechanism is known [28] to contribute to the T 1 decay of 77 Se + : incident roomtemperature blackbody radiation possesses sufficient energy to ionize both neutral and singly-ionized 77 Se, directly effecting T 1 via time-varying local charge configurations. Under our experimental conditions, blackbody radiation generated within the cryogenic apparatus is negligible compared to the room temperature incident blackbody radiation optically coupled to the sample. Correspondingly, this blackbody T 1 decay mechanism is largely independent of the sample temperature. In contrast, the direct and Raman decay mechanisms display a 1/T and 1/T 9 temperature dependence, respec- Temperature dependence of 77 Se + electronnuclear spin singlet/triplet T1 taken near Earth's magnetic field (blue), revealing a low temperature limit of T1 = 4.6(1.5) hours, and comparison with published data, collected with less blackbody shielding (green) reprinted from Ref. [28] with permission, as well as electron spin T1 data taken at 0.35 T (orange) reprinted from Ref. [27] with permission. (Inset) Schematic diagram of optical pumping and readout sequence to measure singlet/triplet T1. For a given wait time, τ , the total remaining polarization signal is measured as the difference between two integrated absorption transient areas, both measuring the population of the triplet state (solid), after two different initialization pulses (dashed). First (A) after initializing into the singlet by pumping on the 1s:A:T ⇔ 1s:T2:Γ7 transition, here labeled T , and secondly (B) after initializing into the triplet by pumping on the 1s:A:S0 ⇔ 1s:T2:Γ7 transition, here labelled S0.
tively [30,31]. Measurements of the electron T 1 in a low-concentration (∼2 × 10 13 cm −3 ) 77 Se + bulk sample (sample 28 Si: 77 Se:LB, see Supplementary Materials [33]) as a function of temperature were used to determine the prevalence of these possible mechanisms.
In order to minimize room temperature blackbody effects, optical bandpass filters centered at 2.9 µm as well as neutral density filters were mounted within the cryogenic assembly in the optical beam path, and the sample was shielded from room temperature blackbody radiation from all other directions.
The singlet/triplet qubit was initialized by resonantly pumping one arm of the lambda transition, for example initializing into the singlet state by selectively pumping 1s:A:T ⇔ 1s:T 2 :Γ 7 , as described in Ref. [28]. Following this, a mechanical shutter blocked the resonant light. After a chosen delay, the remaining spin hyperpolarisation was measured by recording the absorption transient of unblocked resonant light (see Fig. 1 inset). For a given delay time, two different measurements were taken and the difference between their absorption transients constituted the measured signal. The first of these measurements hyperpolarised into the singlet state and the second into the triplet state. Both measurements' absorp-tion transients consistently probed the final triplet population. This subtraction method ensured that the signal would necessarily decay to zero in the long delay limit where the spins reached equilibrium. The singlet/triplet T 1 lifetime at a given temperature was determined by iterating this measurement with variable delay times.
The temperature dependence of T 1 over the range 2.1 to 6.4 K is shown in Fig. 1. The data is well fit by 1/T 1 = AT 9 + B, with A = 2.0(3) × 10 −9 s −1 K −9 and a temperature independent contribution with a low temperature limit of T 1 = 4.6(1.5) hours, representing a T 9 Raman process and most likely a residual blackbody-related decay process dominating below 2 K. This T 9 Raman process is in agreement with Ref. [27] taken at 0.35 T, which is fit well by 1/T 1 = CT 9 (C = 1.2 × 10 −8 s −1 K −9 ). The disagreement near 5 K may be due to temperature offsets between these two different experimental setups; alternatively, although the T 9 relaxation process is expected to be independent of magnetic field for electron spins [31], this may not apply when comparing between singlet/triplet spin qubits and nearly pure electron spin qubits. These trends indicate that a spin T 1 of 19 ± 3 minutes is available at the easily accessible temperature of 4.2 K.

B. Absorption
In this section we present measurements based on optical absorption spectra. We improve upon previous transition dipole moment estimates, and use this data to provide a concentration conversion factor.

Transition dipole moment
The optical interaction strength of a spin-photon interface is characterized by its transition dipole moment, µ. The dipole moment can be calculated from absorption spectra of a bulk sample, combined with an accurate defect concentration value, and a known optical path length [33]. Previous work [28] employed a bulk sample with non-uniform 77 Se + concentration and consequently only lower bounds on the transition dipole moment could be made.
Here we calculate the transition dipole moment using a selenium diffused, 28 Si: 77 Se, wafer sample (sample w 28 Si: 77 Se:IB, see Supplementary Materials [33]). An absorption spectrum was measured using a Bruker IFS 125HR Fourier transform infrared (FTIR) spectrometer with gold mirrors, a KBr beamsplitter, and a mercurycadmium-telluride (MCT) detector to obtain an absorption coefficient spectrum of the Se + 1s:A ⇒ 1s:T 2 :Γ 7 transition. Where the absorption coefficient spectrum is calculated according to: where I s and I 0 are FTIR spectra with and without the sample in the beam path, respectively, and L is the length of the sample. This sample was confirmed to have a near-uniform [Se + ] concentration by observing the complete compensation of all boron in the sample [33]. In this case one might expect [B] = [Se + ] throughout the sample, however, the precise distribution of donors and acceptors in the sample may modify this value. To measure [Se + ] precisely, we applied a tip-angle measurement [13], whose details have been described in Ref [28]. We measured [Se + ] = 5.2(4) × 10 14 cm −3 which is less than the measured [B] of 5.9(8) × 10 14 cm −3 , likely indicating the presence of doubly ionized selenium, Se 2+ , or ionized selenium pairs, Se Combining this with the absorption coefficient spectrum we calculate a transition dipole moment of µ = 1.96(8) Debye [33]. This value is more than a factor of 2 higher than the previously established lower bound.

Selenium conversion factor
From the tip-angle concentration and absorption coefficient spectrum we determined a conversion factor, for the 1s:A ⇒ 1s:T 2 :Γ 7 zero phonon spectral line, where α dν is the integrated absorption coefficient spectra of the zero phonon spectral line. Peak conversion factors, k Se+ = [Se + ]/α max , are tabulated in the Supplementary Materials [33].

C. Photoluminescence
The radiative properties -both the radiative efficiency and the zero phonon line fraction -of the Se + spinphoton interface have not been previously established. In this section we report the observation of the phononassisted luminescence sideband of the 1s:T 2 :Γ 7 ⇒ 1s:A optical transition, which reveals a zero phonon line fraction of 16(1) %. Subsequently we measured the excited state lifetime (7.7(4) ns) and compared this with the calculated radiative lifetime to infer a radiative efficiency of 0.80(9) %.

Zero phonon line fraction
Photoluminescence spectra were obtained using a Bruker IFS 125HR FTIR spectrometer with gold mirrors, a CaF 2 beamsplitter, and a liquid nitrogen-cooled InSb detector with a 2440 nm long pass filter. A high [Se + ] sample (w nat Si: nat Se:HB, see Supplementary Materials [33]) was pumped with 1 W of laser light resonant with the Se + 1s:A ⇒ 2p ± transition (4578 cm −1 , or 2184 nm), which was generated using a Cr 2+ :ZnS/Se narrowband tunable laser pumped by an erbium fiber laser (IPG Photonics) operating at 1567 nm. From the excited state 2p ± , the electron can decay via phonon cascade to 1s:T 2 :Γ 7 followed by photon emission to 1s:A. The resulting photoluminescence spectrum, including the phonon-assisted sideband, is seen in Fig. 2. The integrated phonon sideband is 5.6 times larger than the area of the zero phonon line, resulting in a ZPL fraction lower bound of 15 %. After correcting for re-absorption of light given the known ZPL transition dipole moment, which will disproportionately affect the integrated area of the ZPL, we obtain a ZPL fraction of 16(1) %.
The total radiative lifetime includes both the zerophonon and the phonon-assisted radiative pathways, resulting in a total calculated radiative lifetime of τ = 0.90(7) µs [33].

Excited state lifetime and radiative efficiency
The decay of the 1s:T 2 :Γ 7 valley state to the ground state 1s:A can occur through purely radiative, phononassisted radiative, and fully nonradiative pathways. The ratio of the measured 1s:T 2 :Γ 7 excited state lifetime to the calculated radiative lifetime reveals the technologically consequential radiative efficiency of this spinphoton interface.
Conventional methods of directly measuring a total luminescence lifetime employ optical pulses and timeresolved, high-sensitivity detectors which are at least comparable in speed with the transition lifetime of interest. Such sources and detectors are not yet routinely available in the 2.9 µm region. Hence, previous to this work, only lower bounds on the total lifetime of this centre were known. Hole-burning measurements, limited by FTIR spectrometer resolution, indicated [28] a total excited state lifetime longer than 5.5 ns corresponding to a homogeneous linewidth smaller than 0.001 cm −1 .  Fig. 3. Schematic of experimental set-up. A laser, tuned to the Se + 1s:A ⇒ 2p± transition (4578 cm −1 , or 2184 nm), whose wavelength was monitored using a pick-off beam routed into a wavemeter, was focused through a lens (L1) to minimize the beam waist within a 10 MHz bandwidth germanium acousto-optic modulator (AOM). The first diffracted (modulated) beam was recollimated (L2) and passed through a 1 mm aperture, to reject the main beam and higher order diffracted beams, and focused (L3) onto the w nat Si: nat Se:HB sample held in superfluid helium. A portion of the resulting 1s:T2:Γ7 ⇒ 1s:A luminescence signal was captured by an elliptical mirror and sent through 2440 nm and 2850 nm longpass filters, Filter 1 and Filter 2, to selectively pass 1s:T2:Γ7 ⇒ 1s:A light into an MCT detector. A lock-in measurement was applied to the detected signal using the AOM driving frequency as the reference.
To directly measure the excited state lifetime, we performed a modulated excitation experiment [34] using a continuous-wave, single-frequency laser modulated by an acousto-optic modulator (AOM). The measurement configuration is shown in Fig. 3. The laser was brought into resonance with the 1s:A ⇒ 2p ± transition (4578 cm −1 , or 2184 nm), as in Sec. II C 1, to efficiently pump to 1s:T 2 :Γ 7 via the 2p ± state. This pump laser was sinusoidally modulated with a germanium AOM (IntraAction AGM-802A9) with a nominal bandwidth of 10 MHz, which was increased to 20 MHz by reducing the laser spot size using a converging lens pair. Approximately 400 mW of laser light was incident on the sample. The resulting 1s:T 2 :Γ 7 ⇒ 1s:A luminescence from the sample w nat Si: nat Se:HB (see Supplementary Materials [33]) was spectrally filtered and detected using an MCT detector (VIGO Systems, PVI-4TE-1-0.5x0.5), and fed into a lock-in with the AOM modulation drive as its reference.
After correcting for the instrumental frequency re- sponse by measuring scattered pump laser light, the frequency dependence of the resulting signal revealed the excited state lifetime. At frequencies much lower than the inverse of the excited state lifetime the system has time to equilibrate and a high AC photoluminescence signal is detected, whereas at higher frequencies the AC signal amplitude will drop. Alternatively put, the system behaves as a low-pass filter with a characteristic amplitude (A) and phase (Θ) response, as a function of modulation frequency, f , given by [34]: where T 1 is the decay time of the optically excited state. The resulting data, corrected for the system response, are shown in Fig. 4. The characteristic amplitude and phase drop-off points, at 1/ √ 2 and 45 • , agree and reveal a T 1 time for the 1s:T 2 :Γ 7 excited state to be 7.7(4) ns.
This gives a radiative efficiency of 0.80(9)% when compared to the radiative lifetime of 0.90(7) µs, as well as a homogeneous linewidth of 0.00069(4) cm −1 . However, as thermally activated transitions to higher excited states are possible [28] this homogeneous linewidth is likely to be a lower bound. For the purposes of estimating cou-pling cooperativity [33] between the Se + 1s:A ⇔ 1s:T 2 :Γ 7 transition and a photonic cavity we use the upper bound determined by hole burning, 0.001 cm −1 . With a ZPL dipole moment of µ = 1.96(8) Debye, a Se + spin in the mode maximum of a cavity with an unloaded Q-factor of 1.5 × 10 4 and a modal volume, V = (λ/n) 3 , would display a cooperativity of C = 1.

D. Raman spectroscopy
The 1s:A ⇔ 1s:T 2 :Γ 7 transition amounts to at least a seven phonon transition, and yet results from Sec. II C 2 show that relaxation from 1s:T 2 :Γ 7 is predominantly nonradiative. Although Altarelli [35] predicted the Se + 1s:E state to lie above 1s:T 2 , the Se + 1s:E state has not yet been experimentally observed. It is conceivable, however highly unusual, that 1s:E lies below 1s:T 2 . If 1s:E were to lie below 1s:T 2 :Γ 7 it could provide a nonradiative decay pathway which could account for the low radiative efficiency of the 1s:T 2 :Γ 7 ⇔ 1s:A transition.
The 1s:A ⇔ 1s:E transition is both EMT and symmetry-forbidden, in contrast with 1s:A ⇔ 1s:T 2 :Γ 7 which is symmetry-allowed, and so indirect methods are needed to deduce the binding energy of the 1s:E state of both Se 0 and Se + . In the neutral charge state, Se 0 , the location of the 1s:E state has been shown to lie above 1s:T 2 , which for the neutral state Se 0 splits into levels 1s: 1 T 2 and 1s: 3 T 2 (see Ref. [36]). The position of 1s:E was extrapolated from strain-induced hybridization of the 1s:E and 1s: 1 T 2 levels [36], with a projected unstrained binding energy of 31.4 meV, corresponding to a 1s:A ⇔ 1s:E transition of 2220 cm −1 . Here we show the results of Raman spectroscopy in an effort to observe forbidden transitions in both Se + and Se 0 , specifically the 1s:A ⇔ 1s:E transition which has been observed for shallow donors [37].
Raman spectra of the 28 Si: 78 Se:IB sample [33] were measured using a Bruker IFS 125HR FTIR spectrometer using tunable narrowband 1080 nm (∼9260 cm −1 ) and 1064 nm (∼9400 cm −1 ) excitation sources, amplified using an IPG Photonics amplifier (YAR-10K-1064-LP-SF), a CaF 2 beam splitter, and detected using either a liquid nitrogen-cooled Ge diode detector (for Se 0 Raman experiments) or a liquid nitrogen-cooled InSb detector (for Se + Raman experiments) with a band-pass filter mounted in the InSb detector's cryogenic assembly to reduce incident room temperature blackbody radiation and increase sensitivity (although the cold-filtered InSb was still much less sensitive than the Ge diode detector). In the detection arm, 1150 and 1200 nm long pass filters were used for laser rejection, with an additional 1100 nm long pass filter used in the Se 0 Raman experiments.
In Fig. 5a we see the results of Raman spectroscopy centred near (9260 − 2220) cm −1 where we expect to observe Raman features corresponding to the 1s:A ⇔ 1s:E transition of Se 0 when driving with laser light near 1080 nm. We observe a feature which shifts linearly with laser frequency closely matching the projected value for  the 1s:A ⇔ 1s:E transition. Although unexpected from shallow donor Raman measurements, we also observe a Raman-active feature that matches the measured value of the 1s:A ⇔ 1s: 1 T 2 transition. We measure an average shift from the laser position of 2223.1(5) cm −1 corresponding to 1s:A ⇔ 1s:E which agrees with the projected strain-free transition frequency of 2220 cm −1 from Ref. [36]. We measure an average shift from the laser position of 2195.5(5) cm −1 which agrees with the 1s:A ⇔ 1s: 1 T 2 transition energy of 2195.4(5) cm −1 directly observed in absorption (See inset of Fig. 5a).
In Fig. 5b we show the spectral region where one would expect to observe Raman transitions associated with the 1s:A ⇔ 1s:E transitions of Se + . Energies labelled 1s:E, denoted by dashed vertical lines in Fig. 5b, are based on the calculations of Altarelli [35] who predicted the 1s:E level of Se + to have a binding energy of ∼130 meV, corresponding to a 1s:A ⇔ 1s:E transition near 3740 cm −1 . We note no observable feature shifts over the broad range we would expect to detect Raman Se + transitions. It is possible that 1s:E is simply very broad making it ex-tremely difficult to observe. The 1s:A ⇔ 1s:T 2 :Γ 7 transition was not observed, which agrees with similar shallow donor Raman experiments. The precise binding energy of 1s:E level of Se + remains the subject of future investigation.

III. CONCLUSION
We have demonstrated that a variety of performance metrics of the 77 Se + spin-photon interface, built upon its 1s:A ⇔ 1s:T 2 :Γ 7 transition, are more favourable than previously thought. A number of key properties of this interface were examined and shown to have encouraging features, including long spin T 1 lifetimes exceeding 4.6(1.5) hours at low temperatures and near Earth's magnetic field, a larger transition dipole moment of 1.96(8) Debye, a 1s:T 2 :Γ 7 excited state lifetime of 7.7(4) ns, a total radiative efficiency of 0.80(9) %, and a zero phonon line fraction of 16(1) %. These results imply that the spin-dependent cavity cooperativity threshold of 1 may be crossed with routinely achievable photonic cavities having mode volumes of ∼ (λ/n) 3 and Q-factors of 1.5 × 10 4 . A broad variety of silicon quantum technologies may be built based upon this key and highly sought-after spin-dependent nonlinearity.