Purcell Enhancement of Erbium Ions in TiO2 on Silicon Nanocavities.

Isolated solid-state atomic defects with telecom optical transitions are ideal quantum photon emitters and spin qubits for applications in long-distance quantum communication networks. Prototypical telecom defects, such as erbium, suffer from poor photon emission rates, requiring photonic enhancement using resonant optical cavities. Moreover, many of the traditional hosts for erbium ions are not amenable to direct incorporation with existing integrated photonics platforms, limiting scalable fabrication of qubit-based devices. Here, we present a scalable approach toward CMOS-compatible telecom qubits by using erbium-doped titanium dioxide thin films grown atop silicon-on-insulator substrates. From this heterostructure, we have fabricated one-dimensional photonic crystal cavities demonstrating quality factors in excess of 5 × 104 and corresponding Purcell-enhanced optical emission rates of the erbium ensembles in excess of 200. This easily fabricated materials platform represents an important step toward realizing telecom quantum memories in a scalable qubit architecture compatible with mature silicon technologies.

Rare earth ion defects in solid-state hosts are key candidate qubits for applications in quantum computing and communication owing to their inherent spin–photon interface and long coherence times. These properties have enabled critical demonstrations of optical quantum memory protocols[1] based on light-matter entanglement[2] and entanglement distribution.[3] Quantum technologies geared toward distribution of quantum information over long distances require qubits that interface with telecom photons to avoid huge propagation losses over optical fiber networks. Because the trivalent ion of erbium (Er3+) has a 4I15/2 → 4I13/2 transition in the telecom C-band, there has been interest in using erbium ions as optically addressable quantum memories using persistent spectral hole burning techniques[4−6] and spin-based[7] quantum memories in quantum communication, including at the level of single ions.[8−10] However, significant engineering steps are needed to enhance the low photon emission rates from individual rare earth ions, which tend to have long radiative lifetimes.

One direct way to reduce the radiative lifetime is to use an optical cavity to enhance the emission through the Purcell effect.[11] The majority of Purcell enhancement studies on rare earth ions have involved devices derived from rare earth-doped bulk crystals, such as heterogeneous integration with deposited amorphous Si resonators[5] or bonded Si photonics,[8,12] focused ion beam milling of bulk crystals,[6,13−15] or incorporating relatively small erbium-doped samples into tunable distributed Bragg reflector-based fiber cavities.[16,17] These approaches are all appealing because they leverage the generally good performance of well-studied host materials for Er3+ (Y2SiO5,[5,6,8,14] YVO4,[18] CaWO4[19,20]). Furthermore, these prior approaches have led to important cutting-edge demonstrations toward single rare-earth ion quantum memories, including single-shot spin state readout.[10,15,21] However, such approaches may not allow for the on-chip scalability needed for wide deployment of quantum memories in large-scale quantum networks. For instance, estimates for fault-tolerant quantum repeater protocols show that hundreds or thousands of communication qubits are necessary to perform the requisite (operational and loss) error correction for quantum communication over long distances (≥1000 km).[22] In addition, the implementation of a fully CMOS-compatible process flow can enable easy integration with filters, phase shifters, and beamsplitters for on-chip photon routing.[23] In the vein of technological scalability with Si, there has also been considerable interest in low concentration implantation of erbium ions into Si nanostructures.[24] While this approach might have the greatest technological upside for directly unifying Si photonics with erbium-based quantum memories, early work has shown that the size mismatch between Er3+ and the crystalline lattice leads to myriad substitutional and interstitial sites with closely spaced spectral emission,[25,26] and further experiments are needed to resolve the best defects for various applications.

In addition to ease of Si photonic integration—assessed by the ability to grow on Si and perform straightforward fabrication—there are a variety of additional considerations for a candidate material to serve as a high-quality host for Er3+. These include a minimal or controlled level of background nuclear spins, a wide bandgap, the number of substitutional sites available, and site symmetries.[27−29] To that end, previous measurements have suggested that rutile TiO2 would be a good host for erbium because of narrow optical and spin line widths in implanted bulk crystals owing to the nonpolar symmetry of the substitutional erbium site and the low natural abundance of nuclear spins, respectively.[30] Furthermore, TiO2 thin films can be grown on Si using a variety of deposition techniques,[31,32] are CMOS-compatible, and are amenable to standard fluorine- and chlorine-based dry etch chemistries for top-down device fabrication.[33] Recent work has shown Er-doped TiO2 thin films grown on Si substrates via molecular beam deposition.[32] Some salient findings from that recent work are that the TiO2 thin films were polycrystalline and the dominant TiO2 phase (rutile or anatase) could be tuned by varying the substrate temperature during growth. Furthermore, the inhomogeneous line widths for the best buffered devices were as low as 5 GHz, which was substantially narrower than some of the epitaxial thin film control samples grown on better lattice-matched substrates (SrTiO3 or sapphire). Molecular beam deposition is particularly appealing for these types of heterostructures because of the inherent control of the Er3+ doping profile and doping density, in order to spectrally resolve single ions. Moreover, unintentional Er3+ doping from the TiO2 itself is anticipated to be lower than for the more common yttrium-containing oxides because of the relatively high concentrations of trace lanthanides in yttrium precursors.

In this Letter, we show early progress on top-down nanofabrication of photonic crystal cavities comprising thin layers of Er-doped TiO2 grown directly atop Si films. The thin films explored are similar to those discussed previously,[32] but consist of an Er-doped TiO2 heterostructure grown on commercial silicon-on-insulator (SOI) substrates typically used by the Si photonics community: Si device layer thickness of 220 nm atop a 2 μm buried oxide (see Supporting Information (SI)). Within each TiO2 heterostructure, there are three TiO2 layers of equal thickness: an erbium-doped layer sandwiched between undoped top and bottom buffer layers, and each layer is ∼7.5 nm, giving a total film thickness of ∼22 nm (Figure a). The estimated Er3+ density within the doped layer is 35 ppm (see SI). The TiO2 layers for this sample are grown at a substrate temperature of 520 °C. As shown in Figure b, transmission electron microscopy (TEM) cross-sectional imaging reveals that the TiO2 layer is polycrystalline, and there is a thin oxide layer (∼2 nm) at the Si/TiO2 interface, as was seen previously for lower temperature growth. However, unlike the previous demonstration, the polycrystalline film has both large and small grains visible, and the grains nearest the Si interface are bigger (13(3) nm) than those near the top of the TiO2 layer (∼1 nm). The cause of this gradient in grain size and effect on eventual Er properties is currently still under investigation. The roughness of the top surface of the TiO2 is ∼1 nm according to the cross-sectional TEM.

Figure 1

Er-doped TiO2 on SOI device platform. (a) Illustration of the as-grown Er-doped TiO2 heterostructure. The Er3+ layer is sandwiched between nominally undoped layers. The thickness of the SOI layers is not drawn to scale. (b) Cross-sectional TEM image of polycrystalline TiO2 film atop the Si layer. A modest SiO layer of approximately 2 nm thickness develops at the interface during growth. (c) FDTD simulation showing the cross-section of the normalized field intensity within a one-dimensional photonic crystal cavity consisting of a holey waveguide (width, w = 671 nm) etched through the TiO2 and Si device layers in panel a. This intensity cross-section is in the plane of the Er-doped TiO2 film, located 10 nm above the surface of the Si. At the simulated resonance (λ = 1536.4 nm), there is strong confinement in the photonic crystal 14-hole cavity defect (C) that is generated by a parabolic taper of the lattice constant between elliptically shaped holes. There are two mirror holes (M) on each side of the cavity region, and extra mirror holes (XM) are included on the left-hand side of the device because all measurements are performed in a one-sided reflection configuration. (d) Top: SEM image of an entire fabricated device showing the tapered waveguide extending from the cleaved edge of the SOI chip. Bottom: An expanded view of the parabolic taper in the lattice constant to generate the cavity defect. (e) Optical image showing an extended view of nearly identical devices, including those in panel d.

Using 3D finite-difference time-domain (FDTD) simulations, we have designed one-dimensional photonic crystal cavities for our Si/TiO2 heterostructure. The photonic crystal devices consist of a waveguide with identical, elliptically shaped holes and a parabolic reduction of the lattice constant to generate a defect in the photonic bandgap[8] (see SI). Figure c shows the computed fundamental (dielectric) mode with a predominant TE-like polarization in the plane of the TiO2 film. Our strategy relies on the evanescent field in the Si waveguide coupling to ions in the doped layer of the nearby TiO2 film. The electric field intensity for a simulated electric dipole oriented normal to the waveguide, parallel to the plane of the TiO2, and 10 nm above the Si/TiO2 interface is approximately 37% of the maximum intensity in the center of the Si waveguide (see SI). The photonic crystal cavities (Figure d, bottom) are patterned via conventional electron-beam lithography and dry etching through both the TiO2 and Si device layers (see SI). After etching and hardmask removal, the waveguide is cleaved along alignment marks under a microscope, beyond the inverse-taper (Figure d, top). We employ an end-fire measurement configuration, whereby a lensed optical fiber is used to couple light in/out of the device. As a demonstration of the inherent scalability of this scheme, we reliably fabricate hundreds of photonic crystal devices on each chip, a representative array of which is shown in Figure e (see SI).

A schematic of our experimental setup used to measure these devices is shown in Figure a. We perform our measurements in a closed-cycle cryostat with a base temperature of T = 3.1 K. The sample is fixed to the coldfinger and the lensed fiber is mounted on a 3-axis nanopositioner to enable addressing of different devices. Using a tunable telecom C-band laser, we primarily probe devices with pulse lengths ranging from 1 to 1000 μs and collection times after the pulse that are sufficient to enable decay of the emission (see SI). The pulses are routed to the sample via a fiber circulator and polarization controller to match the polarization of the cavity mode. We then measure the fluorescence from the sample, back through the lensed fiber and circulator, and directed to either a superconducting nanowire single photon detector (SNSPD), a spectrometer with InGaAs camera, or a photodiode. The one-way coupling efficiency (see SI) is fairly poor at approximately 15%, but it is sufficient to probe these particular devices because of the relatively large number of ions in each device. We also have a fiber wavelength division multiplexer (WDM) that can be added into the path of port 2 of the circulator for off-resonant photoluminescence (PL) measurements using a 1480 nm diode laser. Off-resonant PL measurements on a bare waveguide device (no cavity) reveal a variety of peaks from 1520 to 1560 nm, as shown in Figure b. The largest peak near 1520.5 nm is attributed to substitutional Er in the rutile phase of TiO2,[30] whereas the other dominant peak near 1533 nm is attributed to substitutional Er in anatase,[34] as confirmed previously with electron diffraction measurements.[32] This particular sample is polyphase, which has been seen previously for TiO2 thin films grown at intermediate temperatures.[32] The intensity of the substitutional rutile transition—relative to the substitutional anatase peak—is much stronger in this sample compared to previous thin film results when grown near 520 °C.[32] The origin of this TiO2 phase discrepancy is still under investigation. Similarly, the origin of the minor peaks could be due to a variety of factors, such as different localized phases within the TiO2, Er3+ residing in different substitutional/interstitial sites, or crystal field-split transitions, but additional control samples and experiments are needed.

Figure 2

Optical characterization of Er3+: TiO2 on Si waveguides. (a) Schematic of the experimental configuration. The Er3+: TiO2 waveguide device is situated in a cryostat (T = 3.1 K). A tunable laser in combination with three fiber-coupled acousto-optic modulators (AOMs) enable the production of short pulses of light that are directed to the sample through a lensed fiber (LF) mounted on a nanopositioner (NP). The return light can be routed to either a photodiode (PD), IR spectrometer (Spec), or superconducting nanowire single-photon detector (SNSPD). A fiber polarization controller (FPC) is used to rotate the polarization to match that of the cavity. We can insert optional components (dashed boxes), such as an electro-optic phase modulator (ϕEOM) to generate sidebands for transient spectral hole burning and a fiber wavelength division multiplexer (WDM) for off-resonant excitation. Additional details are given in the Supporting Information. (b) PL spectrum of a bare waveguide (no cavity) device pumped with 1480 nm laser light and detected via spectrometer. The tallest peak (highlighted in yellow) is centered at 1520.56 nm and originates from Er3+ in the rutile phase of polyphase TiO2. Inset: A resonant laser scan showing a similar inhomogeneous line width of 0.4 nm (52 GHz) for the rutile peak. (c) Measurement of the spectral diffusion line width for the rutile transition at 1520.56 nm. The inverted Lorentzian fit (dashed magenta line) yields a spectral diffusion line width of 267(17) MHz.

Resonant photoluminescence excitation (PLE) measurements on the bare waveguide device near 1520.56 nm are performed using a narrowband, tunable CW laser and modulated into pulses with emission from the Er3+ detected during a collection window following each pulse. The lifetime decay curve and associated total PLE intensity at that pump wavelength are integrated after numerous pulses (see SI). Resonant PLE extracts a line width of 0.4 nm (Figure b inset), which is similar to the result from off-resonant pumping. The inhomogeneous line width represents the distribution in Er3+ transition energies along the entire device that is over 40 μm long, and this inhomogeneous line width is similar to that measured in predominantly rutile thin film samples using a confocal microscope geometry with a spot size of approximately 1 μm2.[32] Given that the inhomogeneous line width of the Er3+ in rutile transition is relatively broad, it is important to investigate if the homogeneous line width of the emitters is sufficiently narrow to enable cavity-based lifetime enhancement (i.e., the “bad cavity” limit). To that end, we have performed transient spectral hole burning measurements on a bare waveguide device to find an upper bound on the homogeneous line width and spectral diffusion[24] for the rutile transition (Figure c). Using the pulsed resonant laser PLE scheme described above, we have employed an additional phase modulator (ϕEOM, Figure a) to generate two sidebands each with a frequency detuning, Δ, from the carrier frequency. We can then measure the relative PLE intensity change as Δ is swept but the laser carrier wavelength is maintained at the rutile transition, 1520.56 nm, and the total pump power is near saturation for the ensemble. If Δ is larger than the spectral diffusion line width of the erbium ions, the ions are no longer pumped to saturation and the total fluorescence increases. If we plot the normalized intensity as a function of laser sideband-carrier detuning (Figure c), we can fit a inverted Lorentzian line shape with a half-width half-maximum (HWHM) of 267(17) MHz, which sets the upper bound on the spectral diffusion-limited homogeneous line width.[35] While this homogeneous line width is substantially narrower than the inhomogeneous line width (Figure b), it is still quite large compared to the transform-limited line width of Er3+ in rutile TiO2 (sub kHz). It is possible that further optimization of the top capping layer in these devices can reduce the spectral diffusion of the Er emitters.[32]

We have the ability to tune the cavity resonance in situ using a combination of controlled gas adsorption and desorption techniques while near base temperature. We use N2 condensation via a gas nozzle directed at the sample to deposit a thin layer of ice on the cavity, which increases the refractive index of the mode, thereby resulting in a redshift of its resonance.[36] We can also deterministically desorb the ice through localized heating, whereby we use relatively strong CW laser excitation tuned directly to the cavity resonance to induce two-photon absorption and heating in the Si, but only at the cavity region, which leads to a blueshift of the cavity resonance (see SI). Furthermore, this heating is sufficiently localized that cavities in neighboring waveguides—separated by only 6 μm—can be tuned independently of one another, which can be useful for future two-cavity interference experiments. We can directly measure the spectral position and line width of the cavity resonance by detecting the wavelength-dependent reflection of the narrowband laser light using a photodiode. If we perform this measurement close to the rutile transition, we typically see cavity quality factors (Q) near 5 × 104. A prototypical cavity reflection scan at T = 3.1 K is shown in Figure a. Based on measurements of control devices with and without TiO2 films, the quality factors in general are currently limited by scattering due to the roughness of the top surface of the TiO2 rather than sidewall roughness of the waveguide or cavity holes from the dry etching.

Figure 3

Purcell enhancement of Er3+: TiO2 ensembles on Si photonic crystal cavities. (a) Resonant laser reflection spectrum of a photonic crystal cavity (T = 3.1 K) tuned near the rutile transition, showing a cavity Q near 53 000. The cavity has a corresponding line width (full-width half-maximum, FWHM) of 3.71(0.17) GHz (top axis). (b) Comparison of the ensemble lifetime of Er3+ ions coupled in a bare waveguide device (blue squares) versus the cavity-coupled device (red circles) shown in panel a. The corresponding fits give τ = 23(1) μs (black dashed line) and τ = 4660(20) μs (gray dashed-dot line), which is a 200-fold reduction in the decay time. (c) Plot of the increase in the ensemble decay rate as a function of the cavity-laser detuning (Δ) when the laser is fixed at 1520.56 nm. This is the same cavity as in panel a, which was measured at the start of the detuning experiment. The decay rate enhancement line shape is also fit to a Lorentzian with a FWHM line width of 5.06(0.17) GHz.

Our resonant pulsed laser measurements reveal the optical lifetime of all ions that couple to the device. This includes ions well-coupled to the cavity, ions poorly coupled to the cavity—whether because of position or polarization—and ions that couple only to the bare waveguide. Therefore, we use a stretched exponential function to capture the variety of decay times, where the time constant (τ) in the fit represents the fastest time decay within the ensemble.[37] Using this approach (see SI), the Er ions coupled to a bare waveguide device give a natural lifetime of τ = 4660(20) μs (Figure b), which is close to the time constant of 5.1 ms for Er implanted/annealed bulk TiO2 measured at low temperature.[30] In comparison, the ions which couple most strongly to the cavity—when it is tuned onto the rutile transition at 1520.56 nm—show a greatly decreased decay time of τ = 23(1) μs. This represents a 200-fold decay rate enhancement.

We next measure the emission rate enhancement as a function of the detuning between the cavity resonance and the Er3+ rutile transition. To do so, we perform a systematic redshift of the cavity resonance via gas condensation and measure the optical lifetime with the resonant laser fixed at the rutile transition. Figure c shows the increase in decay rate relative to the natural decay rate (Γ/Γ0) as the cavity resonance is tuned across the transition. The cavity-enhanced emission has a Lorentzian line width of 5.06(0.17) GHz, which is modestly broader than the cavity line width measured via reflection of 3.71(0.17) GHz. However, this can be explained by reduction in Q when the cavity is resonant with the Er3+ transition versus the reflection scan, which is measured at 90 pm (11.7 GHz) to the blue of the transition (see SI). The general agreement of the decay rate enhancement line shape with that of the cavity suggests that the radiative speedup is due to the cavity rather than nonradiative recombination induced by device fabrication. In addition, the lack of a plateau in Figure c confirms that the system is in the bad cavity limit, that is, Γh < κ, where Γh is the homogeneous line width of the emitters and κ is the cavity line width, in agreement with the transient spectral hole measurement in bare waveguide devices. On the basis of our simulated Purcell factor for the ideally placed TE-oriented electric dipole at the center of the cavity (see SI)—after adjusting for the experimental Q (40 000) of this device at T = 3.1 K at 1526.56 nm—we estimate that the maximum Purcell factor in the ensemble should be 326. The discrepancy between this estimate of the maximum Purcell factor and our experimentally determined value is likely due to a combination of the dipole orientations in the polyphase TiO2 film and the specific location of erbium ions in the rutile phase grains probed by this experiment.

In this Letter, we have shown optical addressing of Er3+ ions in rutile phase TiO2 grown on commercial SOI wafers. We have fabricated top-down 1D photonic crystal cavities from the Si/TiO2 heterostructure with Purcell enhancements up to 200. Systematic detuning of the cavity resonance from the Er3+ transition in rutile phase TiO2 reveals a good match of the Purcell enhancement to the Lorentzian cavity line shape, thereby indicating the erbium emission rates are limited by the cavity quality factor, not by the emitters’ homogeneous line widths. The next goal for this platform is to isolate and address individual Er ions as single spin quantum memories by cooling to lower temperatures and applying magnetic fields to address various spin levels. To that end, it is important to push the platform forward in three key areas.

First, it is necessary to reduce the homogeneous and inhomogeneous broadening in this system. The current upper bound of the homogeneous line width and spectral diffusion is estimated to be in the range of a few hundred MHz and could be attributed to a variety of factors, including trapped charges in the interfacial SiO, fabrication-induced damage, and the presence of mixed phases of TiO2. Further improvement of the thin film growth conditions to isolate a single TiO2 phase and to reduce the interfacial oxide, along with optimization of the buffer layer thicknesses could enable large reductions of the homogeneous and inhomogeneous line widths, as was seen already in predominantly anatase thin films.[32] Second, it is important to reduce the number of Er3+ coupled to the cavity to spectrally isolate and address single ions. By further reducing the metallic Er source flux and restricting doping to a single delta-doped TiO2 layer, intentional doping of these films to the single ion level is straightforward via molecular beam deposition. Additional improvements to the homogeneous line width may also be achieved naturally with the reduction in the Er-doping density[32] that would be needed to address single ions. Importantly, telecom quantum technologies based on this platform will be enabled by improving the photonic device performance. Most notably, the current fiber-waveguide coupling efficiency will need to be increased through improved mode-matching via cladding layers[38] or a full undercut of the Si inverse tapered waveguides.[39] Finally, a reduction in the TiO2 surface roughness during growth can lead to improvements in cavity Q for higher photon rates.

This demonstration represents an exciting first step toward a scalable on-chip quantum light source and memory device platform grown on an SOI wafer. This telecom-ready device architecture can be integrated with standard Si photonics and MEMS foundry process lines, enabling integration with other needed photonic elements such as on-chip filters, phase shifters, and beamsplitters. Furthermore, the Si platform is amenable to combination with other important cryogenic quantum technologies, such as on-chip SNSPDs, superconducting qubits, semiconductor quantum dot qubits, and microwave-to-optical transducers to enable powerful quantum computational and communication nodes. With further improvements to the materials and device fabrication, the scalable nature of this Er-doped TiO2-on-SOI platform can meet the future demands for large numbers of communication qubits and quantum light sources needed for fault-tolerant long-distance quantum networking.