# Erbium-Implanted Materials for Quantum Communication Applications

Paul Stevenson  Department of Physics, Northeastern University, Boston,
Massachusetts 02115, USA  Christopher M Phenicie  Department of Electrical
Engineering, Princeton University, Princeton, New Jersey 08544, USA  Isaiah
Gray  Department of Electrical Engineering, Princeton University, Princeton,
New Jersey 08544, USA  Sebastian P Horvath  Department of Electrical
Engineering, Princeton University, Princeton, New Jersey 08544, USA  Sacha
Welinski  Thales Research and Technology, 1 Avenue Augustin Fresnel, 91767
Palaiseau, France  Austin M Ferrenti  Department of Chemistry, Princeton
University, Princeton, New Jersey 08544, USA  Alban Ferrier  Chimie ParisTech,
PSL University, CNRS, Institut de Recherche de Chimie Paris, Paris, France,
75005  Faculté des Sciences et Ingénierie, Sorbonne Université, UFR 933, 75005
Paris, France  Philippe Goldner  Chimie ParisTech, PSL University, CNRS,
Institut de Recherche de Chimie Paris, Paris, France, 75005  Sujit Das
Department of Materials Science and Engineering, University of California,
Berkeley, Berkeley, 94720, California, USA  Department of Physics, University
of California, Berkeley, 94720, California, USA  Ramamoorthy Ramesh
Department of Materials Science and Engineering, University of California,
Berkeley, Berkeley, 94720, California, USA  Materials Sciences Division,
Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA
Department of Physics, University of California, Berkeley, 94720, California,
USA  Robert J Cava  Department of Chemistry, Princeton University, Princeton,
New Jersey 08544, USA  Nathalie P de Leon  Department of Electrical
Engineering, Princeton University, Princeton, New Jersey 08544, USA  Jeff D
Thompson<EMAIL_ADDRESS>Department of Electrical Engineering,
Princeton University, Princeton, New Jersey 08544, USA

###### Abstract

Erbium-doped materials can serve as spin-photon interfaces with optical
transitions in the telecom C-band, making them an exciting class of materials
for long-distance quantum communication. However, the spin and optical
coherence times of Er3+ ions are limited by currently available host
materials, motivating the development of new Er3+-containing materials. Here,
we demonstrate the use of ion implantation to efficiently screen prospective
host candidates, and show that disorder introduced by ion implantation can be
mitigated through post-implantation thermal processing to achieve
inhomogeneous linewidths comparable to bulk linewidths in as-grown samples. We
present optical spectroscopy data for each host material, which allows us to
determine the level structure of each site, allowing us to compare the
environments of Er3+ introduced via implantation and via doping during growth.
We demonstrate that implantation can generate a range of local environments
for Er3+, including those observed in bulk-doped materials, and that the
populations of these sites can be controlled with thermal processing.

##  I Introduction

Quantum networks have myriad applications, including fundamentally secure
communicationEkert (1991), modular quantum computingWehner  _et al._ (2018),
and precision measurementKómár  _et al._ (2014). This has motivated
substantial theoretical and experimental efforts to realize scalable schemes
for both long distance quantum communication and microwave-to-optical
transduction. A major goal is to develop single atom quantum memories that can
be deployed in quantum repeater architecturesKimble (2008); Atatüre  _et al._
(2018).

Erbium-based systems are promising candidates for both single atom quantum
memories in long distance quantum networks and microwave-to-optical quantum
state transduction. Several desirable properties have been demonstrated in
various Er3+-containing systems, such as long electronDantec  _et al._ (2021)
and nuclearRančić  _et al._ (2018) spin coherence times, and telecom-
wavelength spin-photon interfacesRaha  _et al._ (2020). Realizing these
properties simultaneously in a single system, however, is an area of great
current interest.

Many of the systems characterized for quantum information applications are
yttrium-based crystals (e.g. Y2SiO5, YVO4). Er3+ readily substitutes for the
Y3+ site, but the large spin bath formed by the 89Y nuclear spins has
deleterious effects on spin and optical coherence times. While extremely long
optical coherence times can be observed in Er3+:Y2SiO5 ($T_{2}$=4.38 ms at 1.5
K and 7 TBöttger  _et al._ (2009)), these optical coherence times are
ultimately limited by the presence of 89Y nuclei Böttger  _et al._ (2006),
motivating the development of nuclear spin-free host materials.

However, Er3+ in non-yttrium materials has been studied in a variety of other
contexts, such as infrared-to-visible upconversionGolesorkhi  _et al._ (2020),
laser gain mediaSun  _et al._ (2002), and as probes of the local crystal
environmentBaker and Currell (1976), demonstrating that there is a rich
chemical space still to explore for quantum information applications.
Efficiently exploring this space and screening potential new materials remains
an outstanding challengeFerrenti  _et al._ (2020).

A further challenge is encountered when integrating the current generation of
Er3+-containing materials with nanophotonic structures; while nanophotonic
integration can enable single-ion detectionDibos  _et al._ (2018) and quantum
state transductionBartholomew  _et al._ (2020), the emitters addressed by the
device are typically within hundreds of nanometers of the surface. Surface-
related noise processes (trapped charges, dangling bonds etc) can
substantially degrade the optical and spin coherence of nearby emittersDibos
_et al._ (2018); Raha  _et al._ (2020); Sangtawesin  _et al._ (2019).
Developing new material systems with reduced sensitivity to surface noise —
either through non-polar local symmetry, or fortuitously small Stark
coefficients — may help enable stable, narrow optical transitions in these
nanophotonic devices. These new materials would enable nanophotonic
integration with implanted single crystal substrates as a “top-down”
alternative to other cavity-emitter architectures such as nanoparticles in
fiber cavitiesCasabone  _et al._ (2021).

We recently demonstrated that Er3+ implanted in rutile TiO2 exhibits
inhomogeneous optical linewidths below 500 MHz, among the narrowest
inhomogeneous linewidths reported for any host material for Er3+Phenicie  _et
al._ (2019) and especially remarkable for ion-implanted Er3+. Here we build on
this result, using the same methodology to explore the properties of several
other Er-implanted materials. By utilizing ion implantation to introduce Er3+
into a variety of materials, we are able to rapidly generate and screen new
material systems while also ensuring our results are representative of the
properties of the near-surface ions required for nanophotonic integration.

The paper is structured as follows: in Section I, we outline the criteria for
host material selection; Section II briefly outlines the experimental methods;
Sections III-V present results for cubic, non-polar, and polar symmetry
crystals, respectively; and Section VI concludes with general observations.

##  II I: Host Material Criteria

| MgO | PbTiO3:SrTiO3 | ZnS
---|---|---|---
| Experiment | Cubic Model Borg  _et al._ (1970) | Experiment | Site 1 | Site 2
$Z_{1}\xrightarrow[]{}Y_{1}$ cm-1 | 6491.5 | N/A | 6511.7 | 6489.3 | 6486.7
$n$ (energies in cm-1) | Zn | Yn | Zn | Zn | Yn | Zn | Yn | Zn | Yn
1 | 0.0, 0.08 | 0.0 | 0.0, 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0
2 | 110.4 | 48.3, 48.6 | 111.2 | 14.21 | 73.7 | 7.4 | 6.7 | 11.2 | 5.7
3 | 134.8 | 98.7 | 139.7 | 113.47 | 75.1 | 25.6 | 30.7 | 31.4 | 16.7
4 | * | * | 619.2 | * | 204.8 | * | 39.6 | * | 49.0
Lifetime / ms | 20.1 (19.6) | N/A | 3.9 (6.3) | 4.6 (8.4) | 5.6 (8.4)
Table 1: Crystal field energies and other properties of cubic-symmetry host
materials. Lifetimes predicted for purely magnetic-dipole transitions are
given in parenthesis. Crystal field levels for the $Y$ levels are given
relative to the $Z_{1}\xrightarrow[]{}Y_{1}$ transition energy. Levels
assigned to strain-split quartet states are given in the same table entry.
States which are not observed in our experiments are denoted with asterisks.

To narrow our search, we begin with a coarse set of criteria for prospective
host crystals which can be determined from the elemental composition or from
readily available reference data. Specifically, we search for material
properties that allow for long Er3+ coherence times, and a material bandgap
sufficient to host the optical transition. An extensive tabulation of
materials satisfying these properties was presented in Reference Ferrenti  _et
al._ (2020).

Long spin coherence times require an environment with low magnetic noise.
Thus, a good host material should be diamagnetic, composed of elements with
nuclear spin-free isotopes, and have minimal paramagnetic impurities. Spin
coherence is ultimately limited by spin-lattice relaxation, but this can
typically be suppressed by going to sufficiently low temperaturesOrbach
(1961).

Coherent optical transitions are an essential element of a spin-photon
interface. Optical coherence introduces two requirements; first, the band gap
of the host material must be large enough such that emission from the defect
optical transition is not re-absorbed by the host material ($>0.83$ eV for
Er3+), and second, the optical transition frequency should be stable in the
presence of the solid state environment. One approach to realizing this second
requirement is to optimize crystal growth and processing to remove sources of
noiseChu  _et al._ (2014), while a complimentary strategy is to minimize the
sensitivity of the qubit to these noise sources. If the symmetry of the
crystal site does not allow a permanent electric dipole moment, then the Stark
shift from electric field noise is quadratic instead of linear. Narrow ($<$
500MHz) inhomogeneous linewidths previously reported in Er-implanted TiO2 were
attributed to the non-polar symmetry (and thus vanishing first-order Stark
shift) of the Er3+ site in this materialPhenicie  _et al._ (2019), and
inversion-symmetric group IV-vacancy defects in diamond have significantly
less spectral diffusion near surfaces and in nanostructuresSipahigil  _et al._
(2014); Rose  _et al._ (2018) compared to NV centersChu  _et al._ (2014).

Below, we present the optical characterization of a selection of Er-implanted
materials which meet the criteria outlined earlier: they are composed of
elements which have stable nuclear spin-free isotopes, bandgaps greater than 1
eV, and which span a wide range of potential coordination environments for
implanted Er3+. By probing both the inhomogeneous linewidths and implantation
yield for particular sites we are able to gain insight into both the static
disorder in the crystal and the sensitivity of Er3+ to noise sources in the
crystal. These crystals span a wide range of potential Er3+ coordination
environments: cubic (MgO, PbTiO3:SrTiO3, ZnS), non-cubic and non-polar (TiO2,
PbWO4), and polar symmetries (MoO3, ZnO).

This wide-ranging screening approach allows us to identify MgO, PbWO4, TiO2
and ZnO as particularly promising candidates, each showing narrow
inhomogeneous linewidths for near-surface ions. In several material systems we
also demonstrate the importance of post-implantation thermal processing.

##  III II: Experimental Approach

Er3+ is incorporated into host materials via ion implantation (Innovion) at
energies up to 350 keV, which corresponds to an implantation depth of
$\approx$ 100 nm in the materials studied here (see Supplementary Information
for full implantation recipe). The implantation process creates a highly non-
equilibrium distribution of Er3+ coordination environments and implantation-
induced vacancies. To identify different Er3+ environments in the host
crystals and characterize their properties, we employ photoluminescence-
excitation (PLE) spectroscopy, described below. These techniques enable us to
ascertain the site-specific level structure of different Er3+ environments and
their associated inhomogeneous linewidths. Samples are mounted in a sample-in-
vapor optical cryostat held at 4.5 K unless otherwise noted. Multiple samples
are mounted on the same copper cold finger with GE varnish, using copper
barriers between samples to prevent scattered light from exciting fluorescence
in adjacent samples.

An achromatic doublet lens outside the cryostat is used to focus excitation
light and collect emission from the sample, and a tunable narrowband laser
(CTL 1500, Toptica) is used to excite the sample. The resulting emission
spectrum is measured using a grating spectrometer with a cooled InGaAs
detector array (PyLon-IR, Teledyne Princeton Instruments), enabling us to
generate two-dimensional maps of the emission spectrum for various excitation
wavelengths. Fast thermalization of the Er3+ excited states (relative to the
millisecond radiative lifetimeLiu and Jacquier (2005)) results in identical
emission spectra for each Er3+ site regardless of which transition was
excited; thus when Er3+ can occupy multiple different sites the emission
spectrum can be used to group excitation peaks originating from Er3+ ions
occupying the same site.

With site-specific excitation and emission frequencies, we can extract the
ground and excited state energies for each site. The ground state splits into
8 states $Z_{1}-Z_{8}$, (5 in cubic symmetry), while the excited state splits
into 7 states $Y_{1}-Y_{7}$ (5 in cubic symmetry). For each site we also
measure the excited state lifetime, which we can compare to the expected
magnetic dipole (MD) decay rateDodson and Zia (2012). This allows us to
estimate the role of forced electric dipole moments in the decay rate, which
are only allowed in sites without inversion symmetry.

##  IV III: Cubic Systems

###  IV.1 MgO

Structure & Properties: MgO adopts the cubic halite structure, with
octahedrally-coordinated (local $O_{h}$ symmetry) Mg2+ and O2-. The only
native nuclear spin present at an appreciable level is 25Mg ($I=\frac{5}{2}$,
10% natural abundance).

MgO has a relatively low refractive index ($n=1.71$)Stephens and Malitson
(1952), which is advantageous for improving refractive index contrast in
hybrid nanophotonic devices. The large band gap of MgO (7.8 eV) is sufficient
to host not only telecom-wavelegth optical transitions, but can also host
defects with shorter wavelength transitions.

The samples used in this work had a (001) surface and were purchased from MTI
Corp. Samples were stored in a dessicator when not in use because of the
hygroscopic nature of MgO. Prior to implantation, no Er3+ emission was
observed.

Figure 1: Top panel: excitation spectrum of annealed Er3+:MgO at T=4.5 K,
showing all transitions observed. Colored bars indicate different sites.
Bottom panel: excitation-emission spectrum of the same sample, plotted on a
log intensity axis to show all peaks observed. The diagonal feature at
$\omega_{exc}=\omega_{em}$ is from scattered excitation light, and provides a
wavelength reference for the spectrometer.

Optical Spectrum: The excitation-emission spectrum of MgO shown in Figure 1
has a rich structure with peaks corresponding to at least five distinct
incorporation sites. We focus our discussion on the most intense set of peaks,
highlighted with blue arrows in Fig. 1 (other energy levels are tabulated in
the Supplementary Information). The lowest two excitation peaks show small
splittings (0.08 cm-1, 0.3 cm-1 respectively) which are suggestive of some
degeneracy-lifting perturbation. Substantial unresolved fine structure is
evident in the $Z_{1}\xrightarrow[]{}Y_{1}$ peak (Fig. 2), making quantitative
determination of inhomogeneous linewidth challenging; however, we can put an
upper bound of 2 GHz on the width of each peak (post thermal processing),
comparable to the inhomogeneous linewidth observed in many Yttrium-based
crystalsLiu and Jacquier (2005).

The fluorescence lifetime of the $Y_{1}$ level is 20.1 ms (see Supplementary
InformationI). We can estimate the expected radiative lifetime of a magnetic
dipole (MD) transition by scaling the lifetime in the free Er3+ ion (98.3 ms)
by $n^{3}$ (to account for the higher density of states in the crystal), which
yields an estimated MD lifetime of 19.6 msDodson and Zia (2012). The good
agreement with the experimental value suggests that there is no forced
electric dipole contribution and that non-radiative relaxation pathways are
not significant in this case.

Previous ESR measurements have reported that Er3+ occupies the octahedral Mg2+
substitutional siteBaker and Currell (1976); Borg  _et al._ (1970), and has a
quartet ground state ($\Gamma_{8}$ in the Koster notation), rather than the
usual Kramers doublet. Strain can lift this fourfold degeneracyBaker and
Currell (1976), consistent with the closely-spaced sets of peaks observed in
our measurements. Using previously-reported crystal field parametersBorg  _et
al._ (1970); Lea  _et al._ (1962), we determine that the transition from
$Y_{1}$ to the lowest non-quartet state
($\Gamma_{7}\xrightarrow[]{}\Gamma_{6}$) is symmetry-forbidden. To determine
the ground-state splittings, we increase the temperature of the sample to
populate the $Y_{2}$ level. Emission from this level allows us to determine
the ground state splittings, which are in excellent agreement with previously
reported models based on ESR measurements for the substitutional Mg2+ site
(Table 1)Borg  _et al._ (1970).

Annealing: Er3+-implanted MgO was annealed in air for a total of seven hours
at 600$\degree{}$C. Previous studies of MgO implanted with Fe have indicated
aggregation and precipitation above this temperatureWhite  _et al._ (1989).
Post-anneal spectra show a seven-fold increase in the intensity of the $O_{h}$
site. We also observe a number of peaks after annealing which we suggest may
be associated with structural configurations where charge compensation occurs
locally (as in Nd3+ in CaF2Kiss (1963)), though the detailed structure and
symmetry of this site are unknown. (The level structure for this site is
detailed in the Supplementary Information). A number of small peaks initially
present in the as-implanted sample disappear on annealing. Figure 2 shows the
dependence of the peak intensities on annealing conditions.

The increase in intensity of the Site 1 peaks with annealing indicates that
thermal processing is important for Er3+-implanted MgO, though the results
here likely do not represent the optimal annealing method. The detailed
mechanism, and optimization, of this thermal processing will be the focus of
future work.

Figure 2: Upper panel: Changes in the number and intensities of peaks in MgO
as a function of annealing conditions, described in the main text. Bottom
panel: High-resolution scan of the $Z_{1}\xrightarrow[]{}Y_{1}$ transition,
showing the change in linewidth on annealing.

###  IV.2 PbTiO3:SrTiO3

Structure & Properties: PbTiO3 and SrTiO3 are both perovskite structures, with
cuboctahedral coordination of the A-site (Pb2+, Sr2+) and octahedral
coordination of the B-site (Ti4+). Below 105 K, SrTiO3 undergoes a symmetry-
lowering tetragonal distortionCowley (1996), lowering the local symmetry of
the A- and B-sites to $D_{2d}$ and $C_{4h}$ respectivelyEvarestov  _et al._
(2011). Both Ti and Pb have isotopes with nuclear spin, ${}^{207}\mathrm{Pb}$
(I$=\frac{1}{2}$, 22% natural abundance), ${}^{47}\mathrm{Ti}$
(I$=\frac{5}{2}$, 7% natural abundance), and ${}^{49}\mathrm{Ti}$
(I$=\frac{7}{2}$, 5% natural abundance).

This sample is not implanted with Er3+; doping is instead introduced during
growth of the PbTiO3 layer. 100 nm of PbTiO3 is overgrown on a SrTiO3
substrate via pulsed-laser deposition, as detailed in the Supplementary
Information. The Er3+-doping is modulated such that only one unit-cell layer
is doped with Er3+ at 0.1 mol$\%$, then ten layers are undoped, then another
unit-cell layer is doped, and so on. Both SrTiO3 and PbTiO3 have high
refractive indices ($n=2.28$Bond (1965) and $n<2.5$Singh  _et al._ (1972)
respectively).

Optical Spectrum: In contrast to MgO, Er3+:PbTiO3:SrTiO3 shows a much simpler
spectrum, shown in Figure 3. All peaks show the same emission pattern,
consistent with a single occupied site. The extracted crystal field levels are
given in Table 1.

Figure 3: Top panel: Excitation spectrum of Er3+-doped PbTiO3:SrTiO3, showing
all transitions observed. Bottom panel: Excitation-emission spectrum of the
same sample, plotted on a log intensity axis to show all peaks observed.

The inhomogeneous linewidth of the $Z_{1}\xrightarrow[]{}Y_{1}$ transition is
$\approx$9 GHz, with an asymmetric tail. The excited state lifetime of the
$Y_{1}$ state is 3.9 ms. The expected magnetic dipole radiative lifetime is
6.3 ms, which is indicative of a forced electric dipole contribution to the
emission.

While our measurements do not allow us to unambiguously assign a site to the
incorporated Er3+, we note that ESR measurements of Er3+ in BaTiO3 have
suggested Er3+ can substitute in either the A- or B-siteDunbar  _et al._
(2004), and the better matching of ionic radius between Er3+ and Pb2+ with
respect to Ba2+ suggests A-site (distorted cubeoctahedral) substitution might
be expected. The A-site ($D_{2d}$ symmetry at low temperature) permits an
electric dipole contribution to the radiative lifetime via $d$-$f$ mixing,
while the B-site symmetry ($C_{4h}$) does not.

###  IV.3 ZnS

Structure & Properties: ZnS adopts the zinc blende structure, composed of
tetrahedrally coordinated Zn2+ and S2-. Only the 67Zn isotope has non-zero
spin ($I=\frac{5}{2}$, natural abundance 4%). ZnS has a refractive index
$n=2.27$Debenham (1984) and a band gap of 3.5 eV.

The samples described in this work were purchased from SurfaceNet, with (111)
orientation, grown by a seeded vapor-phase free growth method. No Er3+
emission was observed prior to implantation.

Optical Spectrum: Two distinct sites (Sites 1 and 2) can be identified in the
ZnS excitation-emission spectrum, shown in Figure 4. We note that for both
sites, the transitions span a much smaller energy range than either MgO or
PbTiO3:SrTiO3. Extracted crystal field levels are reported in Table 1.

The measured excited state lifetimes for both Sites 1 (4.6 ms) and 2 (5.6 ms)
are shorter than expected for a pure MD transition (8.4 ms). The congested
spectrum makes accurate determination of the inhomogeneous linewidths
difficult, even with site-selective measurements, but both Sites 1 and 2 have
$Z_{1}\xrightarrow[]{}Y_{1}$ inhomogeneous linewidths of $>$25 GHz.

Figure 4: Top panel: Excitation spectrum of Er3+-implanted ZnS (annealed),
showing all transitions observed. Bottom panel: Excitation-emission spectrum
of the same sample, plotted on a log intensity axis to show all peaks
observed.

Emission in the visible wavelength range from Er3+-implanted ZnS has been
previously reported using cathodoluminescenceYu and Bryant (1979), where two
sites were also observed. The $Z$ levels we determine for Site 2 are in
excellent agreement with the reported levels for the substitutional Zn2+ site.
Moreover, the population of this site increased with annealing in a manner
consistent with previous reportsYu and Bryant (1979).

However, the parameters we determine for Site 1 are not consistent with the
reported levels for the interstitial site identified in Reference Yu and
Bryant (1979) despite similar implantation fluences and subsequent annealing.
One possible explanation for this discrepancy is the excitation method;
cathodoluminescence and resonant excitation may excite sites with different
efficiencies. Though we do not propose a detailed structural assignment for
Site 1, we note that some charge compensation must occur in ZnS with Er3+
defects (as with all the materials we present here); differences in charge
compensation (e.g. local or remote, compensating ion identity, local
configuration) would be expected to give rise to distinct sites.

Annealing: Er3+-implanted ZnS was annealed in air at 350$\degree{}$C for 3
hours, as described in Reference Yu and Bryant (1979). Prior to annealing,
Site 1 was observable, but no clear emission from Site 2 was detected. After
annealing, emission from Site 2 increased substantially, having similar
maximum peak height to Site 1.

##  V IV: Non-Cubic, Non-Polar Systems

| PbWO4 | TiO2
---|---|---
$Z_{1}\xrightarrow[]{}Y_{1}$ / cm-1 | 6517.7 | 6575.7
$n$ (energies in cm-1) | Zn | Yn | Zn | Yn
1 | 0.0 | 0.0 | 0.0 | 0.0
2 | 10.7 | 3.6 | 35.0 | 14.8
3 | 31.9 | 47.6 | 40.8 | 22.9
4 | 51.4 | 103.4 | 119.6 | 96.3
5 | 189.5 | 134.9 | 169.7 | *
6 | 228.7 | 147.6 | 208.3 | *
7 | 253.3 | 165.4 | 269.8 | *
8 | 282.1 | N/A | * | N/A
Lifetime / ms | 7.7 ($>9.1$) | 5.25 (5.2-6)Phenicie  _et al._ (2019)
Table 2: Crystal field energies and other properties of non-polar symmetry
host materials. Lifetimes predicted for purely magnetic-dipole transitions are
given in parenthesis. Crystal field levels for the $Y$ levels are given
relative to the $Z_{1}\xrightarrow[]{}Y_{1}$ transition energy

###  V.1 PbWO4

Structure & Properties: PbWO4 adopts the Scheelite crystal structure, in which
the optical properties of doped rare-earth ions have been extensively
studiedEnrique (1971). Both Pb and W have isotopes with nuclear spin,
${}^{207}\mathrm{Pb}$ (I$=\frac{1}{2}$, 22% natural abundance) and
${}^{183}\mathrm{W}$ (I$=\frac{5}{2}$, 14% natural abundance). We observe Er3+
emission in our PbWO4 prior to implantation, suggesting low levels of native
doping; this would suggest that extra care may be required during synthesis to
minimize additional paramagnetic defects. Similar background levels of Er3+
have been observed in other nominally lanthanide-free materialsWolfowicz  _et
al._ (2021a).

PbWO4, like all Scheelite structures, is birefringent. The refractive indices
at 1530 nm are $n_{o}<2.21$ and $n_{e}<2.16$Baccaro  _et al._ (1997). Numerous
values have been reported for the band gap of PbWO4, but all are $>$3.5 eV.
CaWO4, which we compare PbWO4 with below, has the same structure and similar
optical properties ($n_{o}=1.88$, $n_{e}=1.9$Bond (1965), band gap $4.2$ eV).
In Er3+-doped CaWO4, Er3+ is known to occupy the Ca2+ site, which has local
$S_{4}$ symmetryEnrique (1971); Cornacchia  _et al._ (2007).

The PbWO4 substrate with (001) orientation was purchased from MTI Corp. The
comparison CaWO4 sample was grown via the Czochralski method, with Er3+ doping
of approximately 0.8 ppbBertain .

Optical Spectrum: We compare the optical properties of three samples -
Er3+-implanted PbWO4, PbWO4 with native Er3+ (presumably introduced during
crystal growth), and as a reference sample, Er3+-doped CaWO4. By comparing the
intensities of the observed spectra in the implanted and unimplanted PbWO4, we
estimate the background Er3+ doping levels to be on the $<$ppb-level.

The excitation-emission spectrum of implanted PbWO4 (Figure 5) shows only one
site. The peaks are all clearly resolvable, allowing the determination of all
eight $Z$ levels and all seven $Y$ levels (Table 2). The splittings reported
are qualitatively similar to those known for isostructural Er3+-doped
CaWO4Enrique (1971).

Figure 5: Top panel: Excitation spectrum of Er3+-implanted PbWO4 (annealed).
Bottom panel: Excitation-emission spectrum of the same sample, plotted on a
log intensity axis to show all peaks observed.

The excited state lifetime of implanted PbWO4 is 7.7 ms, shorter than the
$9.3$ ms expected from a pure MD transition, suggesting a forced electric
dipole contribution. The $Z_{1}\xrightarrow[]{}Y_{1}$ transition of the
implanted sample (Figure 6) shows significant structure, but the FWHM of the
central peak is approximately 1 GHz. As noted earlier, our PbWO4 samples have
trace Er3+ contamination pre-implantation, enabling us to directly compare
implanted and bulk Er3+ in PbWO4 (Figure 6). We find that the peak positions
are identical between the implanted and trace-Er3+ samples, though the bulk
Er3+ inhomogeneous linewidths are threefold narrower. This might suggest there
is still some residual disorder from implantation; however, we also note that
our local Er3+ concentration is high ($\approx$100 ppm) in the implanted
region, and 1 GHz inhomogeneous linewidths have been observed in bulk-doped
Er3+:CaWO4 of similar concentrationsSun  _et al._ (2002).

To further explore the similarities between CaWO4 and PbWO4, we compare the
the spectrum of the implanted PbWO4 and a bulk-doped CaWO4 sample. The same
hyperfine structure around the $Z_{1}\xrightarrow[]{}Y_{1}$ transitions is
observed for both CaWO4 and PbWO4, which arises from the $23\%$ natural
abundance 167Er. The near perfect correspondence between the PbWO4 and CaWO4
spectra suggest their hyperfine constants (and thus underlying $g$-tensors)
are extremely similar, from which we conclude that Er3+ occupies a similar
site in both cases. In CaWO4, Er3+ is known to occupy the substitutional
cation siteEnrique (1971); Cornacchia  _et al._ (2007).

The prominent hyperfine-split transitions are a result of the large transverse
component of the hyperfine tensorEnrique (1971); this acts in the same manner
as a large off-axis magnetic field, giving rise to optical transitions which
flip the electron or nuclear spin. Well-resolved hyperfine transitions may
find use in optical manipulation of the nuclear spinWelinski  _et al._ (2020),
potentially serving as an ancilla qubit.

Figure 6: Top panel: high resolution scan of $Z_{1}\xrightarrow[]{}Y_{1}$
transition for implanted PbWO4, bulk-doped CaWO4, and unimplanted PbWO4 with
trace Er3+ impurities. The same hyperfine structure is observed in all cases.
PbWO4 and CaWO4 spectra are shifted by their respective
$Z_{1}\xrightarrow[]{}Y_{1}$ transition energies, but the frequency axis is
not otherwise altered.

Annealing: Implanted PbWO4 was annealed for one hour at 900$\degree{}$C. Prior
to annealing, the signal observed (both magnitude and linewidth) was similar
to the native Er3+ in the unimplanted crystal, suggesting implanted Er3+ is
not optically active. After annealing the sample the signal increased by a
factor of $>200$.

###  V.2 TiO2

Structure & Properties: TiO2 adopts the rutile structure in our samples.
Previous studies of Er-implanted TiO2 demonstrated that the Er3+ occupies the
substitutional Ti site, with local $D_{2h}$ symmetryPhenicie  _et al._ (2019).

Ti has two isotopes with nuclear spin, ${}^{47}\mathrm{Ti}$ (I$=\frac{5}{2}$,
7% natural abundance) and ${}^{49}\mathrm{Ti}$ (I$=\frac{7}{2}$, 5% natural
abundance). TiO2 has a large refractive index ($n>2.4$) and is highly
birefringent. The bandgap of TiO2 is 3.0 eV. The preparation of the samples
described below have been previously describedPhenicie  _et al._ (2019).

Optical Spectrum: The excitation spectrum and inhomogeneous linewidth of
implanted TiO2 have been previously reported in Ref Phenicie  _et al._ (2019).
Here, an improved optical setup enables us to report a more complete
excitation-emission spectrum (Figure 7), which is consistent with the
previously reported crystal field levels (Table 2). Experimental improvements
in resolution and sensitivity allow us to report here several previously-
unreported $Z$ levels.

Figure 7: Top panel: Excitation spectrum of Er3+-implanted TiO2 (annealed),
showing all transitions observed. Bottom panel: Excitation-emission spectrum
of the same sample, plotted on a log intensity axis to show all peaks
observed.

##  VI V: Polar Systems

| MoO3 | ZnO
---|---|---
$Z_{1}\xrightarrow[]{}Y_{1}$ / cm-1 | 6512.5 | 6504.2
$n$ (energies in cm-1) | Zn | Yn | Zn | Yn
1 | 0.0 | 0.0 | 0.0 | 0.0
2 | 36.5 | 55.6 | 19.8 | 14.8
3 | 135.6 | 82.5 | 27.8 | 22.9
4 | 163.0 | 117.2 | 116.9 | *
5 | 177.4 | * | 152.9 | *
6 | * | * | 195.4 | *
7 | * | * | 217.8 | *
Lifetime / ms | 5.5 (11.0) | 5.8 (13.6)
Table 3: Crystal field energies and other properties of polar symmetry host
materials. Lifetimes predicted for purely magnetic-dipole transitions are
given in parenthesis. Crystal field levels for the $Y$ levels are given
relative to the $Z_{1}\xrightarrow[]{}Y_{1}$ transition energy

###  VI.1 MoO3

Structure: MoO3 forms orthorhombic crystals composed of distorted octahedra of
Mo6+ coordinated by O2-. Only two sites of non-trivial symmetry are found in
this crystal, $C_{s}$ (Mo and O positions) and $C_{i}$ (interstitial sites).
Mo has two isotopes with nuclear spin, ${}^{95}\mathrm{Mo}$ (I$=\frac{5}{2}$,
15% natural abundance) and ${}^{97}\mathrm{Mo}$ (I$=\frac{5}{2}$, 10% natural
abundance). The refractive index of MoO3 is $n=2.07$Lajaunie  _et al._ (2013).
The bandgap of MoO3 is $3.2$ eVSabhapathi  _et al._ (1995). The samples used
in the work below were grown by the vapor transport method.

Optical Spectrum: The spectrum of implanted MoO3 is consistent with a single
dominant environment for Er3+, showing a sparse pattern of excitation and
emission peaks. The excited state lifetime of MoO3 is 5.5 ms, shorter than the
11.0 ms expected from a pure magnetic dipole transition in this material. The
inhomogeneous linewidth of the $Z_{1}\xrightarrow[]{}Y_{1}$ transition is 90
GHz, which is the broadest linewidth we report here. There are several
possible sources of disorder in this system; not only is Er3+ in MoO3
sensitive to implantation-induced damage, but the variety of oxidation states
that can be adopted by Mo has the potential to serve as an intrinsic source of
inhomogeneity.

The broad inhomogeneous linewidths in this sample highlight another source of
information accessible from our spectroscopic approach. Several of the two-
dimensional lineshapes show distinct slopes (such as the inset of Figure 8)
which reveal the correlations between excitation and emission frequencies of
sub-ensembles of Er3+ ions (e.g. a sub-ensemble may have a red-shifted
$Z_{1}\xrightarrow[]{}Y_{1}$ transition, but a blue shifted
$Z_{1}\xrightarrow[]{}Y_{2}$ transition). These correlations describe how the
different energy levels of the Er3+ ions shift in response to the main source
of disorder in the system (electric field, strain, etc), which may be useful
in site assignment or identifying transitions which are minimally sensitive to
the local disorder. This approach is currently limited by our spectrometer
resolution ($\approx 1$ cm-1), but improvements in detection resolution would
allow this information to be extracted for narrower inhomogeneous linewidths.

Figure 8: Top panel: excitation spectrum of Er3+-implanted MoO3 (annealed),
showing all transitions observed. Bottom panel: excitation-emission spectrum
of the same sample, plotted on a log intensity axis to show all peaks
observed. Inset shows the correlated lineshape in the excitation-emission
spectrum for two peaks.

Annealing: The implanted MoO3 sample was annealed in air at 550$\degree{}$C
for 4 hours. Previous studies assessing Er3+-implanted MoO3 as a potential
optoelectronic material found this annealing procedure increased the visible
emission from Er3+ in MoO3Vila  _et al._ (2014). Er3+ emission was observed
both pre- and post-anneal, the main effect of the annealing was the removal of
a number of small, barely-resolvable peaks, but did not impact the
inhomogeneous linewidth. Because of the irregular size and shape of the
crystals, it is not possible to make a quantitative comparison between pre-
and post-anneal peak heights. The post-anneal excitation-emission spectrum is
consistent with a single environment for the implanted Er.

###  VI.2 ZnO

Structure: ZnO adopts the hexagonal Wurtzite structure. The Zn2+ ion is
coordinated by four O2- in a distorted tetrahedral fashion with $C_{3v}$
symmetry. The polar crystal structure of ZnO gives rise to a piezoelectric
effect in the crystal. Only the 67Zn isotope has non-zero spin
($I=\frac{5}{2}$, natural abundance 4%).

The refractive index of ZnO is $n=1.93$Bond (1965), and the bandgap is 3.3 eV.
The samples described here had a (0001) orientation and were purchased from
MTI Corp. No emission from Er3+ was observed prior to implantation.

Optical Spectrum: The optical spectrum of Er-implanted ZnO, shown in Figure 9,
is dominated by a single site. The inhomogeneous linewidth of the
$Z_{1}\xrightarrow[]{}Y_{1}$ transition is 1.5 GHz, which is among the
narrowest of the materials we present here. This narrow linewidth is observed
despite the polar symmetry and piezoelectric nature of the crystal. An
interesting point of comparison here are “Pseudo-$C_{3v}$” defects in SiC,
where similarity between dipoles in the ground and excited states results in
minimal sensitivity of the optical transition to electric fieldsUdvarhelyi
_et al._ (2019).

Figure 9: Top panel: Excitation spectrum of Er3+-implanted ZnO (annealed),
showing all transitions observed. Bottom panel: Excitation-emission spectrum
of the same sample, plotted on a log intensity axis. Several smaller features
are visible in the excitation range 6507cm-1 to 6512cm-1; these are
transitions from thermally populated states of the Er3+.

The lifetime of Er3+-ZnO is substantially smaller than would be expected for a
magnetic-dipole transition (5.8 ms vs 13.6 ms), which indicates a forced
electric dipole contribution.

Rutherford backscattering measurements of implanted ZnO have observed that
Er3+ occupies the substitutional Zn2+ siteAlves  _et al._ (2003), while
optical measurements of Er3+-implanted GaNAlves  _et al._ (1999), which adopts
the same structure and has similar lattice constants, also find that Er3+
occupies the cation substitutional site. Our observation of a single, well-
defined site in the excitation-emission spectrum is consistent with a picture
of Er3+ substituting for Zn2+, where the sparseness of the spectrum suggests
either remote charge compensation or one dominant charge compensation
configuration.

Annealing: ZnO was annealed at 750$\degree{}$C for a total of sixteen hours;
this was the total time at 750$\degree{}$C over three annealing runs of
duration 1 hour, 6 hours, and 9 hours. Annealing at higher temperatures is
known to lead to out-diffusion of Er3+Alves  _et al._ (2003). As-implanted,
the spectrum showed a wide range of low-intensity, spectrally broad features;
after annealing for one hour, a new set of peaks with much narrower
inhomogeneous linewidths was observed. The intensity of these peaks increased
with longer annealing times, reaching a maximum increase of 10x relative to
the as-implanted peak height. Spectra for these annealing steps are shown in
the Supplementary Information.

##  VII VI: Discussion

Ion implantation and doping during growth are two distinct approaches to
introducing Er3+ ions into a host material; understanding to what extent the
two approaches can generate similar coordination environments of Er3+ is
necessary for exploring new host materials for quantum communication
applications. We find that, where the coordination environment for the doped
samples is known (i.e., MgO, PbWO4 and ZnO), ion implantation is capable of
generating the same local environment.

However, we are also able to identify several other sites occupied by
implanted Er3+ in various samples using ion implantation. In MgO, we can
resolve at least four other sites in addition to the $O_{h}$ site (detailed in
the Supplementary Information); multiple sites are observable in ZnS; and the
spectrum of ZnO does not resolve into a clear single site until the sample has
been annealed. To explain this observation, we consider the effects of charge
compensation and implantation-induced damage to the host crystal. In all
systems described here, Er3+ is an aliovalent defect, requiring charge
compensation in the crystal; different configurations of local charge
compensation can give rise to multiple spectrally distinct peaks, as in the
case of Nd3+ in CaF2Kiss (1963) and Er3+:SiPrzybylinska  _et al._ (1996);
Gritsch  _et al._ (2021). Additionally, ion implantation generates vacancy
defects which may produce additional coordination environments of Er3+ which
would not be observed in a sample doped during growth.

The effect of ion implantation damage is not limited to generating new,
distinct, Er3+ sites, but can also give rise to disorder in the crystal host.
The inhomogeneous linewidth reflects the extent of the disorder, as well as
the sensitivity of the Er3+ optical transitions to this disorder. In multiple
implanted systems (MgO, PbWO4, TiO2, ZnO) we see inhomogeneous linewidths on
the order of a few GHz (summarized in Table 4), comparable to what is
typically observed in conventional host materials such as Er3+:Y2SiO5Liu and
Jacquier (2005), suggesting that the effect of static disorder in the
implanted samples can be similar to that in doped materials. These linewidths
will also include contributions from defects already present in the crystal,
and may have scope for further improvement using optimized substrates. The
presence of native Er3+ ions in our unimplanted PbWO4 samples enables a direct
comparison of inhomogeneous linewidths between doped and implanted samples;
here, we observe that the implanted sample is approximately three times
broader than the doped Er3+, but with a linewidth sufficiently narrow to
resolve several hyperfine-related features.

Material | Inhomogeneous Linewidth
---|---
MgO |  $<$2 GHz
PbTiO3:SrTiO3 | 9 GHz
ZnS |  $>$25 GHz
PbWO4 | 1 GHz
TiO2 | 500 MHz
MoO3 | 90 GHz
ZnO | 1.5 GHz
Table 4: Summary of the observed inhomogeneous linewidths for
$Z_{1}\xrightarrow[]{}Y_{1}$ transitions after thermal annealing.

A necessary tool in realizing these GHz-wide inhomogeneous linewidths,
however, is thermal processing. The annealing conditions for each sample are
given in the appropriate material section, but the effects we observe can be
generally categorized as changing site occupancies and changing inhomogeneous
linewidths. These effects are summarized in Table 5. The effect of annealing
is particularly striking in PbWO4 and ZnO; in these cases, annealing
significantly changes the nature of the implanted Er3+ ions, which are not
initially optically active in the case of PbWO4 and occupy a highly disordered
site in the case of ZnO. The thermal processing conditions we outline for each
material do not necessarily represent the optimal conditions; given the
complex interplay of Er3+ diffusion, charge compensation, and implantation
damage repair there is likely scope for improvement for each of the materials
outlined here.

Material | Effect of Annealing
---|---
|  Site Occupancy |  Inhomogeneous Linewidth
MgO |  $O_{h}$ site increases, additional sites also appear |  Narrows, quartet splitting decreases
ZnS |  Site 2 appears |  No change
PbWO4 |  No implanted Er3+ observable prior to annealing; large increase after anneal |  N/A
TiO2 |  Increase in $D_{2d}$ site |  Narrows
MoO3 |  Minor peaks disappear on annealing |  No change
ZnO |  Initial site disappears, replaced by new site |  New site has tenfold narrower inhomogeneous linewidth
Table 5: Summary of the effects of annealing on different host materials

##  VIII Outlook and Conclusions

Several materials presented here are promising candidates for future single-
Er3+ studies. MgO is a low refractive index material with reports of
millisecond spin $T_{1}$ for Er3+ at temperatures $>$ 1 KBorg  _et al._
(1970), while PbWO4 and CaWO4 have interesting hyperfine structure which may
be useful for initializing ancilla qubits. Beyond simply replacing yttrium-
based crystals as passive host materials, both PbTiO3:SrTiO3 and ZnO (which
are respectively ferroelectric and piezoelectric) have promising optical
properties. The prospect of long optical and spin coherence in polar crystals
is particularly intriguing; the ability to actively control the host material
could enable rapid frequency tuning of optical transitions, novel control
schemesGeorge  _et al._ (2013); Liu  _et al._ (2021), and spectral shaping of
emitted photonsLukin  _et al._ (2020).

While our discussion has focused on integration with nanophotonic devices,
many of these materials may be useful in ensemble applications. Our results
show that ion implantation can be used to identify promising candidate
materials, which could then be doped during crystal growth. This would provide
a route to combining the flexibility and relative ease of sample preparation
associated with ion implantation with the higher doping levels and high-
quality materials possible with careful crystal growth. More generally, the
combination of ion implantation and thermal processing we present will enable
efficient searches through material parameter space, providing new data which
could be used in future computational or data-mining studies to identify new
candidate hostsFerrenti  _et al._ (2020). This approach is not limited to
screening host materials, but could also be used to efficiently search for new
emitters in established host materialsThiel  _et al._ (2011); Wolfowicz  _et
al._ (2021b); Graham  _et al._ (2017).

##  IX Acknowledgements

Funding for this research was provided by the AFOSR (contract
FA9550-18-1-0334), the Eric and Wendy Schmidt Transformative Technology Fund
at Princeton University, and the Princeton Catalysis Initiative. The materials
processing work was supported by the U.S. Department of Energy, Office of
Science, National Quantum Information Science Research Centers, Co-design
Center for Quantum Advantage (C2QA) under contract number DE-SC0012704. P.G.
acknowledges funding from ANR Mirespin project, grant ANR-19-CE47- 0011 of the
French Agence Nationale de la Recherche. The work at UC Berkeley was supported
by the Center for Probabilistic Spin Logic for Low-Energy Boolean and Non-
Boolean Computing (CAPSL), one of the Nanoelectronic Computing Research
(nCORE) Centers as task 2759.002, and a Semiconductor Research Corporation
(SRC) program sponsored by the NSF through CCF 1739635

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