††thanks: Currently at HRL Laboratories LLC††thanks: Currently at HRL
Laboratories LLC††thanks: Currently at AWS Quantum Technologies

# Niobium coaxial cavities with internal quality factors exceeding 1.5 billion
for circuit quantum electrodynamics

Andrew E. Oriani  James Franck Institute, University of Chicago, Chicago,
Illinois 60637, USA  Pritzker School of Molecular Engineering, University of
Chicago, Chicago, Illinois 60637, USA  Fang Zhao  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  Tanay Roy  James Franck Institute,
University of Chicago, Chicago, Illinois 60637, USA  Department of Physics,
University of Chicago, Chicago, Illinois 60637, USA  Alexander Anferov  James
Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
Kevin He  James Franck Institute, University of Chicago, Chicago, Illinois
60637, USA  Department of Physics, University of Chicago, Chicago, Illinois
60637, USA  Ankur Agrawal  James Franck Institute, University of Chicago,
Chicago, Illinois 60637, USA  Department of Physics, University of Chicago,
Chicago, Illinois 60637, USA  Riju Banerjee  James Franck Institute,
University of Chicago, Chicago, Illinois 60637, USA  Department of Physics,
University of Chicago, Chicago, Illinois 60637, USA  Srivatsan Chakram
Department of Physics and Astronomy, Rutgers University, Piscataway, New
Jersey 08854, USA  David I. Schuster  James Franck Institute, University of
Chicago, Chicago, Illinois 60637, USA  Department of Physics, University of
Chicago, Chicago, Illinois 60637, USA

(September 1, 2024)

###### Abstract

Group-V materials such as niobium and tantalum have become popular choices for
extending the performance of circuit quantum electrodynamics (cQED) platforms
allowing for quantum processors and memories with reduced error rates and more
modes. The complex surface chemistry of niobium however makes identifying the
main modes of decoherence difficult at millikelvin temperatures and single-
photon powers. We use niobium coaxial quarter-wave cavities to study the
impact of etch chemistry, prolonged atmospheric exposure, and the significance
of cavity conditions prior to and during cooldown, in particular niobium
hydride evolution, on single-photon coherence. We demonstrate cavities with
quality factors of $Q_{\rm int}\gtrsim 1.4\times 10^{9}$ in the single-photon
regime, a $15$ fold improvement over aluminum cavities of the same geometry.
We rigorously quantify the sensitivity of our fabrication process to various
loss mechanisms and demonstrate a $2-4\times$ reduction in the two-level
system (TLS) loss tangent and a $3-5\times$ improvement in the residual
resistivity over traditional BCP etching techniques. Finally, we demonstrate
transmon integration and coherent cavity control while maintaining a cavity
coherence of $11.3\text{\,}\mathrm{m}\mathrm{s}$. The accessibility of our
method, which can easily be replicated in academic-lab settings, and the
demonstration of its performance mark an advancement in 3D cQED.

##  I  Introduction

Three-dimensional (3D) superconducting cavities, which can preserve long
cavity lifetimes while maintaining high-cooperativity when coupled with a
transmon qubit, have been used to successfully construct state-of-the-art cQED
systems Reagor  _et al._ (2016). These advances have enabled universal cavity
control Heeres  _et al._ (2015, 2017) and allowed for demonstrations of
quantum error correction Ofek  _et al._ (2016); Hu  _et al._ (2019); Campagne-
Ibarcq  _et al._ (2020) and fault tolerance Reinhold  _et al._ (2020). These
ideas have been extended to multimode systems Wang  _et al._ (2016); Chakram
_et al._ (2021), demonstrating two-mode gate operations Rosenblum  _et al._
(2018); Gao  _et al._ (2019), and multimode entanglement Chakram  _et al._
(2020). In addition, 3D cQED systems have also been used for quantum chemistry
simulations Wang  _et al._ (2020), realizing topological photonic matter Owens
_et al._ (2021), and dark matter detection Dixit  _et al._ (2020); Agrawal
_et al._ (2023), demonstrating the utility of such 3D systems for applications
in quantum information and simulation.

The majority of the cavities used in the aforementioned works have been made
of aluminum, thanks to its well-behaved oxide with low dielectric and TLS loss
Reagor  _et al._ (2013), the availability of aluminum in ultra-high purity
grades ($>$5N), and its relatively straightforward etching process. Aluminum
can be consistently employed to construct seamless $\lambda/4$ co-axial
cavities with intrinsic quality factors of $>1\times 10^{8}$ Kudra  _et al._
(2020), which can easily be integrated with transmon qubits to realize cQED
systems with one millisecond coherence times Reagor  _et al._ (2016); Kudra
_et al._ (2021).

An avenue for increasing the cavity coherence times of 3D cQED systems is to
make the cavities out of bulk niobium. Elliptical niobium cavities used for
accelerator applications have recently demonstrated single-photon lifetimes of
$\tau_{\rm int}>$$2\text{\,}\mathrm{s}$ for a
$1.3\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ cavity, with loaded lifetimes of
approximately $230\text{\,}\mathrm{m}\mathrm{s}$ for a
$5.0\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ cavity after reducing TLS loss at
the surface Romanenko  _et al._ (2020a); Romanenko and Schuster (2017),
showing the potential for such cavities in creating a next-generation of
quantum memories. Recent results have also demonstrated qubit integration into
elliptical cavities without severe degradation to overall cavity performance
Milul  _et al._ (2023).

In this paper, we study the impact of niobium material properties in the
context of operating such cavities at single-photon powers and millikelvin
temperatures necessary for cQED. In particular, we delve into the impact of
etch chemistry on cavity performance, highlight the significance of air
exposure on the TLS loss tangent, and demonstrate only marginal degradation of
cavity quality due to hydride evolution when cooling to dilution temperatures.
We develop a modified etching process which consistently achieved internal
quality factors of $\mathrm{Q_{\rm int}}>1.4\times 10^{9}$ at single-photon
powers and frequencies of $f_{0}\approx\leavevmode\nobreak\
$$6.5\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, all while using the
aforementioned easy-to-implement 3D coaxial cavity design while keeping the
processing steps accessible to small-scale research labs. Finally, we
demonstrate transmon integration and coherent control of an 11.3 ms cavity
quantum memory.

Figure 1: Cavity performance survey and cavity spectroscopy (a) shows a survey
of all the cavities measured, organized by etch recipe (H3PO4 and H2O),
hermetic sealing immediately following etching, and NbHx formation
(H-disease). Solid circles represent single-photon data at
$T<$$40\text{\,}\mathrm{m}\mathrm{K}$, while solid circles represent
$\mathrm{Q_{int}}$ data at $1.2\text{\,}\mathrm{K}$. All cavities etched using
the water based buffered oxide etch show 5$\times$ improvement over H3PO4
buffered etch. The mean $\mathrm{Q_{int}}$ for all H2O BCP cavities was
1.40$\pm 0.128\times 10^{9}$. (b) Pulsed-probe spectroscopy of the cavity
highlighted in (a) by the arrow showed no power dependence in the cavity
linewidth (inset upper right) between $\bar{n}\approx 1-2000$ photons. A fit
of the data, also presented for the real and imaginary quadratures, give
$\mathrm{Q_{\rm int}}=1.47\times 10^{9}$ for all powers. Measurement setup
shown in Fig. S2.

##  II Cavity Design and Preparation

The coaxial cavity design was chosen due to its intrinsically seamless design
and ease of manufacturing. The design is made up of a section of coaxial
waveguide that is shorted at one end, leading to a $\lambda/4$ mode. This
coaxial section is coupled to a circular waveguide with a cutoff frequency
higher than the $\lambda/4$ mode, leading to evanescent loss that is
exponentially suppressed along the waveguide’s length. By machining the
coaxial section and waveguide out of a single piece of material, we can
exclude loss induced by supercurrents crossing a seam, allowing for the more
careful study of intrinsic material loss mechanisms Brecht  _et al._ (2015).

Figure 2: Quality factor dependence on etch chemistry and cooldown speed. (a)
Cavity Nb2-1 quality factor comparison between phosphoric acid and water
buffered etch. The first two etchings in H3PO4 showed only mild improvement
between successive etchings
($100\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ each). Successive water
buffered etches saw single-photon improvements of 5$\times$. An aborted
cooldown between etch 1 and 2 led to a persistent fall-off in $\mathrm{Q_{\rm
int}}$ as a function of temperature. This phenomenon is further explored in
(b), where a cavity is repeatedly held at $100\text{\,}\mathrm{K}$ for 1 hour
before being remeasured. A noticeable decrease in $\mathrm{Q_{\rm int}}$ at
high temperature is suggestive of NbH evolution in the bulk, which acts as a
magnetic loss mechanism. ToF-SIMS spectroscopy (c) of the cavity following
this shows elevated hydrogen concentrations within the London penetration
layer extending deep into the bulk, and comparatively low oxygen
concentrations after only the first 10 nm.

Following etching, rinsing and drying (Appendix A), the cavity was clamped in
between two copper flanges. The microwave coupler and top flange were
hermetically sealed using indium O-rings (see Fig. S2). The cavity was
evacuated to a pressure
$P<$$1\text{\times}{10}^{-5}\text{\,}\mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$
and sealed via a copper pinch-off tube to ensure that atmospheric gases don’t
condense on the surface and to reduce continued surface oxide formation. The
cavity was cooled to $\leq$$45\text{\,}\mathrm{m}\mathrm{K}$ in a dilution
refrigerator. A detailed discussion of the measurement setup can be found in
Appendix B.

##  III Temperature Dependence of $\mathrm{Q_{\rm int}}$

To understand the effect that etch chemistry has on performance, two buffered
chemical polish (BCP) recipes were used; one with the traditional 1:1:2 ratio
of HF:HNO3:H3PO4, and one with 1:1:2 HF:HNO3:H2O. The results, shown in Fig. 1
(a), show cavities etched using H2O based BCP had $3-5\times$ improvement in
single-photon coherence, and lower two-level system loss and residual
resistivity when compared with H3PO4. This was even true for cavities that had
previously been etched with H3PO4 BCP before being re-etched using the H2O
buffered mixture, showing that performance was not intrinsic to a cavity, but
a function of etch chemistry. This difference in performance and evidence of
the underlying mechanism is discussed in Sec. IV.

All cavities etched with H2O BCP exhibited performance in excess of $1.3\times
10^{9}$ when cooled directly after etching. Power sweeps, presented in Fig. 1
(b), showed no noticeable impact on performance from $\bar{n}\approx 1-2000$
photons (insets), suggesting weak coupling of defects to the electromagnetic
field. The measurements, done near critical coupling ($Q_{\rm int}\approx
Q_{c}$), had loaded coherence times of $\geq$$15\text{\,}\mathrm{m}\mathrm{s}$
(Fig. 1 (b)).

Achieving such high intrinsic quality factors in Nb cavities requires managing
multiple loss channels, notably magnetic loss due to niobium hydride,
dielectric loss due to surface oxide, and additional loss from impurities
introduced during etching.

By studying the temperature or power dependence of the internal quality we can
extract the two-level system loss tangent ($\delta_{TLS}$), and the residual
resistivity ($R_{s}$) simultaneously. The temperature dependence of $Q_{\rm
int}$ was used due to the linearity of the cavity at drive strengths of $\geq
2000$ photons. For these measurements the mixing chamber plate was stabilized
to a temperature accuracy of $\pm$$5\text{\,}\mathrm{m}\mathrm{K}$ prior to
conducting time-domain spectroscopy.

One noticeable source of magnetic loss are niobium hydride (NbHx) precipitates
found near the cavity surface. The species form when interstitial hydrogen
form NbHx compounds between $50-$$100\text{\,}\mathrm{K}$. These NbHx act like
a proximitized superconductor with a lower $T_{c}$ than the surrounding
niobium. Fig. 2 (a) shows the temperature dependence of cavities that have
undergone traditional H3PO4 etching, and that of water-based buffered etch on
the same cavity. Although the etching shows improvement in single-photon
performance following the H2O BCP etch, the temperature-dependent $Q_{\rm
int}$ deviates from the first etch, with a faster falloff in $Q_{\rm int}$ at
$T\geq$$200\text{\,}\mathrm{m}\mathrm{K}$, suggesting a lowering in
$\mathrm{T_{c}}$.

To systematically study this effect, a new cavity was etched using the H2O
buffer recipe and cooled. The cavity was measured before and after repeatedly
being raised to $100\text{\,}\mathrm{K}$, and cooled back down, with 10 hours
being spent between $50-$$100\text{\,}\mathrm{K}$ during each cycle.

The results, shown in Fig. 2 (b), show a monotonic decrease in quality factor
after only several temperature cycles. This is congruent with the lowering of
$\mathrm{T_{c}}$ due to NbHx formation at the surface due to the presence of
hydrogen interstitials introduced during the etching process Knobloch (2003).
Single-photon quality factor decreased by 36$\%$ over the same range. To
determine the cause, time-of-flight secondary ion mass spectroscopy (ToF-SIMS)
of the cavity’s center pin, taken post-cooldown and shown in Fig. 2 (c), shows
a large hydrogen background extending deep into the bulk. By comparison,
oxygen content becomes vanishingly small beyond $10\text{\,}\mathrm{nm}$. In
SRF cavities this effect has been well characterized, with experiment
suggesting cooldown rates in excess of 1K/min needed to avoid NbHx formation
Knobloch (2003); Antoine and Berry (2003). By comparison, all cavities in this
paper, except for Nb2-1, were initially cooled at rates of $\approx
0.3-$$0.5\text{\,}\mathrm{K}\mathrm{/}\mathrm{min}$ between
$150-$$75\text{\,}\mathrm{K}$ without significant impact on performance, even
after subsequent cooldowns, with temperature-dependent performance being
consistent with elliptical SRF Nb cavities cooled in dilution refrigerators
Romanenko  _et al._ (2020a).

Figure 3: Effect of air exposure time on oxide evolution and cavity
performance (a) temperature dependent cavity performance for cavities
hermetically sealed and placed under vacuum following etching when compared to
cavities left exposed to air for extended time. The unsealed cavity shows both
a 22$\%$ decrease in single photon performance, and 75$\%$ increase in the TLS
loss tangent ($\delta_{TLS}$). X-ray photoemission spectroscopy (b) for the
cavity directly following a water buffered etch and exposed to air for 22
days, showing the evolution of the oxide. Fitted peaks show an evolution of
Nb2O5 in that time, with an extracted increase in oxide thickness of 38$\%$ in
that time. Analysis of the sub-surface layer also suggests the continued
presence of NbHx compounds, corroborating results in Fig. 2 (b) and (c).

With NbHx evolution explored, a third cavity was cooled to better investigate
the evolution of the oxide and subsequent two-level system (TLS) loss
mechanisms during and after the H2O etching process. Niobium is known to host
TLS in its oxide layer, which is believed to be caused by the presence of NbOx
states within a disordered $\approx$$5\text{\,}\mathrm{n}\mathrm{m}$ thick
Nb2O5 surface oxide Romanenko and Schuster (2017); Premkumar  _et al._ (2021).
To quantify this the extracted temperature-dependent quality factors were fit
to the following TLS temperature model Gao  _et al._ (2008); Lei  _et al._
(2020); Romanenko  _et al._ (2020a):

$\dfrac{1}{Q_{\rm
int}(T)}=\dfrac{1}{Q_{0}}+F_{e}\tan{(\delta_{TLS})}\tanh{\bigg{(}\alpha\dfrac{\hbar\omega_{0}}{2k_{b}T}\bigg{)}}$
(1)

Where $F_{e}=t_{\rm ox}S_{e}/\epsilon_{r}$, with $S_{e}$ and $t_{\rm ox}$
being the surface to volume participation ratio of the electric field and
surface dielectric thickness respectively.
$Q_{0}=\mu_{0}\omega_{0}/R_{s}S_{m}$, where $S_{m}$ is the magnetic surface to
volume participation ratio, and $R_{s}$ is the residual surface resistivity.
The loss tangent product, $F_{e}\tan{(\delta_{TLS})}$ for the H2O buffered
process ranged from $1.8-5.3\times 10^{-10}$ when hermetically sealed within
30 minutes of etch quenching, which is as good or better than state of the art
EP etched elliptical cavities prior to additional oxide removal Romanenko  _et
al._ (2020b), and $2-4\times$ better than H3PO4 buffered etching.

To study the long-term oxide evolution and TLS loss, cavity Nb2-4 was etched
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and placed under vacuum within 30
minutes of quenching before being loaded into the refrigerator, versus the
same cavity undergoing an identical $150\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ etch and left in a lab dry box, unsealed, for 22 days before being cooled.

The results, shown in Fig. 3 (a), show a noticeable effect in both single-
photon performance and in the TLS loss tangent. The unsealed cavity exhibits a
$\approx 75\%$ higher loss tangent product ($F_{e}\tan{\delta_{TLS}}$) while
the single-photon $\mathrm{Q_{\rm int}}$ also decreased by $\approx 22\%$.
Counterintuitively, the TLS saturated $\mathrm{Q_{\rm int}}$ actually
increased, suggesting that the additional etching decreasing $\mathrm{R_{s}}$.

To investigate this evolution more closely, the unsealed and exposed Nb2-4
cavity was cut open and its surface analyzed immediately following the
cooldown. The oxide thickness and composition was analyzed using X-ray
photoelectron spectroscopy (XPS). XPS was done at varying depths using in-situ
argon ion-sputtering. Etch time versus depth was calibrated against an Nb
thin-film deposited on sapphire with an atomic force microscopy (AFM)
characterized film thickness (see Appendix D). Following initial
characterization, the cavity was re-etched and analyzed within 30 minutes of
being quenched.

To understand the relative concentrations of compounds at the surface, the XPS
spectra, shown in Fig. 3 (a), was fit for both freshly etched and unsealed
cavities that had been exposed to the atmosphere for prolonged periods of
time. The fit spectra reveal four oxidation states and the presence of NbHx,
particularly in the underlying Nb-metal surface, which are absent in the Nb
thin-film shown in Fig. S4 (c), that was etched using fluorine reactive ion
etching instead of using an acid based etch. The relative ratios of the Nb
metal phase to the Nb2O5, NbO, NbO2, and disordered NbOx suggest a structural
change in the oxide. Using techniques outlined in, Appendix E, these ratios
were also used to determine oxide thickness Premkumar  _et al._ (2021); Soda
_et al._ (2013). From the fits, the oxide layer grew by 38$\%$, from
$3.59\text{\,}\mathrm{nm}$ to $4.97\text{\,}\mathrm{nm}$. These oxide
thicknesses are comparable to previously reported values in un-annealed
electropolished (EP) cavities Romanenko and Schuster (2017); Premkumar  _et
al._ (2021). Given the linear dependence of the TLS loss-tangent with oxide
thickness, this increase does not fully account for the 75$\%$ increase in
measured loss tangent product in Fig. 3 (a). This implies that oxide
morphology and composition play a comparable role in the measured loss.

Figure 4:  Comparison of phosphoric acid and water buffered etch surface
chemistry (a) shows XPS results for the top surface and the immediate
underlying oxide layer for a test strip from a phosphoric acid buffer etched
cavity (Nb2-1). The inset shows the fitted C1s peak, with deconvolved peaks
showing the presence of organic carbon, and fluorine-containing carbon
compounds. This coincides with a noticeable F1s peak (684 eV) which persists
into the oxide layer. A small C1s peak is also present at
$0.5\text{\,}\mathrm{n}\mathrm{m}$. A test strip from the water buffered etch
of Nb2-1 shows a lack of the F1s and Fkll peaks, and a C1s peak that lacks the
asymmetry characteristic of CFx compounds.

##  IV H3PO4 vs H2O buffered etch surface chemistry

A further question is why the water buffered etch consistently performed
better than the more common phosphoric acid buffered etch. During the etch of
each cavity, a high-purity ($99.9\%$) Nb test strip was placed in the etch
solution, and was measured periodically to determine the etch rate, which
varied depending on the temperature and the amount of dissolved NbF products
in solution. The test strips from the 2nd H3PO4 buffered etch, and the 3rd H2O
buffered etch of Nb2-1 (shown in Fig. 2 (a)) were studied using XPS.

Survey scans of both test strips, shown in Fig. 4 (a) and (b), show measurable
differences in composition. For the H3PO4 buffered etch, the presence of the
flourine 1s peak ($684\text{\,}\mathrm{e}\mathrm{V}$) in (a) both at the
surface and in the oxide bulk indicates contamination from fluorine-containing
products. A careful fitting of the C 1s peak, shown in the Fig. 4 (a) inset,
corroborates this, showing the presence of CF and CF2 containing compounds. By
comparison, the H2O buffered etch shows none of these features, with only
adventitious organic carbon species at the surface, as indicated in the Fig. 4
(b) inset.

##  V Discussion

Surface analysis using XPS and ToF-SIMS shows both the significant
introduction of hydrogen to depths of $50\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and the strong dependence of exposure time to atmosphere, increased oxide
thickness, and a subsequent increase in the TLS loss of the resonator. Rapid
sealing and evacuation ($<$$90\text{\,}\mathrm{m}\mathrm{i}\mathrm{n}$) seems
to keep the TLS loss product at values comparable to electropolished Nb
elliptical cavities before any additional mid-T annealing to diffuse the oxide
Romanenko  _et al._ (2020b); Romanenko and Schuster (2017). This is notable
since the geometric participation is $\approx 3\times$ greater in the coaxial
design than the $\rm TM_{010}$ mode of an elliptical cavity, with a filling
fraction $F_{e}$ that is also $\approx 3\times$ greater than that reported for
$5\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ TESLA designs Romanenko  _et al._
(2020b). This means that, when scaled, the $R_{s}$ are within a factor of 3 of
the state-of-art Nb elliptical cavities of similar frequencies, and effective
TLS loss-tangents are between $2-5\times$ lower than normal EP treated
cavities with no additional oxide annealing Romanenko  _et al._ (2020b). XPS
analysis in Fig. 3 (a) seems to hint at the source of this discrepancy, with
the H2O BCP etched cavities showing a thin oxide
($<$$4\text{\,}\mathrm{n}\mathrm{m}$) that is largely composed of Nb2O5. The
use of HNO3, which is a strong oxidant, may preferentially produce pentoxide
over other suboxides, producing a lower-loss dielectric surface.

Another insight was the effect that hydrogen interstitials and NbHx formation
play on single-photon performance, with NbHx formation not leading to a
significant decrease in single-photon $\mathrm{Q_{\rm int}}$ at cooldown rates
between
$0.3-$$0.5\text{\,}\mathrm{K}\mathrm{/}\mathrm{m}\mathrm{i}\mathrm{n}$. While
annealing would improve $\mathrm{R_{s}}$, the above data shows a peak in
$\mathrm{Q_{\rm int}}$ at temperatures consistent with cavities that have
undergone $>$$650\text{\,}\mathrm{\SIUnitSymbolCelsius}$ annealing, suggesting
that the cavity $T_{c}$ is not noticeably affected after a single cooldown
cycle Romanenko  _et al._ (2020b).

The final point is the discrepancy between the use of H3PO4 and water as a
buffer for the etch and the effect on cavity performance. The consistently
higher residual resistance, with no noticeable change in the $T_{c}$, suggests
that the presence of fluorine at the surface, both bonded to carbon but also
to Nb, may lead to higher overall loss. Heidler et. al Heidler  _et al._
(2021), who used a nearly identical coaxial design and a similar actively
cooled H3PO4 BCP recipe, recorded nearly identical results in TLS and single-
photon performance to the highest performing H3PO4 buffer oxide etched (BOE)
cavities shown in Fig. 1 (a).

Previous analysis of electropolished Nb elliptical cavities, using an H2SO4
electrolyte, found the presence of similar CFx compounds at the surface, in
addition to hydrolyzed niobium flouride species Chouhan  _et al._ (2021). A
correlation was found between the agitation and removal of a viscous product
layer at the Nb surface, and poor post-etch rinsing, with the presence of
these surface impurities. The closed nature of the coaxial design makes
constant agitation and steady-state removal of products from the participating
surfaces difficult. By comparison, BCP etching is typically done under
constant flow for elliptical cavities Tereshkin  _et al._ (2003); Boffo  _et
al._ (2006). During regular pipetting, the viscous layer can be seen as a dark
blue (H2O BCP) or green (H3PO4 BCP) film that forms at the surface. The
difference in color, and the presence of these deleterious species in XPS
suggests that the presence of H3PO4 changes the reaction kinetics in a
meaningful way, however further investigation into the exact mechanism would
need to be undertaken.

##  VI Integration of Transmon Circuit

While the primary result of this paper was to characterize and reduce surface
loss in niobium superconducting cavities through an improved etch chemistry,
we were also able to demonstrate the preservation of cavity lifetimes even
after integrating a transmon qubit. We demonstrate the integration of a
transmon into the coaxial cavity geometry by measuring the single-photon
quality factors using a transmon ancilla. We chose to keep the dispersive
coupling small ($29\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$) to limit the
decoherence from the inverse Purcell effect via coupling to the lossy
transmon. We injected small coherent states into the cavity and observed
photon number splitting using the transmon, enabled by sufficiently large
transmon coherence
($T_{1},T_{2}=60,$$29\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{s}$),
satisfying $\chi>1/T_{2}$. By fitting the time dependence of the photon-
number-resolved qubit spectrum, we extracted a cavity lifetime of $11.3\pm
0.42$ ms at single-photon powers, which is comparable to the loaded ringdown
time of the bare cavities ($\approx$12-16 ms). The measured loss is not
limited by the participation of the cavity in either the qubit ($\approx$1/300
ms) or the readout resonator ($\approx$1/2 s), while the coupling to the drive
pin leads to a limit of ($\approx$1/25-1/100 ms). Therefore, the measured
single-photon loss is a combination of intrinsic cavity loss and additional
loss introduced by coupling to the qubit’s sapphire substrate. Details of the
qubit integration are provided in the Appendix C.

##  VII Conclusion

In summary, we have introduced a repeatable method to achieve single-photon
internal quality factors of $1.5\times 10^{9}$ using a compact coaxial cavity
design that is both easily manufacturable and readily integrated with
superconducting circuits. This achievement represents a $15\times$ improvement
over aluminum cavities of the same geometry. We also showed that NbHx does not
pose a significant threat to single-photon performance during normal cooldown
to dilution temperatures. We have also shown that, while surface oxide
evolution can degrade cavity performance, TLS loss can be minimized if the
time spent between etching and initial cooldown is kept to less than a few
hours. Moreover, we’ve demonstrated that our method surpasses traditional BCP
etching techniques in certain metrics, realizing a $2-4\times$ reduction in
TLS loss, and a $3-5\times$ improvement in $R_{s}$ in identical geometries.
This implies that the etch chemistry may be more effective in scenarios where
removing etching byproducts from the viscous surface layer is challenging.
When adjusted for geometry and frequency, our cavities’ performance is within
a factor of 3 of comparable-frequency Nb elliptical cavities, with limitations
set by dielectric loss in the oxide layer. By integrating established oxide
removal and N2 doping methods, we project at minimum a tripling in single-
photon performance. Finally, we achieve transmon integration while maintaining
high cavity and transmon lifetime and low thermal populations, and a cavity
lifetime of 11.3 ms cavity quantum memory.

Using the techniques outlined here, we hope to enable higher performance
quantum memories, and make niobium cavity manufacturing accessible to a wider
scientific audience, while also illuminating the effects of niobium surface
chemistry on superconducting RF performance at millikelvin temperature and
single-photon powers.

##  VIII Acknowledgments

###### Acknowledgements.

The authors would like to acknowledge Alexander Filatov for his assistance in
XPS analysis and Aaron Chou for his programmatic support of this project. ToF-
SIMS measurements were done with assistance from Eurofins EAG Laboratories. We
would also like to acknowledge Justin Jureller and Luigi Mazzenga for
technical assistance throughout. This work was supported by the Samsung
Advanced Institute of Technology Global Research Partnership. This work is
also supported by the U.S. Department of Energy Office of Science National
Quantum Information Science Research Centers as part of the Q-NEXT center.
Material fabrication and characterization was partially supported by the
University of Chicago Materials Research Science and Engineering Center, which
is funded by the National Science Foundation under award number DMR-2011854.
Transmon qubit devices were fabricated in the Pritzker Nanofabrication
Facility at the University of Chicago, which receives support from Soft and
Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-2025633), a node
of the National Science Foundation’s National Nanotechnology Coordinated
Infrastructure. This document was prepared using the resources of the Fermi
National Accelerator Laboratory (Fermilab), a U.S. Department of Energy,
Office of Science, Office of High Energy Physics HEP User Facility. Fermilab
is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No.
DE-AC02-07CH11359.

##  Appendix A Cavity Manufacturing and Etching

The cavity was machined out of a piece of pure niobium metal with a residual
resistivity ratio (RRR) of $\geq 300$ which conformed to ASTM B393 R04220
standards and was purchased from Ningxia Nonferrous Metals. For more even
material removal during etching, sharp edges and corners of the co-axial
design were radiused for smooth transitions. The cavity was initially
degreased using an Alconox© and DI-water mixture at temperatures
$>$$50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ under sonication. Following
this, the cavity was thoroughly rinsed in DI-water and dried using an
isopropyl alcohol (IPA) solvent exchange and dry nitrogen. A toluene-acetone-
methanol-IPA cleaning was done using semiconductor (semi) grade solvents under
sonication for $\geq$$5\text{\,}\min$ at each step, before being dried under
high-purity nitrogen that had been passed through a
$0.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ filter before being bagged in a
ISO100 clean-bag. All cavities were stored in a desiccated dry box after
cleaning and prior to etching.

Figure S1:  Etching process steps: A depiction of the primary etching steps
and layout of components. (a) shows a cartoon of the etch setup in cutaway,
depicting the copper cooling coil surrounding the primary teflon etch
containment. Below is a table of pertinent etching parameters used in this
paper. (b) depicts the quenching process and information about the quench step
in the table below. (c) depicts final DI rinsing and the solvent exchange
process used for drying. Notes about the processing steps are provided below
the tables for each step.

The top $100-$$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of the surface is
etched away to remove the damaged layer that is created from machining
processes, and to remove any contaminants that may be at the surface. Buffered
chemical polish (BCP) etching, works by first oxidizing the surface before the
oxide is etched by hydrofluoric acid (HF). Here the reaction kinetics are
primarily dependent on the relative ratios of oxidizer (HNO3) to HF, with a
buffer added to slow the reaction rate. In addition to a buffer, kinetics are
also dependent on the etch temperature and the relative concentration of
products in the solution.

The addition of an H3PO4 or H2SO3 buffer has shown reduced etch rate and
improved polishing action Kinter  _et al._ (1970); Uzel  _et al._ (1983);
Antoine  _et al._ (1999). The limiting action of the buffer is believed to be
due both to kinetics, but also the presence of a viscous product rich layer at
the Nb surface Aspart and Antoine (2004). For lower relative concentrations of
buffer, the polishing action is reduced, with selective etching occurring at
the grain boundaries Uzel  _et al._ (1983). For the commonly used 1:1:2
mixture of HF:HNO3:H3PO4 buffered chemical polished solution at an etching
temperature of $\gtrsim 10^{\circ}$C, $\approx 480-900$W of power is
dissipated per $1\text{\,}\mathrm{m}^{2}$ of Nb etched at a rate of
$\approx$1$\mu$m/min Tereshkin  _et al._ (2003); Kelly and Reid (2017).
Another important factor in final etch quality is the amount of dissolved NbF5
precipitate in the etch solution, with conventional wisdom being $<20$g/l of
dissolved Nb5+ ions in solution, with our recipe designed to have $<10$g/l for
a $\approx 100\leavevmode\nobreak\ \mu$m etch Tereshkin  _et al._ (2003);
Kelly and Reid (2017).

The etch recipe used in this paper diverges from the traditional BCP
procedure, using a 1:1:2 HF:HNO3:H2O etch chemistry. The smaller surface area
of our cavity, as listed in the Fig. S1 (a) table, means that our dissipated
power is $10\text{\,}\mathrm{W}$ for even our highest etching rates. This,
combined with the smaller volume of etchant required, means that an unbuffered
etch can be used with minimal degradation in etch quality while keeping the
reaction kinetics in a safe and manageable regime. In addition, the closed
nature of the cavity geometry, with poor acid circulation, means that higher
viscosity BCP mixtures can greatly affect the etch performance at the surface.

The main etching steps of the cavity are depicted in Fig. S1 Cav etch. A
custom Teflon© PTFE holder was built to facilitate rapid and safe transfer of
the cavity between etching step (depicted in Fig. S1). PCTFE/PVDF screws were
used to attach the cavity to the holder. The main etching was done in a
$600\text{\,}\mathrm{mL}$ PTFE beaker. The beaker was placed inside of a water
bath, and surrounded by a copper coil attached to a $400\text{\,}\mathrm{W}$
thermoelectric cooler which circulates a water/glycol mixture through the
coil. The whole water bath was set on a magnetic stirring plate to circulate
the primary acid volume. A pure niobium test strip is placed into the etch
container alongside the cavity. The strip is periodically removed, rinsed, and
thickness measured using a micrometer to check etch-rate. Fig. S1 (a) provides
a diagram of the aforementioned etch setup. To circulate the acid inside the
cavity volume, the etchant is manually exchanged using a clean polypropylene
pipette at $5-15$min intervals. Other pertinent etching parameters are listed
in the tables of Fig. S1 (a$-$c).

To prevent unwanted reaction products from adhering to the surface and leaving
residue, the etchant is manually exchanged via a pipette for the final minute
of etching, before evacuating the BCP solution and dunking it into a (UHP/Type
I) DI water bath while vigorously agitated for $\approx 1$min, quenching the
etching reaction and reducing the chance of dissolved Nb salts and fluorinated
compounds from depositing onto the surface. This step is done twice to further
dilute any residual etching solution. Pertinent parameters of this step are
presented diagrammatically and in a table in Fig. S1 (b), with water purity
tightly controlled to reduce the introduction of dissolved ions onto the
surface, with measured parameters listed in detail in both Fig. S1 (a) and
(b).

Figure S2: Measurement Setup: (a) Room temperature and cryogenic measurement
setup used to do spectroscopy and time-domain measurements of the bare storage
cavity. A Keysight PNAX was used to do both CW spectroscopy and time domain
measurements as shown in Fig. 1 (b) Shows a cross-section of the hermetically
sealed cavity, highlighting the location of indium seals at the top of the
cavity and coupler, along with the integrated pinch-off tube for hermetically
sealing the cavity following vacuum pumping of the cavity. (c) shows the
modified room temperature and cryogenic measurement setup used to take data on
the integrated cavity-qubit system. This includes the addition of a separate
coherent drive to the storage cavity and the use of an Xilinx ZCU216 RFSoC in
place of the PNAX. (d) is a picture showing the complete storage cavity,
Eccosorb filtering, and integrated readout cavity after hermetic sealing. A
detailed cutaway of the hermetic readout cavity is shown in Fig. 4 (a).

Following this initial quenching step, the cavity is rinsed under a gravity
fed stream of UHP Type-I water for $\approx$$5\text{\,}\mathrm{min}$ to remove
any stubborn contaminants. Following this the cavity undergoes a two-step
solvent exchange process. Here we use semi-grade isopropol alcohol (IPA) to
displace water, with each soak being $\approx$$5\text{\,}\mathrm{min}$.
Following this, the cavities are dried under high pressure dry nitrogen which
has undergone two-stage filtration, with the final stage being a
$0.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ filter.

Following drying the cavity is sealed. An indium ring is sandwiched between
the top of the cavity and the cap. A 3mm stainless steel tube is brazed into
the copper cap. A Swagelok VCR© fitting is brazed at the other end. A second
VCR fitting is attached to a copper pinch-off tube, allowing for easy
replacement and reuse of the cap. A Corning-Gilbert GPO (SMP) hermetic
connector (Part$\\#$ 0119-783-1) is sealed into the top of the cap via a
second indium o-ring, and allows for microwave feedthrough. An antenna is made
on the vacuum-side of the feedthrough to couple RF power into the cavity.
Because of the evanescent decay of the field energy, the coupling quality
factor $Q_{ext}$ is exponentially sensitive to this antenna distance from the
cavity center pin. The cavity is left under vacuum for
$\approx$$24\text{\,}\mathrm{h}$ before being sealed via a hydraulic pinch-off
tool and placed into the fridge. A diagram of the sealed cavity with pinch-off
tube is shown in Fig. S2 (b).

Figure S3: Qubit-Cavity integration and characterization (a) a cutaway of the
device showing the qubit mount, chip, and readout couplers, showing the
monolithic clamp used to affix the chip and provide thermalization. An indium
washer was used at the front and rear of the mount to hermetically seal the
cavity. A hermetic GPO connector with a pin extending over the stripline
readout resonator was used for qubit readout and manipulation. (b) A plot
showing qubit spectroscopy in the presence of photons in the storage cavity,
comparing two cases: (1) where the weak dispersive interaction is resolved
(orange), and (2) where the interaction is not resolved ($\chi<\kappa$). The
only change in the experimental conditions arose from modifying the coupling Q
to the readout resonator, and the resulting change in $T_{2}$ from a reduction
in photon shot noise dephasing ($Q_{c}=2400\rightarrow 20k$. Both data are fit
to the functional form obtained for a coherent state, accounting for photon
number resolved qubit peaks and including qubit and photon-number-dependent
cavity decay Gambetta  _et al._ (2006); Schuster  _et al._ (2007). Both fits
result in a $\chi\approx$ $28\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$.(c)
Qubit spectroscopy was fit to extract the population vacuum state, which was
performed as a function of the delay between the cavity drive and qubit
spectroscopy pulse to extract the T1 of the cavity.

##  Appendix B Measurement Setup

The cavity was measured in reflection ($S_{11}$). The input line uses discrete
attenuation at 4K and the mixing chamber plate (MXC) of the dilution
refrigerator, with an additional $20\text{\,}\mathrm{dB}$ of attenuation being
added at the insertion port of a Quantum Microwave cryogenic directional
coupler, giving at total of $\approx$$60\text{\,}\mathrm{dB}$ of cryogenic
attenuation. The reflected signal is sent to a Josephson-parametric amplifier
(JPA) through an additional circulator and second directional coupler, which
is used to couple the RF pump power into the JPA. Niobium titanium (NbTi)
lines then pass the signal to 4K where they are amplified via a
$4-$$8\text{\,}\mathrm{GHz}$ HEMT amplifier (Low Noise Factory model $\\#$
LNC4-8C).

The cavity is measured via a Keysight PNA-X N5242A network analyzer. The time-
domain setup is shown in Fig. S2 (a). A sequence of pulses generated
internally by the PNA-X is used to trigger high-speed
($20\text{\,}\mathrm{n}\mathrm{s}$ switching time) reflective SPDT RF switches
(Mini-circuits model $\\#$ ZASW-2-50DRA+) which pulse the PNAX outputs with
the ADC triggered internally. Ringdown measurements are performed by pulsing
on the cavity drive and sweeping a delay before turning on the ADC. The JPA RF
pump power is provided via a Signalcore SC5510A RF synthesizer, while the DC
flux was provided by an external NbTi coil, with the bias current provided by
a Yokogawa GS200 precision current source. A picture and cutaway of the
hermetically sealed coaxial cavity is shown in Fig. S2 (d), highlighting the
location of indium seals, the copper pump-out and pinch-off tube, and the
coupler location.

For integrated qubit measurements a different time-domain setup was used, and
is shown in Fig. S2 (c). An additional cavity drive line was added, while the
cryogenic RF drive and readout hardware shown in Fig. S2 (a) was moved to the
stripline readout cavity, shown in Fig. S3 (a). Coherent cavity, qubit, and
readout pulses were generated using a Xilinx ZCU216 RFSoC with the QICK
firmware Stefanazzi  _et al._ (2022). The signals were upconverted using
double-sideband mixing (Mini-circuits model $\\#$ ZX05-83-S+), following the
readout topology used in Ref. Stefanazzi  _et al._ (2022). Additional Eccosorb
filtering was added to the cavity and readout drive lines to reduce readout
cavity and qubit excited state populations and resulting shot-noise dephasing
of the qubit and the storage cavity, respectively. Fig. S2 (d) shows a picture
of the mounted cavity-qubit system attached to the thermalization brackets.
The entire device, along with the eccosorb filters, were placed inside of a
copper-lined double-layer Mu-metal shield to precent errant IR impingement.

##  Appendix C Transmon Integration and Measurements

To keep cavity performance degradation to a minimum, the qubit chip—with
integrated stripline readout—was hermetically sealed inside of an evanescent
waveguide that was inserted into the side of the cavity, as depicted in Fig.
S3 (a). Thermalization of the qubit was done via a novel one-piece mount that
held the qubit between two prongs made by cutting a $500\leavevmode\nobreak\
\mu$m slit into a copper post. A bronze-filled PTFE collet was slid over the
prongs of the clamp to provide increased clamping force while cold thanks to
its high coefficient of thermal expansion. This simplified design made sealing
the coupler, qubit mount, and waveguide section to the cavity far easier, with
indium o-rings used to create a reliable hermetic connection.

The readout was probed in reflection by coupling a GPO connector to a
stripline resonator at
$\omega_{r}=2\pi\times$$7.4\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. The qubit
frequency was set at
$\omega_{q}=2\pi\times$$3.75\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ with
$\chi_{rq}\approx$$1\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$. To maintain high
cavity coherence we drastically reduce its coupling to the transmon in order
to mitigate errors inherited from the lossy qubit. These errors include the
inverse-Purcell effect arising from the participation of the transmon in the
cavity mode ($\Gamma_{c}=\frac{g^{2}}{\Delta^{2}}\Gamma_{q}$) and cavity-
dephasing from excitations of the transmon. We set the coupling to achieve a
dispersive shift of $\chi_{sq}=$$28\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$,
resulting in a Purcell limited lifetime of $T_{p}\geq 500$ ms assuming a qubit
$T_{1}\approx\leavevmode\nobreak\ 100\leavevmode\nobreak\ \mathrm{\mu}$s.

With such a small dispersive shift, resolving the number-splitting of the
storage resonator required a narrow enough qubit linewidth ($1/T_{2}$). We
also used long spectroscopy pulses ($T_{q}\geq T_{2}$). The $T_{2}$ of the
transmon was limited by photon-shot-noise dephasing, arising from thermal
photons in the readout cavity. We reduced the dephasing from photon-shot-noise
by increasing the coupling Q of the readout cavity. Fig. S3 (b) shows qubit
spectroscopy in the presence of a cavity drive for two different qubit
linewidths, achieved by changing the readout coupling Q. Both spectra were
taken with cavity displacement drives corresponding to $\bar{n}\approx 1$
photon, and fit using the same dispersive shift but different qubit $T_{2}$s.
The qubit linewidths were obtained by first fitting the $\ket{0}$-photon qubit
peak, with peaks corresponding to higher photon numbers having an additional
photon-number-dependent broadening Gambetta  _et al._ (2006). The photon-
number states were resolved despite the weak dispersive coupling with qubit
coherence times of $T_{1},T_{2}=60,29\mu s$.

Once the cavity displacement was calibrated, the storage cavity $T_{1}$ in the
single-photon regime was obtained by displacing the cavity and measuring the
amplitude of the $\ket{0}$ qubit peak following different delay times, as
shown in Fig. 1 (c), resulting in a cavity
$T_{1}=$$11.3\text{\,}\mathrm{m}\mathrm{s}$.

##  Appendix D Surface Characterization

Figure S4:  Surface roughness and Nb film characterization: (b) A high
contrast image using a white-light confocal microscope of a post-etched
surface, showing clearly delineated crystal domain edges, with some domains
highlighted in green. (b) The distribution of the surface roughness of the
patch shown in (a) is plotted as a percentage of the total area, with the
surface roughness map shown as an inset. The data gives a surface roughness
RMS value of $1-2\mu$m across the top of the center pin. (c) The XPS spectra
of a thin-film Nb sample that was patterned and etched using reactive-ion
etching (RIE). This sample was used to calibrate the argon ion sputtering rate
and to act as a control for the Nb spectra shown in Fig. 3 (b). The sample had
been exposed to air for an extended period of time ($>$1 month) to allow for
the oxide to fully stabilize, with the surface spectra of the Nb film showing
similarities to the spectra of the cavity, following prolonged exposure to
air. By using reactive ion etching, we removed any possibility of hydrogen
diffusion into the bulk, allowing for the collection of a clean Nb 3d spectra.
By comparison, the Nb 3d bulk data shown in Fig. 3 (b) shows a distinct lack
of definition due to the formation of NbHx compounds.

We performed measurements of surface roughness, as well as the composition of
lossy dielectric and conductive compounds within the London penetration depth
of the niobium. The surface roughness measurements were performed using an
Olympus OLS5000 laser confocal microscope with a 50x objective and a $405$nm
scanning light source capable of $1\text{\,}\mathrm{n}\mathrm{m}$
$z$-resolution. Fig. S4 (a) shows a white-light image of the center pin
surface following etching, with green used to highlight several crystal
domains. The material used showed a fairly fine-grain crystal structure, with
delineated domains ranging in size from $10-50\leavevmode\nobreak\ \mu$m. A 3D
scan of this region gave an arithmetic surface roughness of $R_{a}\approx
2\leavevmode\nobreak\ \mu$m. Several other regions studied showed surface
roughness ranging from $1-2\leavevmode\nobreak\ \mu$m, which is comparable to
values seen in the literature for BCP-treated polycrystalline Nb cavities, and
at least an order of magnitude higher than EP etched cavities Antoine  _et
al._ (1999) over the same surface area. Fig. S4 (b) provides a color
$z$-height map of (a) (inset), with a distribution of these deviations as a
percentage of area, showing a peak centered at $\approx
1.6\leavevmode\nobreak\ \mu$m of surface roughness.

The compositions of both surface oxides and the underlying niobium metal were
determined using X-ray photoemission spectroscopy (XPS). Analysis was
performed on a Kratos Axis Nova spectrometer using a monochromatic Al
K$\alpha$ source (1486.6 eV). Nb 3d, C 1s, and O 1s high-resolution spectra
were collected using an analysis area of $0.3\times 0.7$ mm and 20 eV pass
energy with the step size of 100 meV. The survey spectra were collected using
100 eV pass energy. Charge neutralization was performed using a co-axial, low
energy ($\approx$ 0.1 eV) electron flood source to avoid shifts in the
recovered binding energy. The C 1s peak of adventitious carbon was set at
284.8 eV to compensate for any remaining charge-induced shifts. Deconvolution
of the high-resolution XPS spectra was performed in CasaXPS software using
Lorentzian asymmetric curves for the Nb metal phase, symmetric Gaussian-
Lorentzian curves for all other elements’ fitting, and a Shirley fitting for
the background. The Nb 3d region consists of the two 3d5/2 and 3d3/2 spin-
orbit split components. The peak area ratio of 3d5/2 to 3d3/2 was fixed to
3:2. The Nb 3d region was fit using six doublet components (Nb metal, Nb2O5,
NbO2, NbO, NbOx, NbHx) of 3d5/2 and 3d3/2 components for each sample. The
energy splitting of each doublet component is 2.7 eV.

Figure S5: XPS Parameters Table for Nb2-4 and Nb Thin Film analysis: A table
showing the peak positions and fitting parameters used in the surface scan of
Nb2-4. These fit values were used in the XPS peak fitting shown in Fig. 3 (b)
and Fig. S4 (c).  Figure S6: Depth profile and extracted oxide thickness: (a)
A plot of niobium metal and oxygen concentration based on XPS analysis. Each
sputter cycle is 15 seconds, giving a cumulative etch of
$0.47\text{\,}\mathrm{n}\mathrm{m}$ per sputter cycle. Longer air exposure
requires more sputter cycles before reaching a stable value, indicating a
thicker oxide. (b) A table summarizing the relative thickness of various oxide
species using Eq. 2. The calculated values predict a systematically lower
value when compared with the direct observation, however the difference is
bound by the precision of the depth profiling shown in (a), with a maximum
depth resolution of $0.47\text{\,}\mathrm{n}\mathrm{m}$.

A $5\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ monatomic argon ion sputter
system was used to etch the surface in-situ, allowing for depth profiling of
the oxide thickness and characterization of deleterious compounds near the
surface. To estimate the etch rate of the argon-ion sputter system, an Nb
thin-film sample, with a well-characterized thickness was used. The Nb thin
film was confirmed to be $73$ nm thick by Atomic Force Microscopy (AFM) on a
Bruker Dimension Icon AFM instrument. The argon ion sputter time was 3 min per
cycle, and after 11 cycles the Al peaks from the sapphire substrate became
dominant, setting a nominal etch rate of
$0.3-$$0.4\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\sec$. For the data
presented in Fig. S6, a fine sputter of $15\text{\,}\mathrm{s}$ per cycle was
used. Results of the XPS on the Nb thin film control sample are presented in
Fig. S4 (c). This sample, which was etched using a CF4 plasma, and exposed to
air for $>1$ month, shows a surface oxide composition similar to that of the
Nb2-4 cavity shown in Fig. 3 (b) after exposure for more than 3 weeks. Bulk
analysis of the thin film however shows a deviation from the measured cavity
samples. The Nb 3d peaks are far more resolved, with no sign of NbHx in the
fitted spectra, further highlighting the effects of wet etching on the
presence of hydrogen impurities in the bulk.

##  Appendix E Nb oxide thickness analysis

Two methods were used to determine the thickness of the niobium oxide layer.
The first, ”direct” method, was to directly measure Nb-oxide peaks for various
sputter times and extract an approximate thickness based on the depletion of
oxygen, while the second used relative peak intensities to indirectly
determine the oxide thickness. For indirect thickness estimation, the peak
intensities ($I_{0}/I_{m}$) ratio of the Nb 3d oxide phases to the Nb metal
phase is used to calculate the oxide thickness at the surface. The surface
oxide thickness, $d_{xps}$(nm), was estimated using the equation Alexander
_et al._ (2002); Grundner and Halbritter (1980); Antoine  _et al._ (1999).

$d_{xps}(nm)=\lambda\sin\theta\ln{\bigg{(}\frac{N_{m}\lambda_{m}I_{o}}{N_{o}\lambda_{o}I_{m}}+1\bigg{)}}$
(2)

Where the ratio of the volume densities of Nb atoms in metal to different
oxide phases ($N_{m}/N_{o}$) are listed in Fig. S5. The inelastic mean free
path (IMFP) values, $\lambda$, for Nb2O5, NbO2, and NbO can be found in Ref.
Powell and Jabolonski (2011). These values are specified normal to the surface
($\theta$= 90∘) of the Kratos Axis Nova XPS instrument, which has an angle of
45∘ between the X-ray source and the axis of the electron lens. For direct
determination, a fine sputter etch (15 s per cycle) was used, with the cycle
repeated until the relative concentrations of both niobium and oxygen reached
a constant value. Fig. S6 (a) shows the niobium and oxygen concentrations from
the survey scans as a function of sputter cycle. By 11 cycles the 3 week air
exposed cavity show stable concentrations of oxygen and niobium, while the
cavity exposed to air for 30 minutes reaches a stable value in 8 sputter
cycles. Using the calibration in Appendix. D, this gives a directly measured
oxide thickness of $5.249\text{\,}\mathrm{n}\mathrm{m}$ and
$3.818\text{\,}\mathrm{n}\mathrm{m}$ for 3 week and 30 minute air exposure
respectively. The Nb oxide thickness extracted via the indirect method was
determined to be $4.974\text{\,}\mathrm{n}\mathrm{m}$ and
$3.589\text{\,}\mathrm{n}\mathrm{m}$ for 3 weeks and 30 minutes respectively.
The estimated oxide thickness from the Nb thin film used for sputter
calibration in Appendix. D, and Nb cavities with different air exposure
duration are shown in the Fig. S6 (b) table, along with the relative
thicknesses of the three Nb oxidation states (NbO, NbO2, and Nb2O5).

In both the direct and indirect measurement of oxide thickness, the total
change corresponded to an $\approx$38$\%$ increase in thickness. The effective
loss tangent product $F_{e}\tan{\delta_{TLS}}$ is proportional to thickness.
The fit of the loss tangent data, shown in Fig. 3 suggests a 75$\%$ increase,
suggesting that the relative composition plays an equally important roll in
enhancing dielectric loss. The indirect fit method shows that the relative
thickness of the Nb2O5 grew by $\approx 88\%$ while the NbO2 and NbO species
decreased in relative thickness. This may suggest that Nb2O5 may play an
outsize role in harboring two-level systems. It may also suggest that slow
oxide evolution in the presence of air may yield an oxide layer with defects
capable of harboring two-level systems. In either case, further investigation
would be required.

## References

  * Reagor  _et al._ (2016) M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, _et al._ , Physical Review B 94, 014506 (2016).
  * Heeres  _et al._ (2015) R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Physical review letters 115, 137002 (2015).
  * Heeres  _et al._ (2017) R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Nature communications 8, 1 (2017).
  * Ofek  _et al._ (2016) N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. Girvin, L. Jiang, M. Mirrahimi, M. J. Devoret, and R. J. Schoelkopf, Nature 536, 441 (2016).
  * Hu  _et al._ (2019) L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. Song, C.-L. Zou, S. M. Girvin, L.-M. Duan, and L. Sun, Nature Physics 15, 503 (2019).
  * Campagne-Ibarcq  _et al._ (2020) P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. Frattini, V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. Schoelkopf, _et al._ , Nature 584, 368 (2020).
  * Reinhold  _et al._ (2020) P. Reinhold, S. Rosenblum, W.-L. Ma, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Nature Physics , 1 (2020).
  * Wang  _et al._ (2016) C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. Sliwa, _et al._ , Science 352, 1087 (2016).
  * Chakram  _et al._ (2021) S. Chakram, A. E. Oriani, R. K. Naik, A. V. Dixit, K. He, A. Agrawal, H. Kwon, and D. I. Schuster, Phys. Rev. Lett. 127, 107701 (2021).
  * Rosenblum  _et al._ (2018) S. Rosenblum, Y. Y. Gao, P. Reinhold, C. Wang, C. J. Axline, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, , and R. Schoelkopf, Nature communications 9, 1 (2018).
  * Gao  _et al._ (2019) Y. Y. Gao, B. J. Lester, K. S. Chou, L. Frunzio, M. H. Devoret, L. Jiang, S. Girvin, and R. J. Schoelkopf, Nature 566, 509 (2019).
  * Chakram  _et al._ (2020) S. Chakram, K. He, A. Dixit, A. Oriani, R. Naik, N. Leung, H. Kwon, W.-L. Ma, L. Jiang, and D. Schuster, arXiv:2010.15292 (2020).
  * Wang  _et al._ (2020) C. S. Wang, J. C. Curtis, B. J. Lester, Y. Zhang, Y. Y. Gao, J. Freeze, V. S. Batista, P. H. Vaccaro, I. L. Chuang, L. Frunzio, L. Jiang, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. X 10, 021060 (2020).
  * Owens  _et al._ (2021) J. C. Owens, M. G. Panetta, B. Saxberg, G. Roberts, S. Chakram, R. Ma, A. Vrajitoarea, J. Simon, and D. Schuster, “Chiral cavity quantum electrodynamics,”  (2021).
  * Dixit  _et al._ (2020) A. V. Dixit, S. Chakram, K. He, A. Agrawal, R. K. Naik, D. I. Schuster, and A. Chou, arXiv:2008.12231 (2020).
  * Agrawal  _et al._ (2023) A. Agrawal, A. V. Dixit, T. Roy, S. Chakram, K. He, R. K. Naik, D. I. Schuster, and A. Chou, “Stimulated emission of signal photons from dark matter waves,” (2023), arXiv:2305.03700 [quant-ph] .
  * Reagor  _et al._ (2013) M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, App. Phys. Lett. 102, 192604 (2013).
  * Kudra  _et al._ (2020) M. Kudra, J. Biznárová, A. Fadavi Roudsari, J. Burnett, D. Niepce, S. Gasparinetti, B. Wickman, and P. Delsing, Applied Physics Letters 117, 070601 (2020).
  * Kudra  _et al._ (2021) M. Kudra, M. Kervinen, I. Strandberg, S. Ahmed, M. Scigliuzzo, A. Osman, D. P. Lozano, G. Ferrini, J. Bylander, A. F. Kockum, F. Quijandría, P. Delsing, and S. Gasparinetti, “Robust preparation of wigner-negative states with optimized snap-displacement sequences,” (2021), arXiv:2111.07965 [quant-ph] .
  * Romanenko  _et al._ (2020a) A. Romanenko, R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. Grassellino, Physical Review Applied 13, 034032 (2020a).
  * Romanenko and Schuster (2017) A. Romanenko and D. I. Schuster, Phys. Rev. Lett. 119, 264801 (2017).
  * Milul  _et al._ (2023) O. Milul, B. Guttel, U. Goldblatt, S. Hazanov, L. M. Joshi, D. Chausovsky, N. Kahn, E. Çiftyürek, F. Lafont, and S. Rosenblum, (2023), arXiv:2302.06442 [quant-ph] .
  * Brecht  _et al._ (2015) T. Brecht, M. Reagor, Y. Chu, W. Pfaff, C. Wang, L. Frunzio, M. H. Devoret, and R. J. Schoelkopf, Applied Physics Letters 107, 192603 (2015), https://doi.org/10.1063/1.4935541 .
  * Knobloch (2003) J. Knobloch, AIP Conference Proceedings 671, 133 (2003), https://aip.scitation.org/doi/pdf/10.1063/1.1597364 .
  * Antoine and Berry (2003) C. Z. Antoine and S. Berry, AIP Conference Proceedings 671, 176 (2003), https://aip.scitation.org/doi/pdf/10.1063/1.1597367 .
  * Premkumar  _et al._ (2021) A. Premkumar, C. Weiland, S. Hwang, B. Jäck, A. P. M. Place, I. Waluyo, A. Hunt, V. Bisogni, J. Pelliciari, A. Barbour, M. S. Miller, P. Russo, F. Camino, K. Kisslinger, X. Tong, M. S. Hybertsen, A. A. Houck, and I. Jarrige, Communications Materials 2, 72 (2021).
  * Gao  _et al._ (2008) J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas, B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc, Applied Physics Letters 92, 152505 (2008), https://doi.org/10.1063/1.2906373 .
  * Lei  _et al._ (2020) C. U. Lei, L. Krayzman, S. Ganjam, L. Frunzio, and R. J. Schoelkopf, Applied Physics Letters 116, 154002 (2020).
  * Romanenko  _et al._ (2020b) A. Romanenko, R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. Grassellino, Phys. Rev. Applied 13, 034032 (2020b).
  * Soda  _et al._ (2013) K. Soda, H. Kondo, M. Kato, T. Shiraki, K. Niwa, K. Kusaba, M. Hasegawa, and E. Ikenaga, Journal of Electron Spectroscopy and Related Phenomena 186, 54 (2013).
  * Heidler  _et al._ (2021) P. Heidler, C. M. F. Schneider, K. Kustura, C. Gonzalez-Ballestero, O. Romero-Isart, and G. Kirchmair, Phys. Rev. Applied 16, 034024 (2021).
  * Chouhan  _et al._ (2021) V. Chouhan, S. Kato, Y. Ida, K. Nii, T. Yamaguchi, and H. Hayano, Materials Chemistry and Physics 259, 124044 (2021).
  * Tereshkin  _et al._ (2003) Y. Tereshkin, C. Boffo, G. Davis, H. Edwards, and A. Rowe, in  _11th Workshop on RF Superconductivity (SRF 2003)_ (2003).
  * Boffo  _et al._ (2006) C. Boffo, C. Cooper, A. Rowe, and G. Galasso (Linear Collider), Conf. Proc. C 060626, 469 (2006).
  * Kinter  _et al._ (1970) M. L. Kinter, I. Weissman, and W. W. Stein, Journal of Applied Physics 41, 828 (1970), https://doi.org/10.1063/1.1658770 .
  * Uzel  _et al._ (1983) Y. Uzel, K. Schnitzke, and N. Krause, Applied Physics A 30, 185 (1983).
  * Antoine  _et al._ (1999) C. Antoine, A. Aspart, M. Berthelot, J. Poupeau, F. Valin, and Y. Gasser,  _Morphological and chemical studies of Nb samples after various surface treatments_ , Tech. Rep. (SIS-2002-103, 1999).
  * Aspart and Antoine (2004) A. Aspart and C. Antoine, Applied Surface Science 227, 17 (2004).
  * Kelly and Reid (2017) M. Kelly and T. Reid, Superconductor Science and Technology 30, 043001 (2017).
  * Gambetta  _et al._ (2006) J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Physical Review A 74, 042318 (2006).
  * Schuster  _et al._ (2007) D. Schuster, A. Houck, J. Schreier, A. Wallraff, J. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. Devoret, S. Girvin, and R. Schoelkopf, Nature 445, 515 (2007).
  * Stefanazzi  _et al._ (2022) L. Stefanazzi, K. Treptow, N. Wilcer, C. Stoughton, C. Bradford, S. Uemura, S. Zorzetti, S. Montella, G. Cancelo, S. Sussman, A. Houck, S. Saxena, H. Arnaldi, A. Agrawal, H. Zhang, C. Ding, and D. I. Schuster, Review of Scientific Instruments 93, 044709 (2022), https://pubs.aip.org/aip/rsi/article-pdf/doi/10.1063/5.0076249/16607898/044709_1_online.pdf .
  * Alexander  _et al._ (2002) M. R. Alexander, G. E. Thompson, X. Zhou, G. Beamson, and N. Fairley, Surface and Interface Analysis 34, 485 (2002).
  * Grundner and Halbritter (1980) M. Grundner and J. Halbritter, Journal of Applied Physics 51, 397 (1980), https://doi.org/10.1063/1.327386 .
  * Powell and Jabolonski (2011) C. Powell and A. Jabolonski,  (2011), 10.18434/T4MK5P.