††thanks: These authors contributed equally to the work††thanks: These authors
contributed equally to the work

# Quasiparticle dynamics in a superconducting qubit irradiated by a localized
infrared source

R. Benevides1,2 M. Drimmer1,2 G. Bisson1,2 F. Adinolfi1,2 U. v. Lüpke1,2 H. M.
Doeleman1,2 G. Catelani3,4 Y. Chu1,2 1Department of Physics, ETH Zürich, 8093
Zürich, Switzerland  2Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
3Jülich Aachen Research Alliance (JARA) Institute for Quantum Information
(PGI-11), Forschungszentrum Jülich, Jülich 52425, Germany  4Quantum Research
Center, Technology Innovation Institute, Abu Dhabi 9639, United Arab Emirates

###### Abstract

A known source of decoherence in superconducting qubits is the presence of
broken Cooper pairs, or quasiparticles. These can be generated by high-energy
radiation, either present in the environment or purposefully introduced, as in
the case of some hybrid quantum devices. Here, we systematically study the
properties of a transmon qubit under illumination by focused infrared
radiation with various powers, durations, and spatial locations. Despite the
high energy of incident photons, our observations agree well with a model of
low-energy quasiparticle dynamics dominated by trapping. This technique can be
used for understanding and potentially mitigating the effects of high-energy
radiation on superconducting circuits with a variety of geometries and
materials.

The quantum coherence of superconducting (SC) circuits has steadily improved
in recent years [1, 2, 3, 4]. This has enabled them to not only become one of
the leading quantum information processing platforms, but also a crucial
ingredient in a variety of hybrid devices aiming to combine superconducting
circuits with other quantum systems [5, 6]. However, understanding and
mitigating the sources of decoherence in SC circuits is still an important
effort in this field, particularly when considering hybrid systems where new
components and degrees of freedom are introduced.

One significant decoherence mechanism is the breaking of Cooper pairs in the
superconductor, creating so-called quasiparticles [7, 8, 9]. The presence of
quasiparticles can lead to both energy relaxation and dephasing of qubits [10,
11, 12, 13, 14, 15]. The first of these effects was studied using controlled
injection of quasiparticles near Josephson junctions with microwave drives
[16, 17]. It has also been shown that quasiparticles generated by high-energy
particles, such as high-energy photons or the products of radioactive decay
[18], can even result in correlated errors between multiple qubits [19, 20],
which is especially detrimental for quantum error correction protocols [21].

In an effort to mitigate these detrimental effects, previous studies have
focused on shielding SC circuits from environmental high-energy radiation [22,
23, 18, 24]. However, quasiparticle densities measured are still orders of
magnitude higher than predicted at thermal equilibrium [25, 26]. In addition,
hybrid devices such as microwave-optical quantum transducers require the
introduction of a large number of optical photons near SC circuits, which can
lead to significant additional decoherence that degrades the transducer’s
performance [27, 28, 6, 29].

In this work, we use a complementary approach that introduces, on purpose,
high-energy radiation in the vicinity of a SC circuit. Specifically, we direct
a telecom-band laser beam onto a three-dimensional (3D) aluminum transmon
qubit device [1] in a controllable manner in order to systematically
investigate the impact of the incident photons on qubit properties. We are
able to vary not only the power and duration but also the location of the
focused laser beam relative to the qubit. With this method, we demonstrate
unprecedented temporal and spatial control over the generation of
quasiparticles. We show that the transmon’s excited state lifetime is modified
by the incident light, but recovers about an order of magnitude faster than in
previous experiments with microwave induced quasiparticles [16]. We find that
the recovery dynamics of the qubit coherence follows a universal dependence on
the incident energy and that it is well described by a model of quasiparticle
population decay through trapping and recombination [16]. Moreover,
measurements of $T_{2}^{*}$ allow us to test the contribution of
quasiparticle-induced pure dephasing to the qubit decoherence, which, in
agreement with theoretical models [13, 30], is smaller than the contribution
from induced energy decay.

##  I Experimental design

Our device consists of an aluminum transmon qubit on a sapphire substrate
situated in a 3D aluminum microwave cavity at the base plate of a dilution
refrigerator operating around 10 mK. 0.5 mm wide holes in the walls of the
cavity allow laser light to enter and exit the cavity, as seen in Fig. 1(a).
Light from a 1550-nm-wavelength laser is guided into the dilution refrigerator
via an optical fiber and focused into the cavity to a beam waist of 47 $\mu$m
at the plane of the qubit. Variable optical attenuators (VOAs) and a fiber-
coupled acousto-optic modulator (AOM) are used to control the power and
duration of the laser pulses. At the base plate of the dilution refrigerator,
the fiber is glued to an input lens and mounted on a motorized tip-tilt stage
that allows us to change the position of the focused laser spot with respect
to the qubit. A multimode fiber coupler with a high numerical aperture is used
to collect the light that exits on the other side of the microwave cavity.
This light is then directed out of the fridge and measured with a photodiode.
By changing the position of the laser beam and measuring the transmitted
light, we can take low-resolution images that we use to position the laser
beam relative to the qubit (see Supplementary Material [31], sections C and
D).

Figure 1:  Schematic of the setup. (a) An infrared laser beam enters its
microwave cavity via holes in the walls, reaching the qubit chip. Transmitted
light is sent to a collimator (output fiber) and used to construct a low-
resolution picture of the qubit. (b) Diagram of the three positions of the
laser beam used in this work, labeled A, B, and C.

We performed measurements with three different laser beam locations during a
single cooldown, as shown in Fig. 1(b): In position A, the laser is focused
directly onto the metal pad of the qubit. In position B, the laser is focused
on the bottom edge of the qubit pad. In position C, the laser is focused on
the transparent sapphire substrate, approximately $200~{}\mu$m below the
qubit.

The typical individual photon energy ($h\times 193.4$ THz) in the infrared
regime is orders of magnitude larger than the superconducting bandgap
$2\Delta$ of aluminum ($\Delta=h\times 46.9$ GHz, for thin-film aluminum [1]).
An infrared photon impinging on the device creates high-energy excitations in
the superconducting film and substrate, which are converted into a large
number of low-energy quasiparticles through a cascading microscopic process
consisting of scattering interactions involving phonons, electrons, and other
quasiparticles [32]. The number of low-energy quasiparticles then decreases
over time due to two main processes: First, quasiparticles can be individually
trapped at the edges of the superconductor or in vortices caused by residual
magnetic fields. Second, these electronic excitations can recombine into
Cooper pairs, releasing their energy mostly via phonon creation and returning
to the superconducting condensate [33].

The light-induced quasiparticle density in the vicinity of the transmon’s
Josephson junction $x_{\text{qp}}^{\text{in}}$ can be directly inferred from
the measured decay rate $\Gamma$ of the transmon’s excited state via
$\Gamma=Cx_{\text{qp}}^{\text{in}}+\Gamma_{0}$. Here
$C=\sqrt{2\omega_{\text{q}}\Delta/\pi^{2}\hbar}$, where $\omega_{\text{q}}$ is
the frequency of the qubit transition and $\Delta$ is the superconducting
energy gap [10]. $\Gamma_{\text{0}}$ is the intrinsic decay rate of the qubit
in the absence of laser light, which can be due to a constant background
quasiparticle density in the material or other sources of decay such as
dielectric loss. In our experiment, we measure the qubit energy relaxation
time $T_{1}=1/\Gamma$, from which we extract $x_{\text{qp}}^{\text{in}}$ using
$C\approx 2\pi\times 7.74$ GHz and $\Gamma_{0}$ measured in the absence of
laser light. Measurements using a continuous wave (CW) laser then allow us to
observe the effect of absorbed light on the steady-state quasiparticle
density, while measurements using a laser pulse allow us to study the recovery
dynamics of $T_{1}$ over the timescales in which quasiparticles are trapped or
recombine [16].

##  II Results

Measuring the qubit properties in the presence of a CW laser, we find that an
increase in the laser power $P_{\text{opt}}$ incident on the qubit leads to a
shorter $T_{1}$, as shown in Fig. 2(a). The data is fitted to a model where
the light-induced quasiparticle density depends linearly on the optical power,
i.e, $x_{\text{qp}}^{\text{in}}=\mu P_{\text{opt}}$, with $\mu$ being a
conversion constant between optical power and quasiparticle density. We
provide more information about our model in section B of the Supplementary
Material [31].

Figure 2:  Measurements with CW laser radiation. (a) $T_{1}$ times as a
function of laser power, for position A (laser on the qubit), position B
(laser at the edge of the qubit pad), and position C (laser far from the
qubit). The power axes are scaled for positions A and B by the ratios of the
fitted proportionality constants at each position compared to position C (not
scaled), i.e., $\mu_{\text{A}}/\mu_{\text{C}}\approx 59$ and
$\mu_{\text{B}}/\mu_{\text{C}}\approx 544$ respectively, to show their similar
behavior. Inset: Same data, without scaling the power axes. (b) Decay rate of
the qubit and the corresponding calculated induced quasiparticle density as a
function of power for the laser in positions A, B, and C, illustrating the
linear dependence of $\Gamma$ with the optical power. Power axes of positions
A and B are scaled by the same ratios as in (a). (c) Ramsey measurement of the
decoherence time (circles), $2T_{1}$ (solid line), and inferred dephasing time
(squares), for the three different positions. We observe that the decoherence
times tend to be dominated by decay ($T_{2}^{*}\sim 2T_{1})$ for high powers
in all three positions. (d) Shift of the qubit frequency from its value with
the laser turned off. All three positions show a linear reduction in the qubit
frequency, consistent with an increase in $x_{\text{qp}}^{\text{in}}$. The
power axes are again scaled for positions A and B, using the same ratios as in
(a). In (a) and (d), the error bars in each data point represent the standard
deviation of ten sequential measurements; in (b) the error bars are propagated
from data in (a); in (c), the error bars are calculated using ten sequential
measurements and propagation of the error bars in (a).

We perform this measurement with the laser located in positions A, B, and C
and find a hierarchy of photon-quasiparticle conversion constants given by
$\mu_{\text{B}}=(1.61\pm 0.06)\times
10^{-5}~{}\text{nW}^{-1}>\mu_{\text{A}}=(1.75\pm 0.09)\times
10^{-6}~{}\text{nW}^{-1}>\mu_{\text{C}}=(2.96\pm 0.07)\times
10^{-8}~{}\text{nW}^{-1}$. Position C is the least sensitive to the optical
power, which is unsurprising since the laser is focused on the substrate.
While most of the light passes through or is specularly reflected at the
sapphire-air interfaces and exits through the cavity holes, some diffusely
scattered light can remain in the cavity and eventually impinge on the qubit.
We discuss the possible creation of phonons in the substrate in section III.
Position A shows a higher sensitivity of $T_{1}$ to the optical power than
position C since we are shining the light directly onto the superconducting
film. However, since the reflectivity of the Al film at 1550 nm is 97.5$\%$,
we believe that most of the light is reflected backwards and leaves the qubit
environment through the input hole of the cavity.

Surprisingly, we find that when the laser is focused at the edge of the qubit
(position B), $T_{1}$ is more sensitive to laser power than the other two
cases, including position A. We speculate that this is because light incident
at the border of the qubit diffracts, leading to more photons scattered toward
the qubit or remaining in the 3D cavity instead of exiting through the holes.
Therefore, an effectively higher number of photons are absorbed by the
superconductor and a more pronounced effect is observed when compared to the
other two scenarios. As can be seen in Fig. 2(b), the qubit decay rate and
inferred $x_{\text{qp}}^{\text{in}}$ have a linear dependence on the laser
power for the three positions, and therefore all three datasets can be
collapsed onto a universal curve when the incident power is scaled by the
appropriate ratio of photon-quasiparticle conversion constants.

Figure 3:  Time-resolved measurements at position A. (a) Protocol for
measurement of qubit $T_{1}$ after a laser pulse. (b) Measurement of the qubit
decay rate as a function of variable delay time $\tau_{\text{opt}}$. Here, we
use a $10~{}\mu$s long laser pulse with an optical power of $1~{}\mu$W.
Insets: Qubit ground state population as a function of time for two different
$\tau_{\text{opt}}$. (c) Qubit decay rate as a function of $\tau_{\text{opt}}$
for different optical powers. The data for four powers that span five orders
of magnitude are highlighted. (d) Initial injected quasiparticle density
$x_{\text{qp}}^{\text{in}}$ as a function of pulse power, obtained from
fitting the data in (c). The dashed line is a linear fit to the data where
$P_{opt}\leq$ 0.1 $\mu$W. Error bars in (b) and (c) represent the standard
deviation of measurements, while in (d), they represent the propagated error
using our model and the estimated trapping and recombination constants.

While quasiparticles have already been demonstrated as an important source of
qubit decay, their effects on the decoherence times of the qubits have not
been studied as extensively [12]. In Fig. 2(c), we show the effect of light-
induced quasiparticles on the $T_{\text{2}}^{*}$ decoherence times of our
qubit. We can separate the decoherence into two contributions via
$1/T_{\text{2}}^{*}=1/T_{\phi}+1/(2T_{\text{1}})$,where $T_{\phi}$ is the pure
dephasing time. We see that, in the three different positions,
$T_{\text{2}}^{*}$ decreases with higher optical powers. However, when
compared to the $2T_{1}$ curve obtained from the fits in Fig. 2(a), we see
that while the $T_{\text{2}}^{*}$ is not $T_{1}$ limited for smaller powers,
it becomes more so for higher powers. We also observe a decrease in the
$T_{\phi}$ of the qubit, but the decrease is smaller than that of $T_{1}$.
This indicates that at high powers, the $T_{\text{2}}^{*}$ becomes
increasingly limited by energy relaxation rather than light-induced
quasiparticle dephasing.

Finally, from the Ramsey measurements, we also extract the quasiparticle-
induced qubit frequency shift, $\delta\omega_{q}$, as a function of the
optical power. Fig. 2(d) shows a reduction in the qubit frequency with higher
powers. As described in [10], a reduction in the qubit frequency is another
indication of an increase in the quasiparticle density, given the lack of
Andreev bound states in a Josephson junction-based transmon. We observe that
the frequency shift is negative and linear in the optical power applied, as
one would expect from a model of quasiparticle injection (see Equation 73 of
Ref. [10]). Our linear fits in Fig. 2(d) yield slopes which are on average
17$\%$ $\pm$ 6$\%$ smaller in absolute value than those expected from theory,
when we convert the optical powers to quasiparticle densities. Deviations from
the model of this magnitude have been previously observed in Ref. [16]. Based
on the results of‘[34], the smaller slopes could be indicative of
quasiparticle heating, but it should be noted that the regime considered there
- resonators with a high number of photons below the bandgap - is quite
different from the one explored in this work.

After performing experiments with a CW laser, we move to a pulsed regime to
study the recovery of qubit lifetime after quasiparticle creation. In Fig.
3(a), we show the basic protocol we use for this experiment. We use the AOM to
create laser pulses with controllable pulse lengths and repetition rates.
After the pulse is sent to the qubit, we wait a variable delay time
$\tau_{\text{opt}}$ and perform a $T_{1}$ measurement.

A typical measurement result is shown in Fig. 3(b). Here, we focus on data for
the laser located at position A, but similar results are obtained for the
laser in the other positions. In the first hundreds of microseconds, we cannot
measure the qubit decay rate for higher powers, due to short $T_{1}$ times
[29]. After a certain time that depends on the pulse energy, we are able to
measure a $T_{\text{1}}$ decay curve, as we show in the inset for the first
point in Fig. 3(b). Afterward, we observe a continuous decrease in $\Gamma$
until it reaches an asymptote at $\Gamma_{0}$.

We perform this experiment for a large set of optical powers while keeping the
optical pulse length fixed at $10~{}\mu$s. In Fig. 3(c), we show data for a
range of five orders of magnitude in the incident optical power. All plots
follow a similar behavior, with an initial higher $\Gamma$, followed by a
decline that lasts somewhere between a few hundreds of microseconds to
slightly more than one millisecond. Since we use an extensive set of data,
taken over several days of measurements, we observe different final asymptotes
for the decay rates, which we associate with typical fluctuation observed in
the $T_{1}$ times of the qubit [35]. To understand the physical origin of the
coherence recovery, we fit the data for each power to a model that includes
trapping and recombination as possible sources of quasiparticle density
decrease. Detailed analysis of the fitting parameters leads us to conclude
that we can use a model with a quasiparticle trapping constant of $s=9\pm 2$
kHz and no recombination, as discussed in sections B and H of the
Supplementary Material [31]. This allows us to conclude that we are in a
trapping-dominated regime, leading to an exponential recovery of the qubit
decay rate

$\Gamma(\tau_{\text{opt}})=Cx_{\text{qp}}^{\text{in}}e^{-s\tau_{\text{opt}}}+\Gamma_{0},$
(1)

as we observe in Fig. 3(b). We use this model to extract the injected
quasiparticle density at $\tau_{\text{opt}}=0$ for each laser power. We show
the obtained values in Fig. 3(d), where we see a clear increase in
$x_{\text{qp}}^{\text{in}}$ with optical power. At low optical powers, this
increase follows a linear trend, while at higher powers the relationship
becomes non-linear. Both the optical power and $x_{\text{qp}}^{\text{in}}$
span five orders of magnitude, with the latter reaching values as high as
$10^{-2}$.

Figure 4:  Role of pulse energy. Injected quasiparticle density with laser in
(a) position A, (b) position B and (c) position C. In all cases, light points
are data for variable optical power, with a fixed pulse length of $10~{}\mu$s.
Darker points are data for variable pulse length, with an optical power of
$1~{}\mu$W (position A), $10~{}\mu$W (position B), and $100~{}\mu$W (position
C).

Finally, we can use the pulse length as another way to change the total energy
injected near the qubit. We expect the effect of changing the optical power
and changing the pulse length to be similar, as long as the pulse energy is
the same. We compare these effects for the three laser positions, as shown in
Fig. 4. Indeed, we observe qualitatively similar effects for both variations,
confirming the role of pulse energy as the determinant control on the injected
quasiparticle density. Moreover, we also observe a similar sensitivity
hierarchy as the CW experiments, with position C having the lowest photon-
quasiparticle conversion constant. However, we observe similar sensitivity
values for B and A when taking the error bars into account, which differs from
the CW experiment. We note that the powers used in the pulsed experiment are
much higher than in the CW case.

For positions A and C, we also observe that, for some energy ranges, there is
a discrepancy between the data where power and pulse length are varied.
Furthermore, for all three locations, we find that the dependence of
$x_{\text{qp}}^{\text{in}}$ on pulse energy is linear at low pulse energies.
Slightly below $x_{\text{qp}}^{\text{in}}\approx 10^{-3}$, we observe a
saturation behavior followed by a further linear increase at the highest
energies used. Understanding these effects will require further studies.
However, possible explanations could be related to recombination effects at
higher quasiparticle densities and diffusion dynamics.

##  III Discussion and conclusion

In this work, we introduced a technique to create and control quasiparticle
dynamics in SC devices. Using an infrared laser, we were able to tune the
qubit decay rate by changing the optical energy reaching the device. To rule
out a possible temperature increase in the qubit as a source of increased
loss, we performed finite element method simulations (see Supplementary
Material [31] section E), that indicate a negligible increase in the
temperature of the device. Furthermore, we find that the excited state
population of the qubit is not significantly affected by laser illumination
within the range in which it is measurable (see Supplementary Material [31]
section F). Therefore, we conclude that light-induced quasiparticles are the
main source of loss modification in our devices. The increase in losses is
directly associated with energy exchange between qubit states and
quasiparticle degrees of freedom.

The strong laser location dependence observed in our experiment indicates that
photons directly hitting the SC layer are the most important contribution to
quasiparticle creation. This could indicate that processes that lead to
quasiparticle generation through the substrate, such as the creation of
phonons, do not play a dominant role in sapphire subjected to IR radiation.
This observation is particularly important for the field of hybrid systems
based on SC qubits, where in many situations one needs to bring light very
close to the superconductors [27, 28]. It is also important to stress that a
simple linear model of the absorption of photons, using a photon-quasiparticle
conversion constant, allows us to precisely describe the results of our CW
experiments. This model could be extended by including higher energy levels of
the transmon, which in our model is treated like a two-level system.

Measurements of $T_{\text{2}}^{*}$ also allowed us to observe the behavior of
$T_{\phi}$, which displays a minor reduction in its values for higher powers.
The contribution of a thermal distribution of free quasiparticles to
$T_{\text{2}}^{*}$ through pure dephasing was predicted to be negligible in a
single junction transmon when compared to the decay contribution [13]. We note
that certain assumptions of that model, such as a quasi-thermal equilibrium
energy distribution with an effective temperature for the quasiparticles, may
not hold in our case. Nevertheless, we are able to resolve the effect of
quasiparticles on $T_{\phi}$ [12], and our results contribute to a better
understanding of the quasiparticle-induced decay and dephasing behavior of
$T_{\text{2}}^{*}$.

While the CW dynamics can be easily explained by a linear absorption model,
the pulsed regime shows more complex dynamics. Nonetheless, using a diffusion-
free model with power-independent trapping and recombination rates, we were
able to fit all of our results and demonstrate how the injected quasiparticle
density depends on the pulse energy. We observe that the qubit coherence
recovers with a timescale of $\tau_{qp}=0.11\pm 0.02$ ms, about one order of
magnitude faster than previously reported in an experiment using microwave
pulses for quasiparticle injection [16]. One explanation for this discrepancy
could be that our experiment has a larger stray magnetic field near the qubit,
possibly due to the apertures in the microwave cavity. The higher magnetic
field would lead to a larger vortex density and result in a larger trapping
rate. Alternatively, in our case, highly energetic quasiparticles are created
throughout the SC layer rather than at the junction, which could propagate at
higher speeds in the material, leading to faster trapping. Finally, we expect
to observe a change in the mean free path of the quasiparticles in films with
different morphologies, which can result in a variation in trapping rates.
However, further studies need to be performed to pinpoint the exact mechanism
behind the larger trapping rate. We also note that the quasiparticle lifetime
is a material dependent quantity. In this experiment, the relatively long
quasiparticle lifetime in aluminum allows us to measure the quasiparticle
recovery on the time scale of hundreds of microseconds. For applications where
a faster quasiparticle recovery is desired, SC films with much faster
quasiparticle recovery times such as niobium and tantalum might be more
suitable [33].

We believe the platform we have developed can be particularly useful to
understand catastrophic events associated with cosmic ray or environmental
radiation absorption in large-scale SC circuits [20]. With the precise control
of power, event rate, and location of the events, we can simulate the burst of
injected particles in these circuits and evaluate the robustness of a
particular circuit to these events. Finally, in future experiments, in-situ
control of quasiparticle generation could also be used to study quasiparticle
diffusion in SC circuits, contributing to our understanding of how to mitigate
their detrimental effects.

## Acknowledgements

We thank L. Glazman, A. Grimm, Y. Yang, M. Bild, and T. Schatteburg for
valuable discussions. Funding: This project has received funding from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (Grant agreement No. 948047). This work was
supported by an ETH Zurich Postdoctoral Fellowship. G.C. acknowledges partial
support by the U.S. Government under ARO grant W911NF2210257. Author
contribution: U.v.L. fabricated the device. R.B, M.D., G.B. and F.A.
constructed the setup. R.B. and M.D. performed the measurements and analyzed
the data. R.B., M.D., H.M.D., G.C. and Y.C. interpreted the results. R.B.,
M.D. and Y.C. conceived the experiment. Y.C. supervised the work. R.B., M.D.
and Y.C. wrote the manuscript, which was revised by all authors. Data and
materials availability: All data and software are deposited on Zenodo [36]

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Supplementary Material: Quasiparticle dynamics in a superconducting qubit
irradiated by a localized infrared source

R. Benevides1,2, M. Drimmer1,2, G. Bisson1,2, F. Adinolfi1,2, U. v. Lüpke1,2,
H. M. Doeleman1,2, G. Catelani3,4 and Y. Chu1,2

1Department of Physics, ETH Zürich, 8093 Zürich, Switzerland and

2Quantum Center, ETH Zürich, 8093 Zürich, Switzerland

3Jülich Aachen Research Alliance (JARA) Institute for Quantum Information
(PGI-11), Forschungszentrum Jülich, Jülich 52425, Germany

4Quantum Research Center, Technology Innovation Institute, Abu Dhabi 9639,
United Arab Emirates

##  Appendix A Qubit details

We use an aluminum 3D transmon with an Al/AlOx/Al junction, fabricated with
the use of a single-step, Dolan bridge lithography approach. The typical
device properties measured in the absence of laser light in the cavity are
shown in table 1:

Table 1: Qubit properties. Cavity frequency $\text{f}_{\text{cav}}$ | 9.05 GHz
---|---
Qubit frequency $\text{f}_{\text{q}}$ | 6.30 GHz
T1 | 9-11 $\mu$s
T${}_{2}^{*}$ | 8-11 $\mu$s
Tϕ | 14-22 $\mu$s

We also present the main qubit design dimensions in Fig. 5. Our qubit is
composed of two main pads shunted by a Josephson junction. Additionally, a
circular antenna is connected to it and used in other hybrid systems of our
group. We shine the laser spot onto the pad at the opposite side of the
antenna, to avoid its influence in the results.

Figure 5:  Qubit design used in this experiment with the lengths of key
features labeled.

##  Appendix B Modelling the experiment

Previous works have calculated [10] and demonstrated [16] the relationship
between the loss rate of the first excited state of a weakly anharmonic qubit
and the normalized quasiparticle density, which is given by

$\Gamma=\sqrt{\frac{2\omega_{\text{q}}\Delta}{\pi^{2}\hbar}}x_{\text{qp}}+\Gamma_{\text{ext}},$
(2)

where $\Gamma_{\text{ext}}$ is qubit relaxation rate due to non-quasiparticle
related sources. Here, we expand this analysis to include possible
modifications in this relationship when shining a CW laser on the sample.

###  B.1 Qubit frequency modification

We observe a qubit frequency shift with power in Fig. 2(d) of the main text,
which would modify the observed loss rate as

$\omega_{\text{q}}=\omega_{\text{q}}^{0}-\lambda P_{\text{opt}},$ (3)

where $\lambda$ is a proportionality constant. However, we note that the
observed shift is much smaller than the absolute frequency ($\lambda
P_{\text{opt}}/\omega_{\text{q}}^{0}<<1)$, so we can neglect this contribution
in our analysis.

###  B.2 Energy gap modification

For temperatures $T<<T_{\text{c}}$, where $T_{\text{c}}$ is the critical
temperature of the material, the energy gap would be modified as

$\Delta_{\text{qp}}\approx\Delta(1-x_{\text{qp}}).$ (4)

Considering that we only observe values of quasiparticle density lower than
$x_{\text{qp}}\approx 10^{-2}$, we consider in our model that the energy gap
of the superconductor will remain constant during the experiment, neglecting
any modification in the energy gap with laser power.

###  B.3 Photon-quasiparticle conversion

We assume that the number of created quasiparticles is proportional to the
number of incident photons, i.e.,

$\begin{split}x_{\text{qp}}&=x_{0}+x_{\text{qp}}^{\text{in}}\\\ &=x_{0}+\mu
P_{\text{opt}},\end{split}$ (5)

where $x_{\text{0}}$ is the steady-state quasiparticle density in the absence
of quasiparticles injected by laser light and $\mu$ the photon-quasiparticle
conversion constant, which is position dependent. We disregard any non-linear
behavior and two-photon processes in the dynamics of conversion.

Therefore, the full model that relates CW optical power to qubit decay rate is
given by

$\Gamma=\sqrt{\frac{2\omega_{\text{q}}\Delta}{\pi^{2}\hbar}}\mu
P_{\text{opt}}+\Gamma_{0},$ (6)

where
$\Gamma_{0}=\Gamma_{\text{ext}}+\sqrt{2\omega_{\text{q}}\Delta/\left(\pi^{2}\hbar\right)}x_{0}$
is the qubit relaxation rate in the absence of quasiparticle injection which
includes the contribution of the background quasiparticle density and other
sources of loss such as dielectric loss.

###  B.4 Quasiparticle recovery model

Next, we proceed to understand the temporal behavior of injected
quasiparticles. If we assume that the quasiparticle diffusion has much faster
timescales than recombination and trapping [16], diffusion can be neglected
(see section H) and the following equation models the quasiparticle density
[38]

$\frac{dx_{\text{qp}}}{dt}=-rx^{2}_{\text{qp}}-sx_{\text{qp}}+g$ (7)

where $r$ and $s$, are the quasiparticle recombination and trapping,
respectively, and $g$ is the quasiparticle generation rate in the absence of
laser light. The solution of this equation is

$x_{\text{qp}}(t)=\frac{x_{\text{qp}}^{\text{in}}(s+2rx_{0})}{(s+rx_{\text{qp}}^{\text{in}}+2rx_{0})e^{(s+2rx_{0})t}-rx_{\text{qp}}^{\text{in}}}+x_{0}$
(8)

where $x_{\text{qp}}^{\text{in}}$ is the initial injected quasiparticle
density and $x_{0}$ is the steady-state quasiparticle density (specifically,
the steady-state solution of Eq 7). The quasiparticle density influences the
decay rate of the qubit according to the equation 2, so we can now write down
the expression for the qubit relaxation rate in terms of $r$, $s$,
$x_{\text{qp}}^{\text{in}}$, and $\Gamma_{0}$. To simplify the expression, we
neglect qubit losses from other sources and let
$\Gamma_{0}=\sqrt{2\omega_{\text{q}}\Delta/\pi^{2}\hbar}x_{0}$, meaning that
the solution only puts an upper bound on the background quasiparticle density.
With this assumption, the qubit decay rate can be written as

$\Gamma(t)=\frac{Cx_{\text{qp}}^{\text{in}}\left(Cs+2r\Gamma_{\text{0}}\right)}{\left(Cs+Crx_{\text{qp}}^{\text{in}}+2r\Gamma_{\text{0}}\right)e^{\left(s+\frac{2r\Gamma_{\text{0}}}{C}\right)t}-Crx_{\text{qp}}^{\text{in}}}+\Gamma_{\text{0}}$
(9)

where we define, as in the main text,
$C=\sqrt{2\omega_{\text{q}}\Delta/\pi^{2}\hbar}$ to simplify notation.

##  Appendix C Details of the experimental setup

Figure 6: Experimental setup. A standard circuit QED setup is used to operate
and read our qubit. Scanning the position of the laser with the help of a
cryo-actuator and collecting the transmitted power, we can image the qubit and
locate the laser spot. VOA: variable optical attenuator, LO: local oscillator,
RF: radiofrequency, IF: intermediate frequency.

The qubit measurements are performed using a standard circuit QED setup, as
can be seen in Fig. 6. The qubit is dispersively read-out using the 3D
microwave cavity. An FPGA-based quantum control unit (Quantum Machines OPX)
and IQ-mixers are used to create microwave pulses for addressing the qubit and
readout cavity. The optical pulse is controlled via a tunable laser kept at
$\lambda=1550$ nm, a variable optical attenuator (VOA), and an acousto-optical
modulator (AOM). The AOM is also driven using RF pulses created by the control
unit, allowing the synchronization of the full protocol. The laser light is
sent via an optical fiber into the fridge and outcoupled using a graded-index
(GRIN) lens attached to a motorized actuator (Janssen Precision Engineering
CTTPS1/2) to control the beam position (see Fig. 7). An output collimator
collects the transmitted light and allows for in-situ imaging of the sample.

Figure 7:  Photo of the experimental device. Light enters from the optical
input fiber on the left and is focused by the input lens through the input
hole onto an SC qubit inside the microwave cavity. The inset shows a zoomed-in
alternate angle of the input hole to the microwave cavity. If the light is
transmitted through the cavity, it can exit through an output hole and be
collected by the output collimator on the right side. The cryogenic motors can
move the tip-tilt stage and control the position of the optical beam at the SC
qubit.

##  Appendix D Imaging inside the dilution refrigerator

One experimental challenge we faced in performing the experiments described in
this work was positioning the laser spot with respect to the superconducting
circuit in a dilution refrigerator. We developed a crude imaging technique in
order to get information about the laser beam’s location. By moving the tip-
tilt stage of the input GRIN lens in fixed steps and monitoring the
transmitted laser light collected by the output collimator, we can create an
image of the qubit in the cavity. One such image is shown in Fig. 8(a).

Figure 8:  Imaging protocol and interpretation. (a) A crude picture of the
qubit is taken inside the fridge with the help of the laser and cryogenic
motors. (b) We associate the continuous straight lines at the sides of the
image with microwave cavity walls and (c) the square region with lower optical
transmission with the qubit lower pad.

There are two relevant features in these images. Firstly, when the laser beam
is blocked by the edge of the holes in the microwave cavity, no light is
transmitted. Therefore, we interpret vertical features that span the entire
image as the walls of the microwave cavity (see Fig. 8(b)). Secondly, when the
laser spot is incident on the rectangular piece of aluminum that makes up the
bottom qubit pad, the light is reflected and we measure no transmission (see
Fig. 8(c)). Once we take and interpret an image, we use the motors to choose a
position for the laser beam spot with respect to the qubit.

##  Appendix E Thermal analysis with finite element methods

One potential complicating factor in this experiment is the effect of the
laser on the temperature of the qubit sample. Even short low-power pulses
could potentially increase the temperature of the fridge and modify the
thermal quasiparticle background. To check this effect, we performed finite
element methods simulation to compute the expected increase in temperature in
our device. We modeled our setup as a sapphire chip supported by blocks of
aluminum (representing the cavity) and with a rectangular layer of aluminum in
its surface with the approximate dimensions of the qubit, as shown in Fig.
9(a). We assumed that the precise qubit geometry was irrelevant to the
analysis, so we ignored it to simplify the meshing. We also assumed the cavity
is in thermal contact with a bath at the fridge temperature of 10 mK. During
the experiment, we observed that the temperature of the fridge reaches a
maximum of $\sim 35$ mK for the highest powers in the CW experiment and is not
significantly affected for small powers or the pulsed experiment.

Figure 9:  Simulation of the sample temperature. (a) Temperature distribution
in the sample and aluminum blocks representing the cavity, with the aluminum
assumed to be in its superconducting phase. We use a rectangular aluminum
layer to represent the qubit. The red line represents the line-cut of data
shown in (b), with the origin of the distance axis at the red circle.

We modeled the effect of our laser considering the situation where the highest
CW power was sent to the experiment, i.e., in position C with
$P_{\text{opt}}=1~{}\mu$W. We consider a typical absorption of infrared light
by aluminum layers of $2.5\%$ and that in position C we have a reduction of
$\mu_{\text{A}}/\mu_{\text{C}}\approx 59$ of the power reaching the qubit. We
used thermal conductivities of $0.002~{}$W/(m$\cdot$K) for the sapphire and
the aluminum in the superconducting phase at $100$ mK [40]. Since the
absorption of laser light could lead to a local transition in the
superconductor material to the normal phase, we considered also the situation
where the metal would fully transition out of the superconducting phase, using
the value of $200~{}$W/(m$\cdot$K).

We computed the stationary temperature of the whole system under the
illumination of the laser, as shown in Fig. 9(a). In Fig. 9(b), we show a cut-
line of the temperature across the qubit chip surface. We observed an increase
no bigger than $0.6$ mK above the fridge base temperature for this
configuration. We have also analyzed the effect of a higher temperature bath
(fridge temperature) and of different positions of the laser (with the
respective used optical powers). In all cases, we didn’t see changes in the
temperature that could explain the measured quasiparticle densities. We note
that assumptions made for this simulation, such as the perfect thermal contact
between materials, the lack of absorption in the sapphire and the uncertainty
about the thermal conductivities, limit the precision of the obtained results.
Still, considering the linearity of the heating with respect to absorbed
optical power, these results provide one piece of evidence that heating of the
qubit does not play an important role in our experiments, consistent with the
measurements observed in the next section.

##  Appendix F Measurements of the excited state population of the qubit

To further investigate the possible heating of the qubit chip by the laser, we
performed qubit thermometry measurements. We compared the amplitude in the
power Rabi oscillation of the $e\leftrightarrow f$ transition when preceded by
a $\pi$-pulse between the $g\leftrightarrow e$ states with the same power Rabi
without the initial $\pi$-pulse. Assuming negligible population in the $f$
state, this method provides the excited state population of the qubit [39],
which translates to an effective temperature assuming a Boltzmann
distribution.

Figure 10:  Qubit temperature measurement. Rabi oscillations between states
$e\leftrightarrow f$, with laser off and with CW laser on in position A and
$P_{\text{opt}}=1$ nW, both with and without an initial $\pi$-pulse between
states $g\leftrightarrow e$.

In Fig. 10, we show such a measurement, performed both with the laser off and
with the laser on at position A with a CW power of $P_{\text{opt}}=1$ nW. We
observe in both situations similar temperatures of $T\approx 160-165$ mK,
considerably higher than our fridge base temperature ($\sim 10$ mK) or our
estimations based on finite element methods (section E), but still much lower
than what is necessary to explain quasiparticle densities observed in the
experiment, which reach $x_{\text{qp}}\sim 10^{-2}$. We associate these higher
temperatures with imperfect thermalization to the base plate and with black-
body radiation entering the microwave cavity through its hole, which is known
to contribute to the transition rates of the qubit via photon-assisted
tunneling and breaking of Cooper pairs [37]. Therefore, from the measurements
performed, we believe the optical pulses are not significantly heating up the
qubit. We summarize the measured values in the table 2, with the excited state
population, the qubit temperature, and the corresponding thermal quasiparticle
density $x_{\text{qp}}^{\text{th}}$ [7] for each of the situations presented.

Table 2: Thermometry of the qubit with and without laser. |  $|e\rangle$ population | Qubit temperature (mK) | $x_{\text{qp}}^{\text{th}}$
---|---|---|---
Laser off | $0.191\pm 0.006$ | $\sim 165$ | $\sim 7.8\times 10^{-7}$
Laser on | $0.178\pm 0.007$ | $\sim 160$ | $\sim 5\times 10^{-7}$

##  Appendix G Quasiparticle relaxation as a function of pulse length

Figure 11:  Pulsed laser at position A, pulse length sweep. Qubit decay rate
as a function of $\tau_{\text{opt}}$ for different optical pulse lengths. The
data for four pulse lengths that span four orders of magnitude are
highlighted. Error bars represent the standard deviation of measurements.

In Fig. 3 of the main text, we investigated quasiparticle relaxation after a
pulsed laser experiment while changing the optical power and keeping the pulse
length fixed. Here, we show in Fig. 11 a qualitatively similar behavior when
changing the optical pulse length and keeping the optical power fixed at
$10~{}\mu$W. We observe quasiparticle relaxation on similar timescales.
Nevertheless, both cases allow us to control the injected quasiparticle
density across 4 to 5 orders of magnitude. The data in Fig. 11 were taken with
the laser at position A. These data (as well as similar data taken at
positions B and C) are analyzed and shown in Fig. 3.

##  Appendix H Details on data processing

In this section, we will explain the procedure for data acquisition, fitting,
and analysis from the quasiparticle recovery measurements shown in Fig.
3(b)-(d). Our data starts as a series of $T_{1}$ measurements corresponding to
a particular laser pulse power ($P_{\text{opt}}$), pulse length
($\tau_{\text{pulse}}$), and the time delay between the laser pulse and the
measurement ($\tau_{\text{opt}}$). For each series of such measurements, we
fit the $T_{1}$ measurement to an exponential model and obtain a qubit energy
relaxation rate,
$\Gamma(P_{\text{opt}},\tau_{\text{pulse}},\tau_{\text{opt}})$, and a standard
error of the fit
$\sigma(P_{\text{opt}},\tau_{\text{pulse}},\tau_{\text{opt}})$, which
correspond to the data point and error bar of each point in Fig. 3(b).

When the pulse energies are very high and the time delays between the pulse
and the measurement are short, the $T_{1}$ measurements can become too noisy
to fit. When the signal to noise becomes too low, the fitted $T_{1}$ becomes
larger when $\tau_{\text{opt}}$ is decreased and the fit error increases. If
we observe this unphysical effect, we identify the pulse delay
$\tau_{\text{opt}}$ after which the qubit loss rates decrease monotonically
and only consider data with a delay greater than or equal to that
$\tau_{\text{opt}}$.

For a given laser pulse power and pulse length, we then fit the qubit loss
rates to our model of quasiparticle recovery, Eq. 9. In this model, there are
two free parameters, the initial injected quasiparticle density
$x_{\text{qp}}^{\text{in}}$ and the qubit loss rate in the absence of injected
quasiparticles $\Gamma_{0}$. There are also two unknown constants, the
recombination and trapping rates $r$ and $s$. If we leave
$x_{\text{qp}}^{\text{in}}$, $\Gamma_{0}$, $r$, and $s$ as free parameters,
the magnitude of the cross-correlations between variables in the fit approach
unity and the fit becomes unreliable, so we need to fix $r$ and $s$. We know
that for low enough quasiparticle densities (when $x_{\text{qp}}\ll s/r$),
trapping effects will dominate over the recombination effects. Using
literature values [16], we know that recombination and trapping rates should
be on the order of MHz and kHz, respectively, so we first fit the data for
powers less than 100 nW (where $x_{\text{qp}}^{\text{in}}\leq 10^{-4}$), where
we enforce $r=0$. These fits yield a more reliable estimate of $s$. From the
average and standard deviation of the fitted trapping rates, we find $s=9\pm
2$ kHz. Having estimated $s$, we can compare $1/s\approx 0.11$ ms to the
diffusion time. Using the diffusion constant in [16] and the qubit geometry,
we can estimate that the diffusion time across the pad is about $0.05$ ms,
less than half of the trapping time. So, neglecting diffusion is a reasonable
approximation.

We then fix this value for $s$ and attempt to find a value for the
recombination rate $r$ by simultaneously fitting the qubit recovery data for
all of the powers we measured. We use the average $\chi^{2}$ goodness of fit
parameter to assess how varying $r$ between 0 and 20 MHz affects the model. We
found that $\chi^{2}$ was minimized for $r=0$, and the fit results have a very
weak dependence on $r$, with a change of $\leq 5\%$ in the values of
$\chi^{2}$ for $r\leq 4.86$ MHz. Therefore we set the recombination rate to
zero in our quasiparticle recovery model. With the trapping and recombination
rates fixed, we finally fit our $T_{1}$ recovery data (i.e. Fig. 3(c)),
weighted by the measured variance of each qubit relaxation rate, to ascertain
the quasiparticle relaxation behavior (i.e. Fig. 3(d)).