of 15
Nature | Vol 588 | 24/31 December 2020 |
599
Article
Superconducting qubit to optical photon
transduction
Mohammad Mirhosseini
1,2,3
,5
, Alp
Sipahigil
1,2,3
,5
, Mahmoud
Kalaee
1,2,3,4
,5
& Oskar
Painter
1,2,3,4
Conversion of electrical and optical signals lies at the foundation of the global
internet. Such converters are used to extend the reach of long-haul fibre-optic
communication systems and within data centres for high-speed optical networking of
computers. Likewise, coherent microwave-to-optical conversion of single photons
would enable the exchange of quantum states between remotely connected
superconducting quantum processors
1
. Despite the prospects of quantum
networking
2
, maintaining the fragile quantum state in such a conversion process with
superconducting qubits has not yet been achieved. Here we demonstrate the
conversion of a microwave-frequency excitation of a transmon—a type of
superconducting qubit—into an optical photon. We achieve this by using an
intermediary nanomechanical resonator that converts the electrical excitation of the
qubit into a single phonon by means of a piezoelectric interaction
3
and subsequently
converts the phonon to an optical photon by means of radiation pressure
4
. We
demonstrate optical photon generation from the qubit by recording quantum Rabi
oscillations of the qubit through single-photon detection of the emitted light over an
optical fibre. With proposed improvements in the device and external measurement
set-up, such quantum transducers might be used to realize new hybrid quantum
networks
2
,
5
and, ultimately, distributed quantum computers
6
,
7
.
Recent developments with superconducting qubits have demonstrated
fast, high-fidelity single- and two-qubit logic gates, making them a
promising system for realizing quantum computers
1
. The low-loss envi
-
ronment of a superconductor and the strong single-photon nonlinearity
from the Josephson effect provide an ideal combination for processing
quantum information in the microwave domain
8
, but optical photons
are a natural choice for quantum networking tasks
9
where they provide
low propagation loss in room-temperature environments
10
. A coherent
microwave-to-optical interface can thus lead to hybrid architectures
for quantum repeaters
2
,
5
by connecting superconducting qubits and
ultrahigh-
Q
(quality factor) microwave cavities
11
—serving as logic and
memory registers—to ‘flying’ optical qubits as a means of long-distance
information transfer. Although the process of frequency conversion
can be understood simply as a noise-free and lossless linear operation,
an optical interface for superconducting qubits has not been realized
because of the technical challenges inherent in the vast frequency
difference between microwave (~5 GHz) and telecommunication-band
optical (~200 THz) photons.
Microwave-to-optical frequency conversion can be achieved by bulk
optical nonlinearities
12
. Alternatively, effective nonlinearities can be
realized by intermediary degrees of freedom such as rare earth ions,
magnons or phonons
13
15
that can simultaneously couple to microwave
and optical fields. Using engineered nanomechanical resonators as
such intermediary channels has been a particularly promising direction,
where pioneering work in the past decade has demonstrated electrical
and optical preparation, control and readout of mechanical modes
near their quantum ground state
3
,
16
,
17
. These demonstrations, together
with rapid developments in superconducting quantum circuits
8
, have
motivated recent experimental efforts to combine electromechanical
and optomechanical devices to build a microwave-to-optical quantum
transducer
18
22
. Although this approach has led to impressive conver-
sion efficiencies
23
, all demonstrations so far have been limited to clas
-
sical signals owing to a combination of challenges associated with
optically induced or thermal noise, small transduction bandwidths
and device integration complexities.
Here, we demonstrate the transduction of the microwave-frequency
quantum excitations of a superconducting qubit into light at optical
telecommunication frequencies, and use an optical fibre link and
single-photon detection to register the quantum Rabi oscillations of
the qubit. This is achieved using a chip-scale platform that integrates
a transmon qubit with a piezo-optomechanical transducer. We use a
pulsed scheme to coherently transfer the quantum state of the qubit
into a nanomechanical mode by a piezoelectric swap operation, and
subsequently convert it to the optical domain by using a pulsed laser
drive. This approach separates electrical and optical parts of the
transduction sequence, avoiding the effects of light-induced noise
on the superconducting circuitry. We find an overall added noise
photon level for the transduction process to be 0.57 ± 0.2, approach-
ing the threshold required for remote entanglement generation
of qubits
24
.
https://doi.org/10.1038/s41586-020-3038-6
Received: 10 April 2020
Accepted: 2 October 2020
Published online: 23 December 2020
Check for updates
1
Kavli Nanoscience Institute, Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA, USA.
2
Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of
Technology, Pasadena, CA, USA.
3
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.
4
AWS Center for Quantum Computing, Pasadena, CA,
USA.
5
These authors contributed equally: Mohammad Mirhosseini, Alp Sipahigil, Mahmoud Kalaee.
e-mail:
opainter@caltech.edu
600
| Nature
| Vol 588
| 24/31 December 2020
Article
Figure
1a
shows a schematic of the transduction process used
in our experiment, where an intermediary mechanical mode is
coupled to a qubit via a resonant piezoelectric interaction and to an
optical mode via a parametric optomechanical interaction. The
Hamiltonian for this system can be written as
HH
HH
ˆ
=
ˆ
+
ˆ
+
ˆ
0p
eo
m
.
Here,
ωa
bb
ωt
σ
ˆ
/=
ˆˆ
+
^
ˆ
+(
0c
o
om
m
mq
ee
describes the evolution of
non-interacting subsystems, with
σb
ˆ
/=
b
ˆ
^
)
pe
pe
eg
mg
em
and
Gt
ab
ab
ˆ
/=
()
ˆ
^
)
om
om
o
mo
m
describing the piezoelectric and optom
-
echanical interactions, respectively. The quantum modes are repre
-
sented by: the creation (annihilation) operator of the optical mode,
a
o
(
a
^
o
); the creation (annihilation) operator of the mechanical
mode,
b
^
m
(
b
^
m
); the qubit excited-state projection operator,
σ
^
ee
; and the
raising (lowering) operator of the qubit from ground to excited state,
σ
ˆ
eg
(
σ
^
ge
). The centre frequency of the optical and mechanical modes
are given by
ω
c
and
ω
m
, respectively, the transition frequency between
ground and excited state of the qubit is given by
ω
q
, and
g
pe
is the
single-phonon piezoelectric coupling rate between the mechanical
mode and the qubit. Here, we use the ‘beam-splitter’ form of the
optomechanical interaction which is specific to the case where the
optical drive is red-detuned from the optical cavity resonance
(
Δ
=
ω
c
ω
drive
=
ω
m
) and assumes operation in the resolved-sideband
limit, where
ω
m
κ
o
(
κ
o
is the linewidth of the optical resonance)
25
. In
this case, the optomechanical coupling
G
tn
tg
()
=(
)
om
c
om
is para
-
metrically enhanced from the single-photon rate,
g
om
, by the intra-cavity
photon number
n
c
(
t
) from the pump laser at optical frequency
ω
drive
.
Physical realization of the above Hamiltonian requires a materials
platform that can support both optomechanical and piezoelectric
components. High-fidelity qubit–mechanics swap operations can
be realized based on the piezoelectric effect, where the electric field
from a qubit can be transformed to displacement in a mechanical
resonator
26
,
27
. Quantum coherent optomechanical readout of mechani
-
cal modes can also be realized in optomechanical crystal (OMC)
cavities
4
,
28
, where co-localization of mechanical and optical fields
results in a large parametric coupling. Here we use a high-resistivity
silicon-on-insulator wafer to integrate OMC cavities with large opto
-
mechanical coupling rates and low mechanical loss together with
transmon qubits
29
. By sputter depositing and selectively patterning
a thin film of aluminium nitride (AlN) on the silicon substrate, we are
also able to achieve a localized piezoelectric response (see Methods).
Figure
1b
shows a model of the transducer region of our device, which
consists of a hybridized acoustic cavity formed from a wavelength-scale
piezoacoustic resonator connected by a phonon (acoustic) waveguide
to an OMC optomechanical cavity. To achieve simultaneously strong
electrical and optical coupling to the hybridized cavity modes requires
careful design of the individual (that is, detached) piezoelectric and
optomechanical
30
resonators. The piezoacoustic cavity section (A.S.,
M.M., M.K., S. Messala & O.P., manuscript in preparation) is designed as a
wavelength-scale Lamb wave resonator—made from a slab of AlN on top
of the silicon device layer—that is released from the underlying buried
oxide layer and connected laterally to the peripheral substrate by pat
-
terned silicon tethers that act as acoustic mirrors. A pair of aluminium
electrodes in the form of an interdigital transducer (IDT) connect the
transmon’s capacitive leads to the piezoacoustic resonator as shown
in the schematic of Fig.
1d
. The submicrometre scale of the design in
Fig.
1b
results in a smaller piezoelectric coupling rate compared with
earlier work
3
, but the small mechanical mode density limits the num
-
ber of parasitic modes that can lead to both qubit decoherence and a
reduction in optomechanical coupling. Hybridization of the acoustic
AlN mechanical mode
Phonon waveguide
Si mechanical mode
c
g
pe
g
RO
SC qubit
Mechanical resonator
Optical resonator
Optical bre
G
om
= (
n
c
)
1/2
g
om
g
om
κ
e,o
κ
RO
κ
e,q
κ
m
CPW
RO res.
SC
qubit
Transd.
Si optical WG
SQUID loop
Tapered optical coupler
OMC
cavity
p-a
cavity
500
μ
m
Qubit
RO res.
OMC cavity
Piezo-optomechanical
transducer
p-a cavity
CPW
Optical mode
|
e
|
g
a
b
g
om
/2
π
(kHz)
ω
m
/2
π
(GHz)
ω
m
/2
π
(GHz)
g
pe
/2
π
(MHz)
ˆ
a
o
ˆ
a
out
ˆ
a
in
b
m
ˆ
5.25
0
800
0
4
5
5.25
5
de
RO res. meander
RO res. meander
Fig. 1 | Quantum transducer set-up.
a
, Schematic of the microwave-to-optical
transduction process. The mechanical mode (
b
ˆ
m
) couples to both the
superconducting qubit
(
σ
ge
ˆ=
⟩⟨
ge
) and an optical mode (
a
ˆ
o
) via piezoelectric
(
g
pe
) and optomechanical (
g
om
) vacuum coupling rates, respectively.
Ω
is the
excitation rate applied when exciting the qubit between ground and excited
state.
b
, Numerically simulated resonant modes of the piezo-optomechanical
transducer.
c
, Simulated vacuum optomechanical (top) and piezoelectric
(bottom) coupling rates to the hybridized mechanical modes.
d
, Electrical
circuit representation of the integrated qubit and transducer device.
e
, Optical
micrograph of a pair of fabricated devices, showing the readout resonator
(green), transmon qubit (blue), transducer element (purple) and silicon
out-coupling waveguide (red). Corresponding magnified optical images of the
different device sections are shown to the left and right. Scale bars (white and
black) in magnified images, 10 μm. Electrical and optical readout is performed
in ref lection via the CPW and a lensed optical fibre (not shown; optically
coupled to the tapered silicon waveguide coupler), respectively. OMC,
optomechanical crystal; p-a, piezoacoustic; RO res., readout resonator;
SC qubit, superconducting transmon qubit; SQUID, Josephson-junction
superconducting quantum interference device; transd., transducer;
WG, waveguide.