of 18
nature physics
https://doi.org/10.1038/s41567-024-02409-z
Artic�e
Non-classical microwave–optical photon
pair generation with a chip-scale transducer
In the format provided by the
authors and unedited
S1
CONTENTS
1. Notation and device parameters
S2
2. Device fabrication process
S2
3. Microwave circuit design
S2
4. Piezo-optomechanics design
S4
5. Measurement Setup
S4
6. Piezoelectric coupling to other modes
S6
7. Optical heralding rate contributions
S6
8. Microwave moment inversion
S8
9. Microwave emission envelope function
S9
10. Microwave gain calibration
S10
11. TWPA optimization
S10
12. Transducer heating spectrum
S10
13. A simple model for transducer correlation
functions
S11
14. Simulation of the conditional microwave state
S12
15. Data analysis for correlation functions
S14
16. Classical bound on the conditional second order
intensity correlation
S15
17. Convergence of
g
(2)
AC
to the classical bound
S15
References
S16
S2
1. NOTATION AND DEVICE PARAMETERS
Symbol
Description
ˆ
a,
ˆ
b,
ˆ
c
operators for optical, acoustic, and
microwave modes of the transducer
ˆ
c
+
,
ˆ
c
operators for hybridized electrome-
chanical modes
ˆ
a
in
,
ˆ
c
in
,
a
out
,
ˆ
c
out
)
operators for optical and microwave
input (output) modes in coupling
waveguides
ˆ
A,
ˆ
C
operators for optical and microwave
temporal modes in coupling waveg-
uides
̄
C
mn
moments of the temporal microwave
mode
̄
C
mn
|
click
moments of the temporal microwave
mode conditioned on an optical click
TABLE S1. Notation for various modes and moments.
Symbol
Description
Value
λ
a
optical mode wavelength
1561.3 nm
ω
b
/
2
π
microwave acoustic mode frequency
5.001 GHz
ω
c
/
2
π
|
B
=0
microwave electrical mode frequency
at zero B-field
5.011 GHz
g
om
/
2
π
optomechanical coupling
270 kHz
g
pe
/
2
π
piezoelectric coupling
800 kHz
κ
e,a
/
2
π
external optical coupling rate
650 MHz
κ
i,a
/
2
π
intrinsic optical loss rate
650 MHz
κ
i,b
/
2
π
intrinsic acoustic loss rate
150 kHz
κ
e,c
/
2
π
external microwave coupling rate
1.2 MHz
κ
i,c
/
2
π
intrinsic microwave loss rate
550 kHz
TABLE S2. Coupling rates of transducer internal modes.
Symbol
Description
Value
T
p
Two sigma duration of pump pulse
160 ns
T
r
Repetition period of pump pulses
20
μ
s
-
Peak power of pump pulse
83 nW
n
a
Peak intra-cavity photon number
0.78
p
click
Optical heralding probability
2
.
7
×
10
6
R
click
Optical heralding rate (=
p
click
/T
r
)
0.14 s
1
p
SPDC scattering probability
1
.
8
×
10
4
η
opt
Optical collection efficiency
1
.
7
×
10
2
η
mw
Microwave conversion efficiency
0.56
TABLE S3. Microwave-optical photon pair generation pa-
rameters.
Parameter
Value
Optical cavity to on-chip waveguide
0.50
Waveguide to lensed fiber
0.29
Circulator between excitation and detection
0.90
Total filter bank loss
0.16
(individual components below)
2x2 switches
0.89
Filters (CW transmission)
0.52
Finite pulse bandwidth
0.39
Circulator in filter setup
0.89
SNSPD setup
0.83
Optical collection efficiency (
η
opt
)
1
.
7
×
10
2
TABLE S4. Loss budget along optical detection path.
2. DEVICE FABRICATION PROCESS
The fabrication process for the transducer chip is illus-
trated in Fig. S1 and described in the caption. Masks for
all steps are patterned in ZEP-520A resist via electron-
beam lithography on a Raith EBPG 5200 tool. All dry
etching is performed in Oxford Plasmalab 100 inductive
coupled plasma reactive ion etching (ICP RIE) tools.
The process flow can be sub-divided into sections used
to define various portions of the transducer device. Steps
(i)-(vi) complete the definition of the AlN box essential
for the piezoacoustic cavity. The combination of dry and
wet etch steps ensures that the dimensions of the AlN
box are precisely defined while the silicon device layer is
undamaged on most of the chip. This is important to
achieve optical, mechanical, and microwave modes with
high quality factors. Steps (vii)-(ix) define the NbN res-
onator and step (x) defines the OMC. Steps (xi)-(xiii) are
use to define aluminum electrodes on the piezo-resonator
and galvanically connect them to the NbN resonator us-
ing bandage steps. The bandaid steps involve in situ Ar
milling for two minute and six minute durations respec-
tively to clear the surface of NbN and Al prior to Al
bandaid evaporation. To provide optical fiber access to
coupler sections at the end of the silicon photonic waveg-
uides, we clear a portion of the SOI substrate up to a
depth of 150
μ
m using a deep reactive ion etch at the
edge of the chip. Finally, the buried oxide (BOX) layer
is etched in anhydrous vapor HF to release the device
membrane.
3. MICROWAVE CIRCUIT DESIGN
The kinetic inductance resonator used in our trans-
ducer is fabricated from an NbN film of 10 nm thick-
ness and 50 pH/sq sheet inductance.
The meander-
ing ladder geometry described in the main text is com-
prised of 2
μ
m
×
1
μ
m rectangular loops formed from
traces of width 130 nm. We use extended electrical ter-
minals of length 200
μ
m and width 1
μ
m to spatially
separate the high kinetic inductance section from the
OMC. The resonator is designed to achieve a target fre-
S3
Si
SiO2
AlN
Si
(i)
(ii)
(iii)
(iv)
(v)
(vi)
...
(vii)
(viii)
(ix)
...
(x)
(xi)
(xiv)
(xii)
(xiii)
Piezo box
NbN resonator
+ Si OMC
Al IDT
+ HF release
NbN resonator
Ar/Cl
dry etch
PECVD
SiO2
C4F8/SF6
dry etch
H3PO4
wet etch
BHF 10:1
wet etch
E-beam
lithography
NbN
sputtering
SF6/Ar
dry etch
C4F8/SF6
dry etch
Al
evaporation
Bandaid 1
Bandaid 2
Anhydrous HF
vapor release
FIG. S1.
Device fabrication process
. Images are not to scale.
(i)
Sputter deposition of 300 nm thick c-axis AlN piezoelectric
film (grown by OEM group; stress
T
= +55 MPa; (002) XRD peak of full-width at half-maximum = 1.79
°
) on a silicon on
insulator substrate (Si device layer [float zone grown, 220 nm thick,
ρ
5kΩ-cm]; buried oxide layer [3
μ
m thick, silicon
dioxide]; Si handle [Czochralski grown, 750
μ
m thick,
ρ
5kΩ-cm]).
(ii)
3 minute AlN trench etch (120W RF, 600W ICP)
with Ar/Cl
2
(80/40 sccm) chemistry to define the perimeter of the piezo resonator via a small trench of width
100 nm.
(iii)
Conformal deposition of a 300nm SiO
x
hard mask via plasma enhanced chemical vapor deposition.
(iv)
Patterning of the SiO
x
mask via a 6 minute dry etch (33W RF, 1300W ICP) with C
4
F
8
/SF
6
(40/3 sccm) chemistry.
(v)
Removal of the remaining
AlN on the chip with a 12 minute 80
C H
3
PO
4
wet etch.
(vi)
SiO
x
mask removal with 10:1 buffered oxide etchant for 3
minutes and 30 seconds.
(vii)
Protection of the piezo-acoustic and OMC regions with a resist mask prior to deposition of NbN.
(viii)
Deposition of a 10 nm thick film of NbN via an RF sputtering process.
(ix)
1 minute dry etch (30W RF, 300W ICP)
of NbN with SF
6
/Ar (40/20 sccm) chemistry to define the high-impedance microwave resonator.
(x)
4 minute dry etch (18W
RF, 600W ICP) of silicon with C
4
F
8
/SF
6
(72/30 sccm) chemistry to define OMC, acoustic shield and optical waveguide.
(xi)
Deposition of Al electrodes for the piezo-acoustic resonator using angled electron-beam evaporation.
(xii, xiii)
Bandage steps
with 3 minute Ar milling followed by Al evaporation.
(xiv)
Etching of the buried oxide (BOX) layer using anhydrous vapor
HF to release the device membrane.
quency of 5.0 GHz for the fundamental mode with a ca-
pacitance,
C
res
= 7
.
1 fF, which includes a small con-
tribution of 0.27 fF from the electrodes on the piezo-
acoustic resonator. Nearly the entire inductance of the
resonator mode is due to the kinetic inductance of the
superconducting film. The use of closed superconduct-
ing loops in the resonator allows for tuning of the ki-
netic inductance,
L
k
, via a DC supercurrent,
I
, induced
by an external magnetic field according to the relation
L
k
L
k,
0
[1 + (
I/I
)
2
] as shown in [1]. Here
L
k,
0
is the
kinetic inductance at zero magnetic field.
I
I
is a
characteristic current on the order of the critical current
of the nanowire [2]. This relation leads to quadratic tun-
ing of the resonator frequency in response to an external
magnetic field as observed in Fig. 2b of the main text.
The resonator is capacitively coupled to an on-chip 50 Ω
coplanar waveguide (CPW) patterned in NbN to achieve
an external coupling rate,
κ
e,c
/
2
π
= 1
.
3 MHz. On the
chip used for the experiments in this work, sixteen trans-
ducer devices were laid out in groups of four with each