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Supplemental Document
High-efficiency low-noise optomechanical crystal
photon-phonon transducers: supplement
S
AMEER
S
ONAR
,
1,2,†
U
TKU
H
ATIPOGLU
,
1,2,†
S
RUJAN
M
EESALA
,
1,2
D
AVID
P. L
AKE
,
1,2
H
ENGJIANG
R
EN
,
1,2,3
AND
O
SKAR
P
AINTER
1,2,4,
1
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California
91125, USA
2
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California
Institute of Technology, Pasadena, California 91125, USA
3
Current address: Anyon Computing Inc., Emeryville, California 94608, USA
4
AWS Center for Quantum Computing, Pasadena, California 91125, USA
These authors contributed equally to this work.
opainter@caltech.edu
This supplement published with Optica Publishing Group on 17 January 2025 by The Authors
under the terms of the Creative Commons Attribution 4.0 License in the format provided by the
authors and unedited. Further distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
Supplement DOI: https://doi.org/10.6084/m9.figshare.27948360
Parent Article DOI: https://doi.org/10.1364/OPTICA.538557
Supplementary Information for: ‘High-Efficiency Low-Noise
1
Optomechanical Crystal Photon-Phonon Transducers’
2
1. DEVICE PARAMETERS
3
Parameter
Device I
Device II
λ
0
(nm)
1553.4
1568.3
κ
i
/2
π
(MHz)
706
595
κ
e
/2
π
(MHz)
444
295
m
/2
π
(GHz)
10.44
10.29
γ
0
/2
π
(kHz)
21.46
0.97
g
OM
/2
π
(kHz)
919
742
Table S1.
Summary of measured device parameters:
λ
0
is the optical mode wavelength,
κ
i
is
the intrinsic linewidth of the optical cavity,
κ
e
is the coupling rate between the optical cavity
and the optical coupling waveguide,
m
is the acoustic frequency,
γ
0
is the intrinsic linewidth
of acoustic resonator measured using ringdown technique at 10mK temperature [
1
],
g
OM
is the
vacuum optomechanical coupling rate.
2. MODE OCCUPANCY CALIBRATION
4
The cavity photon occupation
n
c
is calibrated using the input power at the device
P
in
with the
5
following relation:
6
n
c
=
P
in
̄
h
ω
l
κ
e
2
+
κ
2
t
/4
,
(S1)
where
ω
l
is the pump frequency,
κ
e
is the coupling rate between optical cavity and the optical
7
coupling waveguide,
κ
t
=
κ
i
+
κ
e
is the measured total linewidth of the optical cavity, and
8
=
ω
l
ω
c
is the detuning of the laser from the cavity frequency
ω
c
. To calibrate the acoustic
9
mode phonon occupancy to the measured photon count rate on the single photon detector, we
10
perform sideband asymmetry measurements [
2
]. The measured count rate for red and blue
11
detuned pump laser are given by
12
Γ
(
=
±
m
) =
Γ
dark
+
Γ
pump
+
Γ
SB,0

n
th
+
1
2
(
1
±
1
)

,
(S2)
where
n
th
is the occupation of the acoustic resonator.
Γ
dark
is the dark count rate of the SPD,
Γ
pump
13
is the pump bleedthrough, and
Γ
SB,0
is the detected photon scattering rate per phonon.
Γ
SB,0
14
relates to the optomechanical scattering rate
γ
OM
=
4
g
2
OM
n
c
/
κ
t
through the external detection
15
efficiency,
Γ
SB,0
=
η
ext
γ
OM
. We use pulsed laser with repetition rate much smaller than the
16
intrinsic decay rate (
R
γ
0
) such that the
n
th
1 at the beginning of each pulse.
Γ
SB,0
can then
17
be extracted by taking the difference between the count rate at the beginning of the pulse. For
18
pulsed transduction measurements with short optical pulses shown in Figure 4 of the main text,
19
the count rates for the red- and blue-detuned pump laser are averaged over the duration of the
20
optical pulse. This averaging accounts for any finite rise time in the sideband scattering rates.
21
The hot bath measurements in the main text are performed with laser on cavity resonance
22
=
0. The count rate
Γ
(
=
0
)
relates to
Γ
SB,0
through the sideband resolution factor
(
2
m
/
κ
t
)
2
23
Γ
(
=
0
) =
Γ
dark
+
Γ
pump
+

κ
t
2
m

2
Γ
SB,0
n
m
,
(S3)
where
n
m
is the measured thermal occupation in the absence of the optomechanical backaction as
24
defined by equation 1 of the main text.
25
1