of 6
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
1 of 6
OPTICS
Direct Kerr frequency comb atomic spectroscopy
and stabilization
Liron Stern
1,2
*, Jordan R.
Stone
1,2
, Songbai
Kang
1,2
, Daniel C.
Cole
1,2
, Myoung-Gyun
Suh
3
,
Connor Fredrick
1,2
, Zachary
Newman
1,2
, Kerry
Vahala
3
, John
Kitching
1
,
Scott A.
Diddams
1,2
, Scott B.
Papp
1,2
*
Microresonator-based soliton frequency combs, microcombs, have recently emerged to offer low-noise, photonic-
chip sources for applications, spanning from timekeeping to optical-frequency synthesis and ranging. Broad
optical bandwidth, brightness, coherence, and frequency stability have made frequency combs important to
directly probe atoms and molecules, especially in trace gas detection, multiphoton light-atom interactions,
and spectroscopy in the extreme ultraviolet. Here, we explore direct microcomb atomic spectroscopy, using a
cascaded, two-photon 1529-nm atomic transition in a rubidium micromachined cell. Fine and simultaneous
repetition rate and carrier-envelope offset frequency control of the soliton enables direct sub-Doppler and
hyperfine spectroscopy. Moreover, the entire set of microcomb modes are stabilized to this atomic transition,
yielding absolute optical-frequency fluctuations at the kilohertz level over a few seconds and
<1-MHz day-to-day
accuracy. Our work demonstrates direct atomic spectroscopy with Kerr microcombs and provides an atomic-
stabilized microcomb laser source, operating across the telecom band for sensing, dimensional metrology,
and communication.
INTRODUCTION
Spectroscopy of atoms and molecules supports studies of quantum
matter and numerous applications. An important advance in laser
spectroscopy and metrology has been the use of optical-frequency
combs (
1
,
2
). Specifically, combs can interact with atoms and molecules
in direct frequency comb spectroscopy (DFCS), providing concep-
tually important measurements (
3
,
4
). In recent years, DFCS has been
applied to demonstrate sensitive and broadband molecular spectros-
copy (
5
,
6
), breath analysis (
7
), precision atomic spectroscopy (
8
10
),
steering Raman transitions (
11
), atomic clocks, (
12
) Ramsey spectros-
copy (
13
), temperature sensing (
14
), and extreme ultraviolet spectros-
copy (
15
), using numerous techniques such as dual-comb spectroscopy,
cavity-enhanced spectroscopy, fluorescence, and Ramsey spectroscopy.
Such a wide range of application directions and techniques are en-
abled by robust and controllable frequency comb sources.
Recently, dissipative Kerr solitons in optical microresonators have
been demonstrated to provide a compact platform for low-noise,
microwave-rate, and low–power frequency combs (
16
). Pumped with
a continuous laser, stable soliton pulses can be generated in a Kerr-
nonlinear microresonator. Despite the vast progress in using DFCS
in table-top combs, so far, demonstrations of microcomb-based DFCS
have been mainly focused in gigahertz-linewidth molecular spectros-
copy (
6
,
17
). Thus, the question of how to precisely control and direct-
ly interface microcombs with an atomic medium remains unresolved.
Soliton microcombs have already been used for various applications
(
16
), where for most, it is essential to leverage precise frequency
control of the soliton mode spectrum
m
=
f
ceo
+
m
·
f
rep
through two
degrees of freedom, i.e., the repetition frequency
f
rep
and the carrier-
envelope offset frequency
f
ceo
. However, these parameters are cou-
pled together in a complex manner by the soliton dynamics; this was
determined in (
18
) for high-
Q
silica microresonators. Through the
so-called “fixed points” of a microcomb, the possibility exists to de-
couple and precisely control
f
rep
and
f
ceo
. We can use this feature for
high-resolution microcomb DFCS.
A second approach is to stabilize
f
rep
, using phase modulation of the microcomb pump laser at the
free-spectral range (FSR). This technique was explored in (
19
), and
we can use it in DFCS to define a constant
f
rep
with respect to a micro-
wave clock, which completely decouples
f
ceo
from
f
rep
and allows sub-
stantial scanning and stabilization. A parallel benefit of microcomb
DFCS is to derive a compact, low-power, and stable frequency comb
spectrum by stabilization to a DFCS signal. Different avenues of fre-
quency stabilization microcombs have been explored, including micro-
combs locked to a table-top frequency comb system (
20
), all optical
double-pinning methods (
21
), and optical locking of a frequency-
doubled mode of a Kerr resonator to an atomic transition (
22
). Such
approaches often require multiple helper lasers and nonlinear crys-
tals that produce a large footprint. A microcomb-based frequency
comb directly interfaced to a compact atomic medium may serve
the vision to construct a fully chip scale–stable optical ruler. Recent
advances in integrated photonic-atomic systems (
23
,
24
) may further
support such highly compact physics package.
Here, we demonstrate microcomb DFCS of the cascaded 5P
3/2
-
4D
5/2
transition in
85
Rb at 1529.37 nm. By demonstrating our abil
-
ity to physically decouple between the microcomb’s degrees of
freedom in the frequency domain, we are capable of performing
high-
precision microcomb–based atomic spectroscopy and stabili-
zation with megahertz-level resolution and kilohertz-level stability.
This telecom-wavelength band atomic transition is convenient and
unique given the technological advantage of operating microcombs
with telecom lasers and other components. We generate a soliton
microcomb with a 1536-nm phase-modulated (PM) pump laser
and use one microcomb mode to interact with Rb atoms in a micro-
machined vapor cell (
25
). By also probing the near-infrared Rb D2
transition at 780 nm with a second laser, we resolve the dipole-
allowed 4
2
D
5/2
hyperfine manifold composed of ~10-MHz linewidth
1
Time and Frequency Division, National Institute for Standards and Technology,
Boulder, CO 80305, USA.
2
Department of Physics, University of Colorado Boulder,
Boulder, CO 80309, USA.
3
T.
J. Watson Laboratory of Applied Physics, California
Institute of Technology, Pasadena, CA 91125, USA.
*Corresponding author. Email: liron.stern@mail.huji.ac.il (L.S.); scott.papp@
nist.gov (S.B.P)
Copyright © 2020
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
2 of 6
atomic transitions. This double-resonance optical pumping (DROP)
technique (
26
28
) not only enables an enhancement in signal-to-noise
ratio with DFCS but also circumvents photodiode background noise
from modes of the microcomb that are off-resonance of rubidium
transitions. By frequency-locking the microcomb
f
ceo
to the
F
= 4–
to–
F
′ = 3 hyperfine transition among the 4
2
D
5/2
manifold, we stabilize
the fractional-frequency noise at the 10
−11
level. Moreover, we per-
form a day-to-day accuracy assessment, which indicates a <1-MHz
repeatability in the absolute
f
ceo
of the microcomb. The microcomb
DFCS technique that we describe is a general, robust, and compact
approach to implement an atomic transition–referenced micro-
comb, and it could be expanded to other spectral ranges and to
multiphoton DFCS.
RESULTS
Figure 1 presents an overview of our apparatus and results. We gen-
erate a soliton microcomb with a silica resonator that is evanescently
coupled via a tapered fiber (
29
); see the schematic in Fig. 1A. The
resonator is pumped with a 1536-nm laser, and the generated soliton
microcomb spectrum extends approximately 60 nm across the telecom
C-band. For microcomb DFCS, we send the soliton microcomb
light into a Rb atomic vapor. We implement the microcomb-atom
interaction via a pump-probe DROP scheme, involving one mode
of the microcomb and a 780-nm laser; the atomic level diagram is
depicted in the inset of Fig. 1A. The DROP approach is an optical
spectroscopic pump-probe technique implemented in a ladder three-
level atomic system, which detects the ground state to intermediate
level absorption as a probe for intermediate to excited-state popula-
tion. In our system, the 5
2
S ground state
F
= 3 hyperfine state is
primarily coupled to the 5
2
P
3/2
F
= 3 cycling transition. This is
achieved by using the D2 transition at 780 nm, which acts as a probe.
A second transition at the telecom wavelength of 1529 nm couples
the 5
2
P
3/2
state to the 4
2
D
5/2
hyperfine manifold and acts as an
atomic pump (distinct from the frequency comb pump). The DROP
technique has a few prominent advantages for implementation in
DFCS.
First, this pump-probe arrangement allows us to imprint the
spectroscopic information of the telecom hyperfine manifold on the
780-nm probe. Moreover, by nature of the optical-pumping process
(i.e., transfer of atomic population between the two 5
2
S ground states),
we gain a substantial increase in signal due to decrease in popula-
tion in the upper 5
2
S state (
27
). Consequently, the spectrum will consist
of three peaks. The width of these peaks is limited by the excited
state and intermediate states lifetimes and is essentially Doppler free
because of the combination of velocity selection processes and two-
photon coherence effects (
27
,
30
). These features make the cascaded
atomic system appealing for implementation of DFCS (
31
). Figure 1B
shows the devices that we use, namely, a high-
Q
silica wedge resonator
on a silicon chip and a micromachined, dispenser-based Rb atomic
vapor cell.
We create the soliton microcomb by pumping the silica resonator
with a 1536-nm external-cavity diode laser (ECDL). Direct, deter-
ministic single-soliton pulses are generated by pumping the microres
-
onator with 100 mW of PM light (
19
); the PM frequency is derived
from a hydrogen maser–referenced microwave synthesizer that is set
close (with a bandwidth of 80 kHz) to the resonator’s FSR of ~22 GHz.
With the PM light engaged, the microcomb’s
f
rep
is tightly locked
to the PM frequency. An illustration of this process is also shown in
Fig. 1A. This PM technique allows us to initiate single solitons with-
out transitioning through the chaotic regime. Moreover, seeding the
comb with the PM frequency forces the repetition rate of the comb to
align with the seeding frequency and directly controls and decouple
f
rep
from
f
ceo
. The optical-frequency spectrum is presented in Fig. 1C,
where a comb spanning across the C-band is evident, as well as the
seeding PM light. A zoomed section shows the specific comb mode
that interacts with the atomic medium.
We use microcomb
f
ceo
tuning to acquire the DFCS signal of the
cascaded Rb transitions. Operationally, we change the pump-laser
power to exclusively tune
f
ceo
, but this requires a detailed two-part
microcomb control procedure. First, we rely on the PM pumping
1529
1530
mm
Fig. 1. Direct Kerr comb atomic spectroscopy.
(
A
) Conceptual depiction of the microcomb and atomic system. A PM and power-controlled 1536-nm pump laser
energizes a single-soliton pulse in a silica whispering galley–mode resonator. The power control and phase-modulation frequency discipline
f
rep
and
f
ceo
, respectively. The
comb spectrum, in turn, illuminates a millimeter-scale micromachined rubidium cell. The comb has a 1529-nm mode that is resonant with a
85
Rb two-step atomic transition;
see relevant Rb atomic-level scheme in inset. (
B
) Photograph of typical Kerr comb chip and micromachined Rb vapor cell. (
C
) Soliton microcomb optical spectrum
acquired with 20-pm resolution; zoomed section highlights the mode that interacts with the atomic medium. (
D
) Probe transmission signal as function of comb frequency,
revealing the 4
2
D
5/2
dipole-allowed hyperfine manifold. Photo credit: Liron Stern, NIST (B).
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
3 of 6
technique to maintain a fixed value of
f
rep
. Second, we stabilize the
frequency detuning of the pump laser with respect to the silica reso-
nance, using an offset Pound-Drever-Hall (PDH) technique (
18
).
Stabilizing the frequency detuning both allows precise control of the
actual value of the detuning and eliminates the
f
ceo
dependence on
frequency detuning fluctuations. Changing the pump-laser power
causes thermal and nonlinear shifts of the silica resonance and in-
duces an exclusive shift in
f
ceo
of the entire equidistant comb, which
we use for Rb DFCS.
The spectroscopy data of the Rb transitions
obtained with an approximately 50% change in the microcomb pump
power are presented in Fig. 1D. Specifically, the 1529-nm comb mode
induces a variation in the 780-nm probe laser transmission through
the Rb vapor cell. Three clear peaks (as anticipated from the DROP
nature of this process) are evident, corresponding to the three
dipole-allowed transitions from the 5P
3/2
F
= 4 state to the 4D
5/2
3,4,5 states. The linewidth is measured to be ~10 MHz, which is close
to the limit of 6 MHz imposed by velocity selection and two-photon
coherence processes (
27
,
30
). To the best of our knowledge, this
is the first report resolving a hyperfine spectroscopic feature with
megahertz-level resolution directly using Kerr combs.
The ability to decouple the microcomb’s physical controls, i.e.,
pump-laser power and frequency, and the resonator detuning, from
the microcomb’s degrees of freedom, i.e.,
f
ceo
and
f
rep
, is central to
the implementation of high-resolution DFCS and subsequent stabili-
zation. The coupling of these parameters arises in a complex manner
from frequency shifts of the thermo-optic effect, the Kerr effect, and
the self-soliton effect that all act simultaneously. Therefore, a key
question is to what extent our microcomb operation procedure,
which is shown conceptually in Fig. 2A (an elaborate description of
this procedure is introduced in fig. S1), achieves such decoupling.
To answer this, we carry out an experiment in which we scan
f
ceo
and
monitor
f
rep
with a microwave frequency–counting system. For micro
-
wave counting, we select only a portion of the comb separate from
the PM pump modes. We present such a measurement in Fig. 2B
for two different scenarios; the black- and blue-colored traces indicate
f
rep
, and the orange trace is the pump power. In the first scenario,
the pump power is kept constant, and the
f
rep
data indicate a stable
lock. In the second scenario, the power is varied periodically, with
an amplitude corresponding to a 50% change, but
f
rep
remains un-
changed, indicating the robustness of the locking. To compare the
scenarios in detail, we record a more extensive frequency-counter
dataset and calculate the overlapping Allan deviation; see Fig. 2C.
Here, the Allan deviation averages down as
−1
, indicating that the
microcomb
f
rep
is effectively locked to the synthesizer’s frequency
f
and that the nonlinear processes do not write additional noise on
f
rep
even when
f
ceo
is perturbed. When we abruptly vary the pump power,
we do not observe a change in the locked accuracy or precision of
the soliton microcomb repetition frequency. These data confirm the
capability to decouple
f
ceo
and
f
rep
, solving an important challenge
for high-precision soliton microcomb DFCS.
By recognizing that such
power variation induces the spectroscopy presented in Fig. 1D, we
conclude that the soliton pulse envelope remains intact while inde-
pendently controlling underlying carrier wave.
We demonstrate one specific use of microcomb DFCS: stabiliza-
tion of the absolute optical frequency of the entire set of comb teeth.
In this experiment, we maintain the repetition-frequency stability
using PM pumping and its feeding synthesizer as described above
and stabilize
f
ceo
using the direct interface with the atomic medium.
To implement a servo lock of
f
ceo
, with respect to the DFCS signal,
we dither the pump-laser power to obtain an error signal and use a
proportional–integral–derivative (PID) controller to provide feed-
back. The variable optical attenuator indicated in Fig. 2A provides
the dither. Stabilization of the microcomb via the DROP spectroscopy
technique also requires that the 780-nm probe laser is stabilized to
the Rb D2 transition. In this work, we accomplish the 780-nm laser
stabilization in a separate saturated absorption apparatus, but this
could, in principle, also be performed in the same micromachined
cell as the DROP spectroscopy.
We characterize the frequency stability of the Rb-referenced micro-
comb by frequency-counting a specific tooth (a few modes apart in
frequency from the pump frequency), with respect to a self-referenced
erbium-fiber frequency comb (
32
). In Fig. 3A, we present the over-
lapping Allan deviation of the microcomb with Rb stabilization (red
points) and without (blue points). By referencing the microcomb to
A
B
C
Fig. 2. DFCS apparatus and demonstration of
f
rep
control.
(
A
) An ECDL drives fre-
quency shifter, driven by a voltage-controlled oscillator (VCO). The pump beam is PM
(PM1) at FSR.
We implement a PDH servo-loop to control the resonator detuning with
a counterpropagating PM (PM2) beam. This counterpropagating beam is circulated
and detected to create an error signal and control the pump frequency. A portion of
the comb spectrum is amplified and sent to a micromachined atomic cell, which is
also illuminated by a counterpropagating continuous wave (CW) 780-nm probe laser.
By using a dichroic mirror and a Si photodetector, the 780-nm light is monitored to
create an error signal to control a variable optical attenuator to lock
f
ceo
to the atomic
transition. (
B
) Soliton microcomb
f
rep
and pump power setting versus time (red). Blue
and black
f
rep
data indicate the different power conditions. (
C
) Corresponding over-
lapping Allan deviation (ADEV) for the case of constant and swept pump power.
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
4 of 6
the hyperfine structure of Rb, we improve its fractional-frequency
stability to as low as 2 × 10
−11
after 10 s of measurement time. Therefore,
with our system, all the microcomb mode frequencies are stable at the
~10-kHz level.
A potentially more important benefit of atomic-Rb stabilization
of our 1550-nm-band soliton microcomb is the long-term repeat-
ability of the microcomb mode frequencies. In this manner, a microcomb
could be available for an application without need for recalibration
or alignment. To assess day-to-day repeatability, we operate the sys-
tem over a span of 4 days, each day restarting the microcomb and
Rb laser system components, initiate a soliton microcomb, tune the
microcomb into resonance of the Rb transition, apply the stabiliza
-
tion, and count the optical frequency. We leave the Rb temperature
stabilization running at all times. We present these results in Fig. 3B,
where each optical-frequency trace (indicated by different colors)
represents a frequency measurement performed on a separate day.
The maximum day-to-day frequency change is 140(4) kHz (from the
first day to second), and the SD of the shifts is 65(4) kHz. The absolute
deviation corresponds to fractional uncertainty of 7 × 10
−10
, and the
last 3 days are a bit better. Considering that the system is subject to
environmental perturbations, is unshielded from magnetic fields, and
is not packaged, it would likely be possible to improve upon this per-
formance. And yet, for the given system, such accuracies and stability
already support applications such as chip-scale–based dimensional
spectroscopy, hazardous material sensing, and wavelength meter
calibration. Moreover, when considering a miniaturized system, such
demonstrated level of performance for stabilization of
f
rep
is con-
sistent with commercial Rb microwave references and crystal oscil-
lators. For instance, considering a commercial oven-compensated
crystal oscillator, capable of short-time stability and accuracy at the
10
−12
and 10
−8
level, respectively, would allow frequency stabilities
at the level demonstrated above for a bandwidth of ~50 nm (corre-
sponding to ~300 modes).
DISCUSSION
To summarize, we have demonstrated direct Kerr-microcomb atomic
spectroscopy by exploiting the cascaded 5P
3/2
-4D
5/2
transition in
85
Rb.
We use a comb mode near the 5P
3/2
-4D
5/2
transition frequency to
interact with the
85
Rb atoms by sending most of the comb spectrum
directly into the micromachined vapor cell. Our spectroscopy ex-
periments are enabled by fine frequency control of the microcomb,
which allows us to resolve the closely spaced hyperfine manifold with
linewidths of ~10 MHz. Even higher-resolution spectroscopy is
possible because of continuous sweeping of the microcomb. By im-
plementing a servo-loop, we lock the comb to the 5
2
P
3/2
F
= 4 state–
to–4
2
D
5/2
F
′ = 3 state atomic transition with a frequency uncertainty
approaching 10
−11
. Accuracy assessment of the system shows a sub-
megahertz accuracy over a few days. Such level of performance in a
compact footprint is competitive with previous demonstrations sta-
bilizing soliton Kerr-combs. Moreover, leveraging this level of accu-
racy to use the same comb to perform direct and traceable spectroscopy
on a different atomic specimen is possible by tuning the synthesizer
while maintaining the atomic lock. Our ability to decouple
f
rep
and
f
ceo
may further allow to demonstrate multiphoton excitations, such
as the 778-nm two-photon absorption transition in Rb (
33
) and allow
to interact directly with hyperfine transitions in atoms (
34
,
35
) via
Raman transitions or electromagnetic-induced transparency. These
realizations may allow to fully optically stabilize a Kerr comb to an
atomic medium and pave the way to other exciting Kerr-based DFCS
experiments.
MATERIALS AND METHODS
PM soliton initiation
The ECDL was driving a single-sideband (SSB), suppressed-carrier fre-
quency modulator controlled by a high-bandwidth voltage-
controlled
oscillator (VCO) for control of the pump laser. A portion of the laser
was frequency shifted and modulated by means of an acousto-optic
modulator and PM, whereas one sideband of the PM light was locked
to the cavity resonance. The high-bandwidth feedback allowed by
the VCO/SSB scheme allowed thermal instabilities associated with
the red detuning that is required for soliton generation to be over-
come. A counterpropagating (with respect to the acousto-optic
modulator–shifted beam) PM pump beam was coupled to the reso-
nator, thus parametrically seeding the resonator and allowing de-
terministic creation of single solitons. To generate single solitons,
the pump laser was initially detuned ~25 linewidths from resonance,
and subsequently, the detuning was decreased to ~3 linewidths, where
a soliton step was observed. An elaborate schematic of the experi-
mental arrangement is presented in fig. S1.
Micromachined vapor cell fabrication
The vapor cell has been constructed by using a combination of wafer-
scale fabrication silicon frames, anodic bonding, and Rb dispenser
pills (
25
). First, a 3-mm-thick silicon wafer was structured using a
Fig. 3. Direct Kerr comb atomic stabilization and day-to-day accuracy.
(
A
) Uncer-
tainty assessment of the optical frequency precision represented by an overlapping
Allan deviation plot for the locked (red) and unlocked case (blue). The inset shows
the time domain data over ~10
min from which the Allan deviation is calculated.
(
B
) Day-to-day optical frequency traces obtained by reinitiating the Kerr comb and
locking the comb directly to the cascaded atomic transition.
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
5 of 6
deep reactive-ion etching process, to create a silicon frame with two
chambers connected by channels. The large chamber has the di-
mensions of 3 mm by 3 mm, whereas the small chamber has the
dimension of 1.5 mm by 1.5 mm. Next, a 0.7-mm-thick Pyrex
window was anodically bonded to the silicon frame to form a preform.
Following, in a vacuum environment, a Rb dispenser pill was intro-
duced in the small enclosure, and a second Pyrex window was anod-
ically bonded to the exposed side of the silicon frame, creating a
closed cell. Last, the cell was activated by illuminating the dispenser
pill with approximately 1 W of 980-nm laser power to release natural
rubidium into the chambers enclosed within the cell.
Spectroscopy and
stabilization setup
The rubidium spectroscopy setup was based on the two-photon
cascaded transition in
85
Rb. A 780-nm ECDL was locked to the
F
= 2–to–
F
′ = 3 D2 transition in a centimeter-scale rubidium cell
using saturation spectroscopy. The frequency uncertainty of this
laser characterized by comparing its frequency to a commercial fre-
quency comb is 3 × 10
−12
/
1/2
. The laser was sent over fiber to illu-
minate the millimeter-scale micro-machined cell with a beam diameter
of approximately 1 mm. This laser serves as a probe for the counter-
propagating Kerr comb light interacting with the atoms. The Kerr
comb has an approximate beam diameter of 900
m, and the inter-
acting comb mode has an amplified power of approximately 50
W.
The Kerr comb was stabilized to the cascaded transition by feeding
the variable optical attenuator (VOA) with approximately 500-Hz
demodulated error signal. Last, a mode close to the pump frequency
is filtered out, compared to a tooth of the commercial locked fre-
quency comb system, and frequency was counted. Through a sepa-
rate systematic characterization of the DROP atomic transition,
using a telecom ECDL, we assessed two dominant contributions to
frequency shifts in our system: variations in the cell temperature and
optical power of the atomic system’s pump and probe. This analysis
shows that our cell has a normalized frequency temperature coeffi
-
cient of 10
−10
/°C and a frequency power coefficient of ~2 × 10
−11
and
~8 × 10
−11
for a change of 1% of the 780- and 1529-nm powers, re-
spectively. These coefficients allow the stability performance levels
reported here to be reached without any stringent temperature or
power stabilization control.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/6/9/eaax6230/DC1
Fig. S1. Kerr comb DFCS elaborate apparatus.
REFERENCES AND NOTES
1.
J. L.
Hall, Nobel lecture: Defining and
measuring optical frequencies.
Rev. Mod. Phys.
78
,
1279–1295 (2006).
2.
T.
W.
Hänsch, Nobel lecture: Passion for
precision.
Rev. Mod. Phys.
78
, 1297–1309 (2006).
3.
M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, S. A. Diddams, Direct
frequency comb spectroscopy.
Adv. At. Mol. Opt. Phys.
55
, 1–60 (2008).
4.
A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, J. Ye, United time-frequency spectroscopy
for dynamics and global structure.
Science
306
, 2063–2068 (2004).
5.
B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth,
G.
Guelachvili, T.
W.
Hänsch, N.
Picqué, Cavity-enhanced dual-comb spectroscopy.
Nat. Photonics
4
, 55–57 (2010).
6. M. Yu, Y. Okawachi, C. Joshi, X. Ji, M. Lipson, A. L. Gaeta, Gas-phase microresonator-based
comb spectroscopy without an
external pump laser.
ACS Photonics
5
, 2780–2785 (2018).
7.
M. J. Thorpe, D. Balslev-Clausen, M. S. Kirchner, J. Ye, Cavity-enhanced optical frequency
comb spectroscopy: Application to
human breath analysis.
Opt. Express
16
, 2387–2397
(2008).
8.
M.
C.
Stowe, F.
C.
Cruz, A.
Marian, J.
Ye, High resolution atomic coherent control via spectral
phase manipulation of
an
optical frequency comb.
Phys. Rev. Lett.
96
, 153001 (2006).
9.
D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, S. A. Diddams, Optical
frequency stabilization of
a 10
GHz Ti:sapphire frequency comb by saturated absorption
spectroscopy in
87
rubidium.
Phys. Rev. A
80
, 053806 (2009).
10.
I. Barmes, S. Witte, K. S. E. Eikema, High-precision spectroscopy with
counterpropagating
femtosecond pulses.
Phys. Rev. Lett.
111
, 023007 (2013).
11.
C. Solaro, S. Meyer, K. Fisher, M. V. DePalatis, M. Drewsen, Direct frequency-comb-driven
raman transitions in
the
terahertz range.
Phys. Rev. Lett.
120
, 253601 (2018).
12.
V. Gerginov, C. E. Tanner, S. A. Diddams, A. Bartels, L. Hollberg, High-resolution
spectroscopy with
a femtosecond laser frequency comb.
Opt. Lett.
30
, 1734 (2005).
13.
J. Morgenweg, I. Barmes, K. S. E. Eikema, Ramsey-comb spectroscopy with
intense
ultrashort laser pulses.
Nat. Phys.
10
, 30–33 (2014).
14.
A. Klose, G. Ycas, F. C. Cruz, D. L. Maser, S. A. Diddams, Rapid, broadband spectroscopic
temperature measurement of
CO
2
using VIPA spectroscopy.
Appl. Phys. B
122
, 78 (2016).
15.
A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, J. Ye, Direct frequency
comb spectroscopy in
the
extreme ultraviolet.
Nature
482
, 68–71 (2012).
16.
T. J. Kippenberg, A. L. Gaeta, M. Lipson, M. L. Gorodetsky, Dissipative Kerr solitons
in optical microresonators.
Science
361
, eaan8083 (2018).
17.
M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, A. L. Gaeta, Microresonator-based
high-resolution gas spectroscopy.
Opt. Lett.
42
, 4442–4445 (2017).
18.
J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, S. B. Papp,
Thermal and
nonlinear dissipative-soliton dynamics in
Kerr-microresonator frequency
combs.
Phys. Rev. Lett.
121
, 063902 (2018).
19.
D. C. Cole, J. R. Stone, M. Erkintalo, K. Y. Yang, X. Yi, K. J. Vahala, S. B. Papp,
Kerr-microresonator solitons from
a chirped background.
Optica
5
, 1304–1310 (2018).
20.
P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, T. J. Kippenberg, Full stabilization
of
a microresonator-based optical frequency comb.
Phys. Rev. Lett.
101
, 053903 (2008).
21.
S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, S. A. Diddams,
Microresonator frequency comb optical clock.
Optica
1
, 10–14 (2014).
22.
W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, A. B. Matsko, L. Maleki, Stabilized
C-band Kerr frequency comb.
IEEE Photonics J.
9
, 1–11 (2017).
23.
L.
Stern, B.
Desiatov, I.
Goykhman, U.
Levy, Nanoscale light–matter interactions in
atomic
cladding waveguides.
Nat. Commun.
4
, 1548 (2013).
24.
M. T. Hummon, S. Kang, D. G. Bopp, Q. Li, D. A. Westly, S. Kim, C. Fredrick, S. A. Diddams,
K.
Srinivasan, V.
Aksyuk, J.
E.
Kitching, Photonic chip for
laser stabilization to
an
atomic
vapor with 10
−11
instability.
Optica
5
, 443–449 (2018).
25.
L.-A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, J. Kitching, Microfabricated
alkali atom vapor cells.
Appl. Phys. Lett.
84
, 2694–2696 (2004).
26.
H.
S.
Moon, W.
K.
Lee, L.
Lee, J.
B.
Kim, Double resonance optical pumping spectrum
and
its application for
frequency stabilization of
a laser diode.
Appl. Phys. Lett.
85
,
3965–3967 (2004).
27.
H.
S.
Moon, L.
Lee, J.
B.
Kim, Double-resonance optical pumping of
Rb atoms.
J.
Opt. Soc. Am. B
24
, 2157–2164 (2007).
28.
H. S. Moon, W.-K. Lee, H. S. Suh, Hyperfine-structure-constant determination
and absolute-frequency measurement of the Rb 4
D
3/2
state.
Phys. Rev. A
79
,
062503 (2009).
29.
X.
Yi, Q.-F.
Yang, K.
Y.
Yang, M.-G.
Suh, K.
Vahala, Soliton frequency comb at microwave
rates in
a high-Q silica microresonator.
Optica
2
, 1078–1085 (2015).
30.
M. Tanasittikosol, C. Carr, C. S. Adams, K. J. Weatherill, Subnatural linewidths in
two-photon
excited-state spectroscopy.
Phys. Rev. A
85
, 033830 (2012).
31.
H.
S.
Moon, H.
Y.
Ryu, S.
H.
Lee, H.
S.
Suh, Precision spectroscopy of
Rb atoms using single
comb-line selected from
fiber optical frequency comb.
Opt. Express
19
, 15855–15863
(2011).
32.
G.
Ycas, S.
Osterman, S.
A.
Diddams, Generation of
a 660–2100
nm laser frequency comb
based on
an
erbium fiber laser.
Opt. Lett.
37
, 2199–2201 (2012).
33.
S. Y. Zhang, J. T. Wu, Y. L. Zhang, J. X. Leng, W. P. Yang, Z. G. Zhang, J. Y. Zhao, Direct
frequency comb optical frequency standard based on
two-photon transitions of
thermal
atoms.
Sci. Rep.
5
, 15114 (2015).
34.
D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell,
J. Mizrahi, C.
Senko, C.
Monroe, Entanglement of
atomic qubits using an
optical
frequency comb.
Phys. Rev. Lett.
104
, 140501 (2010).
35.
D.
Hou, J.
Wu, S.
Zhang, Q.
Ren, Z.
Zhang, J.
Zhao, A stable frequency comb directly
referenced to
rubidium electromagnetically induced transparency and
two-photon
transitions.
Appl. Phys. Lett.
104
, 111104 (2014).
Acknowledgments:
We thank S.-P.
Yu and M.
Hummon for comments on the manuscript. We
acknowledge the Kavli Nanoscience Institute. This work is a contribution of the U.S.
government and is not subject to copyright in the United States.
Funding:
We acknowledge
funding from DARPA DODOS and ACES programs, NASA, AFOSR award number FA9550-16-1-
0016, and NIST.
Author contributions:
L.S. conceived the concept and analyzed the data. L.S.
Stern
et al
.,
Sci. Adv.
2020;
6
: eaax6230 28 February 2020
SCIENCE ADVANCES
|
RESEARCH ARTICLE
6 of 6
and J.R.S. performed the experiments and wrote the paper. D.C.C. contributed to develop the
phase modulation initialization technique. Z.N., M.-G.S., J.K., and K.V. contributed to fabrication
of the devices. S.K. and J.K. provided the Rb-stabilized reference laser. C.F. and S.A.D.
provided the frequency comb reference system. S.B.P. supervised the project, designed the
experiments, and wrote the paper.
Competing interests:
The authors declare that they have
no competing interests.
Data and materials availability:
All data needed to evaluate the
conclusions in the paper are present in the paper and/or the Supplementary Materials.
Additional data related to this paper may be requested from the authors.
Submitted 8 April 2019
Accepted 5 December 2019
Published 28 February 2020
10.1126/sciadv.aax6230
Citation:
L.
Stern, J.
R. Stone, S.
Kang, D.
C. Cole, M.-G.
Suh, C.
Fredrick, Z.
Newman, K.
Vahala,
J. Kitching, S.
A. Diddams, S.
B. Papp, Direct Kerr frequency comb atomic spectroscopy and
stabilization.
Sci. Adv.
6
, eaax6230 (2020).