of 5
Nanowire photonic crystal waveguides for single-atom trapping and strong
light-matter interactions
S.-P. Yu,
1, 2,
J. D. Hood,
1, 2,
J. A. Muniz,
1, 2
M. J. Martin,
1, 2
Richard Norte,
2, 3
C.-L.
Hung,
1, 2
Se ́an M. Meenehan,
2, 3
Justin D. Cohen,
2, 3
Oskar Painter,
2, 3,
and H. J. Kimble
1, 2,
1
Norman Bridge Laboratory of Physics 12-33
2
Institute for Quantum Information and Matter
3
Thomas J. Watson, Sr., Laboratory of Applied Physics 128-95,
California Institute of Technology, Pasadena, CA 91125, USA
(Dated: February 6, 2014)
We present a comprehensive study of dispersion-engineered nanowire photonic crystal waveguides
suitable for experiments in quantum optics and atomic physics with optically trapped atoms. De-
tailed design methodology and specifications are provided, as are the processing steps used to create
silicon nitride waveguides of low optical loss in the near-IR. Measurements of the waveguide optical
properties and power-handling capability are also presented.
A new frontier for optical physics would become ac-
cessible with the integration of atomic systems and
nanophotonics, which have made remarkable advances in
the last decade [1–5]. Significant progress toward inte-
gration of atomic systems with photonic devices has pro-
gressed on several fronts, including cavity QED, where
atom-photon interactions can be enhanced in micro- and
nanoscopic optical cavities [6–11], and nanoscopic di-
electric waveguides, where the effective area of a guided
mode can be comparable to atomic radiative cross sec-
tions leading to novel photon transport in 1D [12–19], as
recently demonstrated in Refs. [20–23].
Beyond traditional settings of cavity QED and waveg-
uides, new paradigms emerge by combining atomic
physics with photonic crystal waveguides. One- and two-
dimensional photonic crystal structures formed from pla-
nar dielectrics [24] offer a configurable platform for en-
gineering strong light-matter coupling for single atoms
and photons with circuit-level complexity. For instance,
dispersion-engineered photonic crystal waveguides per-
mit the trapping and probing of ultracold neutral atoms
with commensurate spatial periodicity for both trap and
probe optical fields that have disparate free-space wave-
lengths [19]. Such systems can lead to atom-atom inter-
actions efficiently mediated by photons within the waveg-
uide [25–28].
In photonic crystal waveguides, atom-
photon coupling can be enhanced near the band-edge
via slow-light effects [19, 29], and can be tailored to ex-
plore quantum many-body physics with atom-atom in-
teractions that can be readily engineered [28].
Significant technical challenges exist for developing hy-
brid atom-photonic systems arising from the following
requirements: (1) The fabrication is sufficiently precise
to match waveguide photonic properties to atomic spec-
tral lines; (2) atoms are stably trapped in the presence of
substantial Casimir-Polder forces [19] yet achieve strong
These authors contributed equally to this work
opainter@caltech.edu
hjkimble@caltech.edu
a
0.46
0.47
0.48
0.49
330
340
350
360
Frequenc
y (
TH
z)
Axial w
avev
ec
tor
Cs D1
Cs D2
b
c
2
A
a
w
g
Γ
1D
Γ
k
×
(2
π
/a
)
1
FIG. 1. (a) Schematic of the alligator photonic crystal waveg-
uide (APCW) with dimensional parameters thickness
t
=
200 nm, inner waveguide width
w
= 187 nm, gap
g
= 260 nm,
discrete periodicity
a
= 371 nm, and sinusoidally-modulated
outer waveguide edge with ‘tooth’ amplitude
A
= 129 nm. (b)
Photonic bandstructure of the fundamental TE-like modes of
a nominal alligator waveguide device calculated with the di-
mensions derived from a typical fabricated device [30]. Small
adjustments are made to the waveguide parameters within
the absolute uncertainty of the SEM (
<
5%) to obtain bet-
ter agreement between measured band structures and those
computed from SEM images.
atom-field interaction; (3) coupling to and from guided
modes of nanophotonic elements is efficient; (4) suffi-
cient optical access exits for external laser cooling and
trapping; and (5) optical absorption is low and the net
device thermal conductivity is high, permitting optical
power handling to support
1 mK trap depths. In this
Letter, we describe nanowire photonic crystal waveguides
that meet these stringent requirements for integration of
nanophotonics with ultracold atom experiments.
The central component of our device is the ‘alliga-
tor’ photonic crystal waveguide (APCW) region shown
in Fig. 1a. It consists of two parallel Si
3
N
4
waveguides
(refractive index
n
= 2). This configuration is similar to
that proposed in Ref. [19] for the trapping of atoms in
the gap between the dielectrics, where the atomic spon-
taneous emission rate into a single guided mode, Γ
1
D
,
can be greatly enhanced with respect to spontaneous
emission into all other free-space and guided modes, Γ
,
which is approximately equal to the free-space sponta-
neous emission rate, Γ
0
. Figure 1b shows the theoretical
optical bandstructure of the TE-like modes (electric field
arXiv:1402.1147v1 [physics.optics] 5 Feb 2014
2
z
x
y
a
b
c
Γ
1
D
/
Γ
0
-5
-10
-15
-20
-25
0
-1000
-800
-600
-400
-200
0
-50
0
50
0
200
400
-200
-400
z
(nm)
y
(nm)
d
e
Pot
en
tial ( )
μ
K
350
355
330
335
0
1
2
3
4
5
Frequenc
y (
TH
z)
Pot
en
tial ( )
μ
K
f
F
=
4
,
m
F
=
4
F
=
4
,
m
F
=
4
F
=
5
,
m
F
=
0
F
=
4
,
m
F
=
0
FIG. 2. Finite-element-method (FEM) simulation of the near-
X
-point guided mode electric field magnitudes
|
~
E
(
~r
)
|
in the
x
-
y
plane for the (a) air band and (c) dielectric band of the even
parity TE-like supermodes for the periodic structure shown
in (b). The optical frequencies correspond to the Cs D1 and
D2 lines, and the corresponding band structure is shown in
Fig. 1b. (d-e) Numerically computed Casimir-Polder poten-
tial along directions (
x
m
,y
m
,z
) (d) and (
x
m
,y,z
m
) (e) for the
dielectric-band trapping mode around minima of the optical
trapping potential at (
x
m
,y
m
,z
m
) [i.e., the positions of the
green spheres in (c)]. (f) Calculated rate of radiative decay
Γ
1D
into the guided mode in (a) for the cases of an initially
excited atom trapped at (
x
m
,y
m
,z
m
) in an infinite photonic
crystal for transitions between atomic levels as depicted in
the figure. The shaded area indicates the photonic bandgap
region and the dashed lines the Cs D1 and D2 transition fre-
quencies. Here, Γ
0
is the free-space decay rate.
polarized in the plane of the waveguide) for the APCW
studied in this work, computed using the MIT Photonic
Bands (MPB) [30] software package. The waveguides are
designed such that the Cs D1 (
ν
1
= 335
.
1 THz) and
D2 (
ν
1
= 351
.
7 THz) transitions are aligned near the
lower/‘dielectric’ (
ν
D
) and upper/‘air’ (
ν
A
) band-edges,
respectively.
As discussed in detail in Ref. [19], the enhanced den-
sity of states near the
X
-point band-edge, along with the
strong field confinement of the even-parity supermodes in
the gap, can be used to create large atom-photon inter-
actions. Intensity images of the dielectric and air band
modes are plotted in Fig. 2a and b, respectively [30]. The
corresponding enhancement of Γ
1
D
is shown in Fig. 2f.
One strategy for trapping Cs atoms within the gap
of the APCW is to use the dielectric-band mode blue-
detuned from the Cs D1 line as a trapping beam, and the
air-band mode as a probe on the D2 line of the trapped
atoms. In this scenario [19], Cs atoms are trapped be-
tween the parallel dielectrics where the dielectric-band
mode has an intensity null in the
x
-
y
plane (Fig. 2a)
and the Casimir-Polder (CP) force provides additional
confinement in the vertical
z
-direction (Fig. 2d, e). Fur-
ther vertical confinement can be provided by an addi-
tional guided mode red-detuned from the Cs D2 transi-
tion. For the band structure shown in Fig. 1b and with
counter-propagating 30
μ
W TE-mode fields blue-detuned
30-GHz from the Cs D1
F
= 4
F
= 4 transition com-
bined with 15
μ
W of counterpropagating TE-mode fields
red-detuned 300 GHz from the D2
F
= 4
F
= 5
transition, we expect a trap depth of
'
5 mK and trap
frequencies of
{
ν
x
= 3
.
5
, ν
y
= 1
.
4
, ν
z
= 0
.
7
}
MHz.
Here, the total power within the device is 90
μ
W.
As shown in Fig. 3, we incorporate several elements
into the waveguide structure to in- and out-couple light,
to provide mechanical support, and to improve heat dis-
sipation. SEM images taken along the length of the SiN
waveguide show the various sections of the device, in-
cluding a waveguide-to-fiber coupling region (Fig. 3b),
mechanical support and thermal tethers (Fig. 3c), a ta-
pered region of the APCW (Fig. 3d), and finally the cen-
tral APCW region (Fig. 3e).
The waveguide-to-fiber coupling in Fig. 3b consists of
a slow tapering of the nanowire-waveguide from a nomi-
nal width of 300 nm down to an endpoint near the fiber
facet of width 130 nm and provides efficient optical mode-
matching to an optical fiber [31] (Nufern 780HP fiber;
mode field diameter 5
μ
m). To support the nanowire-
waveguide, nanoscale tethers are run from the side of the
waveguide either directly to the substrate or to side ‘rails’
of 7
.
5
μ
m wide SiN that extend the entire waveguide
length and connect to the substrate at either end of the
waveguide (Fig. 3B, C, D show the tethers). The tethers
are each 90 nm wide, and consist of a single tether for
fiber alignment at the ends of the waveguide and multi-
tether arrays of 15 tethers, spaced at a 220 nm pitch.
Finite-difference time-domain (FDTD) simulations [32]
show that the input coupling efficiency of the taper and
single alignment tether is
'
75% for light near the D2
line of Cs. The multi-tether supports provide anchoring
against the high stresses within the device and increase
device-substrate thermal contact. Optical scattering is
minimized at the multi-tether attachment points by ta-
pering the waveguide width up to 1
μ
m (see Fig.3b).
FDTD simulation shows that the scattering loss at the
multi-tether points is
<
0
.
5%.
The nanowire waveguides as shown in Fig.
3 are
formed from a thin film of stoichiometric SiN 200 nm in
thickness, grown via low-pressure chemical vapor depo-
sition on a (100) Si substrate of 200
μ
m thickness. This
sort of SiN has exhibited low optical loss in the near-
infrared [33–35], and large tensile stress (
1 GPa) [36].
A 1
×
5 mm window opened through the Si substrate pro-
vides optical access for laser trapping and cooling, with
the nanowire waveguides extending across the length of
window.
Even with the extreme aspect ratio of the
nanowire waveguides, the high tensile stress of SiN pre-
serves mechanical stability and alignment.
In order to obtain smooth waveguide side walls of ver-
tical profile and to avoid damage during the SiN etch,
we employ an inductively-coupled reactive-ion etch (ICP-
RIE) of low DC-bias and optimized C
4
F
8
and SF
6
gas ra-
tios. A similar etch has been used to create record-high Q
SiN micro-ring optical cavities near 800 nm [1, 33]. Fab-
rication of the waveguide chip begins with a UV lithog-
raphy step to define the back window region. We then
use a single
e
-beam lithography step to define the fine
3
A
B
C
D
E
F
500 nm
2
μ
m
50
μ
m
1 mm
25
μ
m
2
μ
m
a
b
c
d
e
FIG. 3. Center - Schematic of the waveguide chip, illustrating the various regions of the waveguide. Bottom - (a) Optical
image of the fiber-coupled waveguide chip showing the through-hole for optical access. Zoom-in SEM image of (b) the adiabatic
fiber-coupling region (A), (c) the alignment, mechanical support, and thermal heat-sink tethers (B,C,D), (d) the tapered region
of the APCW (E), and (e) the central APCW region (F). The sinusoidal modulation facilitates high-precision fabrication.
Other elements (not shown) are side thermal contacts which consist of a pair 7
.
5
μ
m wide SiN rails extending across the entire
length of the waveguide and connecting to the substrate.
features of the waveguide, and to set the fiber v-groove
position and width (which ultimately determine the fiber-
waveguide alignment). A piranha clean removes any re-
sist residue prior to a potassium hydroxide (KOH) wet
etch, which opens a through-hole in the Si substrate de-
fined by the two SiN windows on back and front. After
additional Nanostrip cleaning, the chip is transferred to
an isopropyl alcohol solution where it is dried using a crit-
ical point drying step to prevent stiction of the double-
wire APCW section. Lastly, an O
2
plasma clean removes
any residual particles on the waveguide surface.
Once fabricated, anti-reflection coated optical fibers
are mounted into the input and output v-grooves in the Si
substrate. The fiber-waveguide separation is set for op-
timal coupling (typically
<
10
μ
m) before the fibers are
affixed in place with UV curing epoxy. The Si chip and
fibers are then attached to a vacuum-compatible mount
(see Fig. 3a) and loaded into a vacuum enclosure (reach-
ing
10
9
Torr) with optical fiber feedthroughs [37].
In order to measure the broadband reflectivity and
transmission of the APCW, we utilize a broadband super-
luminescent diode optical source and optical spectrum
analyzer. Figure 4a shows the measured normalized re-
flection
R
and transmission
T
spectra over a frequency
range of 320-360 THz for a typical APCW waveguide.
The measured spectra demonstrate that the fabricated
APCW has the desired photonic bandgap, with the di-
electric and air band-edges closely aligned with the D1
and D2 lines of Cs, respectively, and in reasonable agree-
ment with the theoretical spectra in Fig. 4c-d. From the
average reflection level within the photonic bandgap, we
estimate the total single-pass coupling from optical fiber
to APCW to be
'
(60
±
5)%. The high-frequency os-
cillatory behavior of the reflected and transmitted inten-
sities is due to parasitic reflections from the AR-coated
input fiber facet (
0
.
1% reflection) and the input tether
(
0
.
2%). Based upon previous measurements for similar
waveguides, we estimate that the power loss coefficient of
the unpatterned nanobeam sections is
4 dB/cm.
Because of the finite length of the APCW reported in
this work, the spectral regions near the bandgap exhibit
slowly oscillating fringes in transmission and reflection
which can be intepreted as low-finesse cavity resonances
of the APCW section. FDTD simulations reproduce the
oscillatory behavior, as shown in Fig. 4(c-d). The en-
hancement of Γ
1
D
will be similarly oscillatory, in analogy
with the Purcell effect in cavity QED (see e.g., [7]). We
image the scattered light directly above the waveguide
as the frequency of a laser source is scanned across the
slow fringes at the band-edge. As shown in Fig. 4b (red
and blue traces), the scattered radiation from the APCW
section is modulated as the input frequency is scanned
from resonance to antiresonance. Based upon the mea-
sured enhancement of intensity within the APCW (nor-
malized with respect to illumination several THz from
the bandgap) of
'
30 (i.e., a cavity finesse of
'
10),
we estimate that at the reflection minimum nearest the
bandgap, Γ
1
D
/
Γ
0
'
20 for a Cs atom in the 6
2
P
3
/
2
|
F
= 5
,m
F
= 0
excited state.
The optical power handling capabilities of our devices
ultimately limit the trapping schemes we can consider.
Figure 4e shows the time- and frequency-dependent re-
flection signal of a single-mode laser, with frequency
tuned to the band edge of the APCW. In this mea-
surement, a heating laser, with frequency of 335 THz,
is abruptly switched on at the input fiber port using an
acousto-optic modulator at time
t
= 0, and then switched
off at
t
= 200 ms. The increase in the temperature for a
device in ultrahigh vacuum can be estimated by measur-
ing the shift of the fast fringe shown Fig. 4a. For an in-
put power of 95
μ
W, which corresponds to an intra-device
power of approximately 60
μ
W, we measure a wavelength
4
849
850
851
852
853
854
0.1
0.2
0.3
0.4
Wavelength (nm)
0.00
0.05
0.10
0.15
0.25
0.26
0.27
0.28
0.29
Time (s)
0
Field intensity enhanc
emen
t
Frequenc
y (
TH
z)
330
340
350
360
0.0
0.1
0.2
0.3
0.4
0.5
Frequenc
y (
TH
z)
a
b
e
c
d
Cs D1
Cs D2
351
352
353
0.4
0.3
0.2
0.1
0
0.4
0.3
0.2
0.1
0
355
354
353
352
351
350
337
336
335
334
333
332
Frequenc
y (
TH
z)
Transmission (
)
0
5
10
15
20
25
30
35
T
R
332.0
332.5
333.0
333.5
334.0
334.5
335.0
FIG. 4. (a) Plot of the measured reflection and transmis-
sion spectra of the complete device. A smoothing filter is ap-
plied to the raw (transparent curves) reflection measurement,
yielding the solid lines. Within the bandgap, the transmitted
optical power is 30 dB below the reflected power, consistent
with the optical spectrum analyzer noise floor. (b) Intensity
of the scattered light imaged from a region near the center
(blue) and 1/3 from the end (red) of the photonic crystal sec-
tion, and (black) reflected optical power as functions of the
wavelength of an incident probe laser. (c,d) Finite-difference
time-domain simulation (red) and measurements (blue) of the
reflection spectra near the air (c) and dielectric (d) band of
the device. (e) Thermal tuning of a waveguide reflection spec-
trum (red line) with respect to the device reflection spectrum
(blue) and time domain response of the device reflectivity (in-
set) to a step function input for which the intra-device power
is
'
60
μ
W. The time-domain response is fit with a double-
exponential function with time constants of 70 ms and 5 ms.
shift of the reflection spectrum of
δλ
= 40 pm. For a
thermo-optic coefficient of SiN of d
n
/d
T
2
.
5
×
10
5
[1],
and an average energy density overlap
η
E
= 0
.
85 of the
guided mode within the SiN, this corresponds to an av-
erage temperature rise of
δT
'
2
C. This rise is roughly
an order of magnitude smaller than the temperature rise
of our waveguide devices without thermal rails.
The waveguide technology presented here represents
an important step towards experiments with ultracold
atoms and nanophotonic chip-based optical circuits. The
chip-based technology allows nearly full optical access for
cooling and manipulation of atoms in the near-field of
nanowire waveguides. Integrated optical fibers also al-
low for highly efficient optical input and output chan-
nels for light coupled to arrays of atoms trapped along
the slot of the APCW. Through lithographic pattern-
ing of the nanowire waveguides, we have shown that
photonic bandgaps and band-edges may be reliably pro-
duced in the vicinity of electronic transitions of atoms,
a key requirement for strongly coupling atoms to the
guided modes of the structure. Indeed, current experi-
ments [23] with similar nanowire waveguides have yielded
an unprecedented spontaneous emission coupling factor
of Γ
1
D
/
Γ
= 0
.
32
±
0
.
08 for one Cs atom localized near
the peak of the probe mode of the APCW (Fig. 2(a)).
Further improvements in waveguide performance re-
sulting from lower optical absorption and scattering loss
in the nanowire waveguides should enable the trapping of
atoms via the fields of far off-resonant guided modes [19].
In addition, the mechanical compliance of the suspended
nanowire waveguides enables novel electro-mechanical
tuning methods, similar to those recently demonstrated
in tunable Si nanophotonic structures [38]. Such fine-
tuning would allow not only for precise alignment of pho-
tonic band-edges with atomic resonances, enabling strong
light-matter interactions, but also dynamic atom-photon
circuits in which optical dispersion of the APCW could
be changed rapidly in comparison to the time scales for
atomic radiative processes (e.g., photon mediated atom-
atom interactions).
This work was supported by the IQIM, an NSF Physics
Frontiers Center with support of the Moore Foundation,
the DARPA ORCHID program, the AFOSR QuMPASS
MURI, the DoD NSSEFF program (HJK), NSF PHY-
1205729 (HJK), and the Kavli Nanoscience Institute
(KNI) at Caltech. SPY and JAM acknowledge Inter-
national Fulbright Science and Technology Awards.
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