arXiv:1512.07389v1 [quant-ph] 23 Dec 2015
Coupling of erbium dopants to yttrium orthosilicate photon
ic crystal cavities for
on-chip optical quantum memories
Evan Miyazono,
1
Tian Zhong,
1
Ioana Craiciu,
1
Jonathan M. Kindem,
1
and Andrei
Faraon
1,
a)
T. J. Watson Laboratory of Applied Physics, California Inst
itute of Technology,
1200 E California Blvd, Pasadena, CA, 91125, USA
Erbium dopants in crystals exhibit highly coherent optical transition
s well suited
for solid-state optical quantum memories operating in the telecom b
and. Here we
demonstrate coupling of erbium dopant ions in yttrium orthosilicate t
o a photonic
crystal cavity fabricated directly in the host crystal using focus
ed ion beam milling.
The coupling leads to reduction of the photoluminescence lifetime and
enhancement
of the optical depth in microns-long devices, which will enable on-chip
quantum
memories.
a)
Electronic mail: faraon@caltech.edu
1
Optical quantum networks
1
are currently investigated for applications that require dis-
tribution of quantum entanglement over long distances. Optical qu
antum memories are
essential network components that enable high fidelity storage an
d retrieval of photonic
states.
2
However, for practical applications, solid-state components are
desirable. Rare-
earth doped crystals are state-of-the-art materials that have
been used for high performance
optical memories.
3,4
Of the rare-earth elements investigated for this application, erbiu
m
distinguishes itself as a natural choice for coupling directly to the low
-loss optical fibers
wiring the internet
5
due to its 1
.
53
μ
m optical transition in the telecommunications C band
with an optical coherence time of over 4 ms in yttrium orthosilicate cr
ystals (YSO).
6
For
quantum memories based on atomic frequency combs or controlled r
eversible inhomogeneous
broadening, initialization of the memory into a Zeeman state is inefficien
t in erbium doped
YSO (Er
3+
:YSO) compared to other rare earth ions because the optical lifetim
e (11 ms)
is comparable to the Zeeman level lifetime (
∼
100 ms).
7
Detailed balance and parameters
from Lauritzen et al.
7
show spin initialization efficiency is limited to 68% for a single pump
beam. Thus, while a few demonstrations of optical quantum memorie
s based on Er
3+
:YSO
have already been reported,
8
the efficiency of those memories were low and can be increased
significantly by improving the memory initialization. Spin mixing using an RF
source, or
driving the spin-flip relaxation path with a second laser can be used to
achieve an efficiency
of over 90%
7
. Alternatively, this lifetime reduction can also be accomplished by cou
pling
the rare-earth atoms to on-chip microresonators with high quality
factors and small opti-
cal mode volumes.
9
A spin initialization of 90% should also result from a reduction in the
effective excited state lifetime by a factor of 6. In this letter, we de
monstrate photonic
crystal resonators fabricated in Er
3+
:YSO. The coupling of Er ions to the cavity results in
enhanced interaction between the ions and photons coupled to the
cavity mode. This allows
for enhanced optical depth in a microns-long device and is thus an en
abling technology for
on-chip integrated telecom quantum memories. Excited state deca
y rate enhancement is
demonstrated, which can be used to achieve higher efficiency optica
l pumping to a Zeeman
level required to initialize the memory in protocols like atomic frequenc
y combs.
10
Triangular nanobeam optical cavities, like those demonstrated in ou
r other work,
11
were
scaled to have a resonant wavelength matching the 1536 nm transit
ion in Er
3+
:YSO. The
cavity consists of an equilateral triangular beam with rectangular g
rooves milled into the
top. Each side of the triangle is 1
.
38
μ
m wide and the grooves are 200 nm wide and 800 nm
2
(a)
(b)
10
μ
m
x
y
z
Top view
Side view
x
y
x
z
E
y
Mode Profile
Cross Section
Cross section
y
z
-1
1
E Field
Scale
Wavelength (nm)
Transmission
(c)
1400
1500
1600
FIG. 1. (a) Cross sectional views of the triangular nanobeam
through the center of the beam
showing the structure of the beam (top) and the simulated cav
ity mode profiles (bottom). (b)
Scanning electron microscope image of the triangular nanob
eam YSO cavity. Angled trenches at
the ends of the beam allow coupling from free space for transm
ission measurements. The x and y
axes correspond to the optical axes
D
2
and
D
1
, respectively while z corresponds to the
b
axis of the
orthorhombic YSO crystal. (c) Measured transmission throu
gh the nanobeam. Broad-spectrum
data taken with a supercontinuum laser; inset shows high-re
solution frequency scan of a narrow
linewidth laser in transmission through the cavity resonan
ce at room temperature; fitting of a
Lorentzian to the transmission spectrum shows the quality f
actor to be 11,400.
deep with a 570 nm period. The TE cavity mode possesses a simulated q
uality factor of Q
sim
= 70,000 and a mode volume of
V
mode
= 1
.
65(
λ/n
YSO
)
3
= 1
.
05
μ
m
3
. Here we have used the
Purcell definition of mode volume.
12
The cavity cross-section and optical mode profiles from
finite difference time domain simulations using MEEP
13
are shown in Fig. 1(a).
The YSO crystal was grown by Scientific Materials Inc. with 0.02% Er d
opants. The
crystal was cut such that the
b
axis was normal to the polished top surface. The resonator
was milled using a focused ion beam system (FEI Nova 600). The comple
ted device is shown
in Fig. 1(b). The nanobeam was oriented along the
D
2
direction of the YSO crystal, so that
3
the electric field of the TE mode was oriented along the
D
1
direction of the crystal, where
D
1
and
D
2
are the optical axes of the biaxial birefringent YSO crystal.
The device was optically characterized using a custom-made confoc
al microscope. The
transmission spectrum was measured over a broad range of frequ
encies using a supercontin-
uum laser for input, with the output measured directly on a spectro
meter with an InGaAs
photodiode array (PyLoN IR 1024-1.7). The transmission through
the beam is shown in Fig.
1(c) showing the cavity resonance peak near 1536 nm. The quality f
actor of this resonance
was determined to be Q=11,400 by least-squares fitting of a Lorent
zian to the transmission
curve. To attain higher resolution spectra, a tunable external ca
vity diode laser was stepped
in frequency across the cavity, with the spectrometer integratin
g the transmission for 0.2
seconds per data point on the photodiode array. Upon cooling to 4.7
K using a continuous
flow liquid helium cryostat, the cavity resonance shifted to a higher f
requency than the
atomic resonance. The atomic transition targeted was the 1536 nm
transition between the
lowest states of the
4
I
15
/
2
and
4
I
13
/
2
multiplets in the 4f orbital, labeled as Z
1
and Y
1
in
Fig. 2(a). This transition has an inhomogeneous broadening of
∼
500MHz at liquid helium
temperatures. Following the method presented in Mosor et al.,
14
the optical resonance of
the structure is precisely tuned to match the erbium absorption line
, illustrated in Fig. 2(b),
by slowly letting nitrogen gas into the cryostat, which deposits onto
the nanobeam. The
bottom scan on Fig. 2(b) shows a dip that is 25% the height of the full
Lorentzian transmis-
sion peak. As the power is lowered to reduce saturation, the size of
the atomic absorption
dip increases to
∼
40%. The expected absorption coefficient in bulk for a field polarized
along the
D
1
direction of the YSO crystal is 24.5 cm
−
1
.
15
A waveguide of the same length
(26 microns) would have an attenuation of 3.8%. The resulting subst
antial increase in the
optical depth is due to the interaction between the cavity mode and
the Er ensemble.
To measure the Purcell enhancement, the laser and resonator we
re tuned to the erbium
transition line, and an electro-optic modulator was used to excite th
e ions with rectangular
pulses 20 ms long with a 75 ms repetition period. The pulse and photolum
inescence decay
are shown in Fig. 3(a) and the additions to the confocal microscope
used for the lifetime
measurement are shown in Fig. 3(b). Time resolved photoluminescen
ce measurements were
taken with an IDQuantique ID220 InGaAs/InP avalanche photodiod
e detector. Given the
measured quality factor and simulated mode volume, the expected P
urcell enhancement for
4
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FIG. 2. (a) Erbium level diagram showing the crystal field spl
itting of the lowest and second
lowest energy states. (b) Resonator transmission spectra a
s the cavity resonance was tuned using
nitrogen deposition onto the 4.7K device. The three steps sh
ow high resolution frequency scans as
the cavity is tuned to the 1536 nm Er transition indicated in r
ed.
an ion positioned at the antinode of the cavity field is
F
P
=
3
4
π
2
(
λ
n
)
(
Q
V
)
∣
∣
∣
∣
E
ion
E
max
∣
∣
∣
∣
2
= 517
.
(1)
Here
F
P
is the Purcell factor,
λ
is the cavity wavelength,
n
is the cavity refractive index,
Q
and
V
are the cavity quality factor and mode volume, respectively. The fin
al term
accounts for positional misalignment between the field and the dipole
moment;
~
E
ion
is the
electric field at the ion and
~
E
max
is the maximum of the electric field. Since the ensemble
of ions is distributed uniformly inside the photonic crystal and the Pu
rcell enhancement
takes into account the emitter’s dipole overlap with the field, most ion
s will not exhibit the
full Purcell enhancement. The non-zero width of the inhomogeneo
us linewidth (
∼
500MHz)
was neglected, as it was much smaller than the cavity linewidth (
∼
17GHz). Taking these
considerations into account
9
gives an effective enhancement of 116.
Furthermore, the excited electrons can follow many decay paths f
rom Y
1
, of which only
the path directly to Z
1
couples to the cavity mode and is thus enhanced. We estimate
the branching ratio by comparing the expected emission rate, comp
uted from the 1536 nm
5
(a)
(b)
Normallized Counts
20
10
0
0
100
200
300
400
Time (ms)
Cavity enhanced
Bulk
-20
0
40
Optical input pulse
Photoluminescence
measurement
Time (ms)
Optical input pulse
Objective
Sample
Beam
Splitter
Spectrometer
Flip Mirror
SPD
Probe Laser
EOM
Timing
Module
Function Generator
L
i
f
e
t
i
m
e
M
e
a
s
u
r
e
m
e
n
t
FIG. 3. (a) Photoluminescence decay from erbium ions as a fun
ction of time. The cavity coupling
decreases the lifetime via the Purcell effect. The cavity-cou
pled luminescence converges to the bulk
curve because all of the excited ions do not experience equal
coupling. Inset shows the pulse used
to excite the luminescence. (b) Simplified schematic of the c
onfocal setup used to characterize the
devices. With the flip mirror up, lifetime measurements were
performed by modulating the input
with an electro-optic modulator (EOM) synchronized with a s
ingle photon detector (SPD).
transition dipole moment, and the measurable 1/11.4 ms spontaneou
s decay rate.
16
For this
calculation, we use the maximum absorption coefficient 24.5 cm
−
1
with FWHM of 510 MHz
for a 0.02% erbium ion dopant density given an electric field polarized alo
ng the
D
1
direction
from B ̈ottger et al.
15
to compute an oscillator strength
f
12
= 1
.
095
×
10
−
7
. This is half the
size of the value in McAuslan et al.
16
for
D
2
polarization due to the factor of two difference
between absorption coefficient for light polarized along the
D
1
and
D
2
directions. Following
the results from McAuslan et al.,
16
we find the spontaneous emission rate that we would
expect from only this decay path to be 10.03 Hz. Comparing this value
to the measured
excited state decay rate of 87.7 Hz (11.4 ms lifetime), we determine t
hat the branching
6
ratio for Er:YSO in our cavity is
∼
0.11. When taking this into account, the aforementioned
factor of 116 increase in the spontaneous emission rate averaged
over the cavity leads to a
reduction in the excited state lifetime by a factor of 13, down to
∼
900
μ
s.
Fitting a single exponential, the lifetime in the bulk was found to be 10.8 m
s, which is
in agreement with values in the literature.
16
This was compared to the decay rate for ions
in the cavity when the cavity is resonant with the ions. In this case tw
o exponential decays
were fit, analogous to the fitting procedure by Y. Gong et al.
17
, and one of the decay curves
had a time constant fixed at the bulk lifetime. The bulk lifetime in this fit c
orresponds
to ions that are not coupled to the optical cavity because they are
located in the mirror
sections. The shorter lifetime was 1.8 ms. The luminescence data aft
er the cavity had been
tuned to be resonant with the ions is shown in comparison to bulk lifetim
e data in Fig. 3(a).
The data was normalized by scaling the coefficient of the bulk decay ra
te.
Accounting for the branching ratio, the observed reduction in lifet
ime would correspond
to an effective Purcell enhancement of
∼
53. Due to the difficulty quantifying the number
of excited ions per homogeneous linewidth, this analysis does not tak
e into account the
collective coupling effect, which could have contributed to the obser
ved enhancement. Future
studies in this system will involve making cavities with higher quality fact
ors, different
dopant densities, and with the mode aligned to the
D
1
direction, which will allow a better
assessment of the discrepancy between the expected reduction
by a factor of 13 and measured
reduction by a factor of 6.
In conclusion, we have fabricated an optical microresonator in an e
rbium-doped yttrium
orthosilicate crystal, and used it to demonstrate enhanced optica
l depth and Purcell en-
hancement of the optical decay rate of the coupled erbium ions. Th
is is the first step to
efficient on-chip solid-state quantum memories in the telecom C band.
Next steps include
the measurement of optical coherence of the cavity-coupled ions
, as was demonstrated for the
883 nm transition of neodymium in YSO,
9
and photon storage using the atomic frequency
comb and controlled reversible inhomogeneous broadening techniqu
es.
ACKNOWLEDGMENTS
The authors sincerely thank Alexander E. Hartz for his contributio
ns. Financial support
was provided an AFOSR Young Investigator Award (FA9550-15-1-
0252), a Quantum Trans-
7
duction MURI (FA9550-15-1-002), a National Science Foundation
(NSF) CAREER award
(1454607), and Caltech. Equipment funding was also provided by th
e Institute of Quan-
tum Information and Matter (IQIM), an NSF Physics Frontiers Cen
ter (PHY-1125565) with
support of the Gordon and Betty Moore Foundation (GBMF-12500
028). The device was
fabricated in the Kavli Nanoscience Institute at Caltech with suppo
rt from Gordon and
Betty Moore Foundation.
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