ARTICLE
Received 15 May 2015
|
Accepted 29 Jul 2015
|
Published 14 Sep 2015
Nanophotonic coherent light–matter interfaces
based on rare-earth-doped crystals
Tian Zhong
1
, Jonathan M. Kindem
1
, Evan Miyazono
1
& Andrei Faraon
1
Quantum light–matter interfaces connecting stationary qubits to photons will enable optical
networks for quantum communications, precise global time keeping, photon switching and
studies of fundamental physics. Rare-earth-ion-doped crystals are state-of-the-art materials
for optical quantum memories and quantum transducers between optical photons, microwave
photons and spin waves. Here we demonstrate coupling of an ensemble of neodymium
rare-earth-ions to photonic nanocavities fabricated in the yttrium orthosilicate host crystal.
Cavity quantum electrodynamics effects including Purcell enhancement (
F
¼
42) and
dipole-induced transparency are observed on the highly coherent
4
I
9/2
–
4
F
3/2
optical
transition. Fluctuations in the cavity transmission due to statistical fine structure of the
atomic density are measured, indicating operation at the quantum level. Coherent optical
control of cavity-coupled rare-earth ions is performed via photon echoes. Long optical
coherence times (
T
2
B
100
m
s
) and small inhomogeneous broadening are measured for the
cavity-coupled rare-earth ions, thus demonstrating their potential for on-chip scalable
quantum light–matter interfaces.
DOI: 10.1038/ncomms9206
OPEN
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 East California Boulevard, MC 107-81, Pasadena, California 91
125, USA.
Correspondence and requests for materials should be addressed to A.F. (email: faraon@caltech.edu).
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Q
uantum light–matter interfaces (QLMIs) are quantum
devices composed of light emitters with quantum states
that can be controlled via optical fields and entangled to
photons
1,2
. They enable distribution of quantum entanglement
over long distances in optical quantum networks for quantum
communications
1
. Quantum networks of atomic clocks have also
been proposed for precise global time keeping and studies of
fundamental physics
2
. Realizing QLMIs requires control of light
and matter at the single atom and single photon level, which
enables optoelectronic devices such as optical modulators and
nonlinear optical devices operating at the most fundamental
level
3
. QLMIs are also expected to play a leading role in realizing
optical to microwave quantum transducers for interconnecting
future superconducting quantum machines via optical fibres
4,5
.
Scalable and robust QLMIs require emitters to have long spin
coherence times and coherent optical transitions. For integrated
optical quantum networks, these emitters need to be coupled to
on-chip optical resonators that capture the photons in a single
mode and further couple them into optical fibres or waveguides.
The solid-state emitters most investigated so far for on-chip
QLMIs are semiconductor quantum dots (QDs)
6
and nitrogen
vacancy (NV) centres in diamond
7
. To date, complete quantum
control of single QD and NV spins, spin–photon entanglement
and entanglement of remote NVs via photons have been
realized
8–10
. Both QDs
11
and NVs
12
have been coupled to
optical nanocavities. However, the challenge in growing optically
identical QDs limits their prospects for a scalable architecture
6
.
NVs embedded in nanostructures have long electronic spin
coherence times
13
, but suffer from optical spectral instabilities
such as blinking and spectral diffusion
14
. These spectral
instabilities have so far impeded the coherent coupling between
optical fields and NV centres in nanoresonators that are essential
for further developments of QLMIs.
Rare-earth ions (REIs) embedded in host crystals at cryogenic
temperatures exhibit highly coherent quantum states in the 4
f
orbital
15
. The Zeeman or hyperfine states of REIs can have
coherence times as long as 6 hours
16
, the longest ever
demonstrated in a solid. These states are connected via optical
transitions with the narrowest linewidth in the solid state (sub-
kHz) and small inhomogeneous broadening (MHz to GHz)
17
.
This outstanding optical and spin coherence makes REI-doped
crystals the state-of-the-art material for macroscopic solid-state
optical quantum memories
18,19
. Integrated REI-doped waveguide
quantum memories have also been developed
20,21
. Detection and
control of single REI spins has been recently demonstrated in
bulk material, but not using the transitions employed in optical
quantum memories at cryogenic temperatures
22,23
. Coupling the
highly coherent optical transitions of REIs to nanocavities will
enable on-chip QLMIs, where REI ensembles act as quantum
memories and single REIs act as qubits
24
.
Here we demonstrate high-cooperativity coupling of a
neodymium (Nd
3
þ
) ensemble to photonic nanocavities
fabricated directly in the yttrium orthosilicate (YSO) host crystal
and show coherent optical control of REIs coupled to
nanophotonic cavities. These results are enabled by the long
coherence time and small inhomogeneous broadening of cavity-
coupled REIs, which are essential properties that may lead to
nanophotonic QLMIs with better prospects for scalability than
those based on NVs and QDs.
Results
Photonic nanocavities in YSO
. The nanocavities, one of which is
shown in Fig. 1a, were fabricated in neodymium-doped YSO
(Nd
3
þ
:YSO) using focused ion beam milling. For this study, we
used devices fabricated in two types of samples with Nd doping of
0.2% and 0.003% (Scientific Materials Inc.). The photonic crystal
cavity is made of grooves milled in a triangular nanobeam
25
(Fig. 1b) (see Methods). Finite-difference time-domain
simulations
26
indicate a transverse electric (TE) mode with
quality factor exceeding 1
10
5
, mode volume
V
mode
¼
1.65(
l
/
n
YSO
)
3
¼
0.2
m
m
3
and mode profile shown in Fig. 1b. Here
V
is
defined as
V
mode
¼
R
V
E
(
r
)|E(
r
)|
2
d
3
r
/max(
E
(
r
)|E(
r
)|
2
), where E(
r
)
is the electric field and
E
(
r
) is the electric permittivity at position
r
. Two 45
°
angled cuts at both ends of the nanobeam (that is,
couplers) allow for coupling light from a direction normal to the
chip (that is, b in Fig. 1b) using a confocal microscope setup
(see Methods). A broadband light source was coupled into the
resonator from one end and the transmitted light was collected
from the other coupler with typical efficiencies ranging from
20% to 50%. The transmitted spectrum shows a resonance with
quality factor
Q
¼
4,400 (Fig. 1c) in the device used for the
following measurements. Arrays of devices were reproducibly
fabricated with similar performance (Supplementary Fig. 1 and
Supplementary Note 1).
Coupling rate between REIs and the nanocavity
. The coupling
of Nd
3
þ
ions to the nanocavity was observed through
enhancement in photoluminescence (PL) and emission rates.
With the 0.2% device cooled at 3.5 K (Montana Instruments
cryostation), an 810 nm laser coupled into the cavity excited PL in
the
4
I
9/2
–
4
F
3/2
transition that was then collected from the output
coupler (Fig. 2a). The PL spectrum shows two lines at 883.05 and
884.06 nm, corresponding to two inequivalent sites (
Y
1
and
Y
2
)of
Nd
3
þ
in YSO. An important observation is that the inhomoge-
neous linewidth of the ions in the cavity is the same as in the bulk
material, for both the 0.2% (
D
inhom
¼
16.0 GHz) and 0.003%
(5.9 GHz) devices (Supplementary Note 2). A small inhomoge-
neous linewidth (on the order of
B
10 GHz) is important for
scaling to networks of multiple QLMIs (Supplementary Note 3).
The cavity resonance was tuned across the Nd
3
þ
PL line using a
gas condensation technique
12
. The spectrograms in Fig. 2b–d
show enhancement of the
Y
1
line when the cavity is resonant with
it, which is a signature of coupling. The
Y
2
line exhibits negligible
enhancement, because its dipole moment is not aligned with the
TE cavity polarization (
D
1
axis of the YSO crystal, Fig. 1b). The
spontaneous emission rate enhancement was characterized via
lifetime measurements. A pulsed laser at 810 nm excited
fluorescence of the
Y
1
line, which was filtered using a
monochromator and detected with a single photon counter
(Fig. 2e). From single exponential fits, we calculated a reduction
in lifetime from 254
m
s
when the cavity is detuned by
D
l
¼
0.3 nm, to 87
m
s
on resonance. Taking into account the
branching ratio of the 883 nm transition (
b
B
4.5%, see Methods),
the reduction in lifetimes corresponds to an ensemble averaged
Purcell factor
27
F
¼
42, which agrees well with the estimations
that assume a uniform spatial distribution of Nd
3
þ
ions in the
resonator (Supplementary Note 4). A single ion positioned at the
maximum cavity field would experience a Purcell factor of
B
200.
A similar result was obtained in a 0.003% cavity with lower
quality factor (Supplementary Fig. 2 and Supplementary Note 5).
Optical coherence time for cavity-coupled REIs
. Coherent and
stable optical transitions are essential for QLMIs. We character-
ized the optical coherence time
T
2
of the 883-nm transition using
two-pulse (
p
/2
p
) photon echo techniques (Fig. 3a), with an
applied magnetic field of
B
¼
0.5 T (see Methods). The laser
pulses were coupled in and the echoes were collected via the
couples when the 0.2% and 0.003% cavities were on resonance
with the Nd transition. As only a small sub-ensemble (
o
100
ions) in the cavity was excited, the weak echo signal required
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detection using single photon counters. A typical echo from the
0.2% cavity is shown in Fig. 3d. The echo decays as a function of
the (
p
/2
p
) time delay
t
are plotted in Fig. 3b together with
photon echoes from bulk substrates. Echo intensity decays by e
for delay
t
1/
e
. For the 0.2% sample,
T
c
2
¼
4
t
1
=
e
¼
2
:
8
0
:
4
m
s
was measured for the cavity, which shows a good agreement with
the bulk value of
T
b
2
¼
3
:
2
0
:
4
m
s. For the 0.003% sample, the
echo exhibited two exponential decays. The slower decays give
T
b
2
¼
100
5
m
s (bulk) and
T
c
2
¼
94
5
m
s (cavity), which
match with values reported in ref. 28. The fast decays are likely
due to the superhyperfine interactions between Nd
3
þ
and its
neighbouring yttrium ions, which commonly manifests as
modulated echoes decaying faster than
T
2
(ref. 28). No
oscillations were observed in Fig. 3a because of the fast mod-
ulation frequency (
B
1 MHz) due to the strong magnetic field.
Oscillations of echoes for the initial 10
m
s delay were observed
when the
B
field was reduced to
o
100 mT. In addition, changes
in the
T
2
values were not observed as the excitation power was
varied, which indicates the measurement was not significantly
affected by instantaneous spectral diffusion. In sum, the good
agreement on
T
2
between the cavity and bulk confirms that the
optical coherence property of Nd
3
þ
ions is not affected by the
nanofabrication. For higher Purcell factors, the
T
2
in cavities
should decrease owing to the
T
2
r
2
T
1
limit and would become
(nm)
878
879
Cavity transmission (a. u.)
0
1
1
–1
0
b
D
1
b
D
2
780 nm
b
D
1
D
2
c
ab
B
= 500 mT
E
Q
= 4,400
Figure 1 | Photonic crystal nanobeam resonator fabricated in Nd:YSO.
(
a
) Scanning electron microscope image of the device. Scale bar, 2
m
m.
The red inset is a zoomed-in view of the 45
°
angle-cut coupler that allows vertical coupling of light from a microscope objective. The blue inset shows the
grooves forming the photonic crystal. (
b
) Schematics of the nanobeam resonator with simulated electric field (
E
along
D
1
) profiles of the fundamental TE
resonance mode. The TE polarization aligns with the
D
1
axis of the YSO crystal. A magnetic field of 500 mT is applied in the
D
1
–
D
2
plane at an angle of
a
¼
135
°
with respect to the
D
1
axis. (
c
) Broadband cavity transmission spectrum showing the cavity resonance with quality factor
Q
¼
4,400.
(nm)
(nm)
883
883
884
884
885
885
Photoluminescence counts
0
50
100
150
0
50
100
150
Detuning (GHz)
–100 –50
50
0
100
Lifetime (
μ
s)
100
150
200
250
t (
μ
s)
0
200
400
600
Counts
10
2
10
1
Δ
=0 nm
Δ
=0.3 nm
883 nm
via cavity
Via other states
4
F
5/2
4
F
3/2
4
I
9/2
810 nm
70
60
50
40
30
Time (a. u.)
20
10
ab
f
e
d
c
Δ
Δ
=0 nm
Y
1
Y
2
Figure 2 | Purcell-enhanced coupling of Nd
3
þ
ions to the YSO cavity mode.
(
a
) Schematic of energy levels for Nd
3
þ
in YSO. Optical excitation at
810 nm results in PL at several wavelengths with only the 883-nm transition enhanced by the cavity. (
b
) Spectrogram showing the Nd
3
þ
PL, while the
cavity is tuned across resonance using gas condensation. The dashed line is a guide to the eye indicating the central wavelength of the cavity resonanc
e.
The cavity resonance is not visible, because there is no background luminescence to populate the cavity mode. PL spectra in the uncoupled (
c
) and coupled
(
d
) cases. The cavity resonance was drawn to indicate the cavity location. (
e
) Lifetime measurements for coupled (
t
c
¼
87
m
s,
D
l
¼
0) and uncoupled
(
t
0
¼
254
m
s,
D
l
¼
0.3 nm) cases. (
f
) Change in lifetime as a function of the cavity detuning, which fits well with the calculation (red curve) using quality
factor
Q
¼
4,400, 4.5% branching ratio and field intensity averaged over the mode volume.
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smaller than the bulk value. This regime is not reached here,
because the Purcell enhanced 2
T
1
is not smaller than
T
b
2
.
The observation of photon echoes demonstrates coherent
optical control of the quantum state of cavity-coupled ions. This
control was further extended by varying the
p
pulse duration and
observing Rabi oscillations in the echo intensities as shown in
Fig. 3c. A Rabi frequency of
B
6 MHz is estimated. The same
oscillation was not observed in the bulk. For the coupled laser
power, the optimal
p
pulse duration is 0.4
m
s. The oscillations are
not visible for pulse duration
o
0.3
m
s, because of the limited
rise/fall times (
B
200 ns) of the pulse-generating setup (Methods).
A
B
12-fold increase in the echo intensity is observed in the
cavity-coupled case compared with the uncoupled case (that is,
detuning
D
l
¼
15 nm) as shown in Fig. 3d. This enhancement can
be attributed to a combination of several effects: the higher
atomic absorption rate through the Purcell effect
29
, stronger
intracavity field intensity and high echo collection efficiency as
the ions emit dominantly into the cavity mode. The spectral
diffusion of the coupled ions using three-pulse photon echoes was
also investigated. The homogeneous linewidths were broadened
at rates of 6.1 kHz
m
s
1
for the 0.2% doped cavity and
380 Hz
m
s
1
for the 0.003% cavity. These slow spectral
(
μ
s)
3
2
16
5
4
Counts
0
20
40
60
80
pulse width (
μ
s)
0.3
0.4
0.5
0.6
0.7
0.8
Echo intensity (a.u.)
10
20
30
40
50
60
(
μ
s)
01020
2
1
30
40
50
Photon echo counts (log scale)
–6
–5
–4
–3
–2
–1
0
0.2% Cavity
0.2% Bulk
0.003% Cavity
0.003% Bulk
Time
Echo field
/2
3
–5
–4
–3
–2
a
c
d
3
5
Coupled
Uncoupled
b
Figure 3 | Photon echo measurements from an ensemble of Nd
3
þ
ions in the cavity.
(
a
) Two-pulse photon echo sequence (
p
/2
p
) used to measure
T
2
.
(
b
) Two-pulse photon echo decays measured in both the cavity (red) and the bulk (black) samples with two different doping concentrations. The inset plot
s
the echo decays measured with a 0.2% doped sample. (
c
) Oscillation of echo intensity with increasing width of the
p
rephasing pulse. The periodic
signal reveals the ensemble averaged Rabi frequency of the coupled ions. The ideal
p
pulse duration for the input power was 0.4
m
s. (
d
) Enhanced photon
echo intensity (by
B
12-fold) when the cavity is coupled, compared with the uncoupled case (cavity detuned by
D
l
¼
15 nm so that the transition is outside
the photonic bandgap).
Detuning (GHz)
–30 –20 –10
0
Counts
0
100
200
300
400
500
600
700
800
900
10
20
30
Counts
150
200
250
Trace 1
Trace 2
Transmission (a.u.)
(nm)
882
882.5
883
883.5
Frequency (MHz)
a
b
4
F
3/2
-
4
I
9/2
c
1
0
1
0
1
0
0
100
50
Figure 4 | Control of cavity transmission and observation of SFS.
(
a
) Broadband transmission spectra as the cavity is tuned to the 883 nm Nd transition.
A dip is observed when the two are on resonance. The negligible dip at far detunings confirms that this effect is not due to absorption, but quantum
interference between the intracavity field and the ions. (
b
) High-resolution transmission spectrum (red curve) obtained by scanning a narrow linewidth
(
B
20 kHz) Ti:Sapphire laser over the inhomogeneous line. The green curve is the fit using parameters:
g
¼
2
p
6 MHz,
G
h
¼
2
p
100 kHz,
G
inhom
¼
16.0 GHz, and assuming a Gaussian ion density distribution. The green shaded region is the estimated fluctuation in the transmitted laser intensity
caused by
ffiffiffiffi
N
p
statistical variations of the ion density. Large fluctuations are expected, because the density
N
is low (few tens), which agrees with the
measurement. The fluctuation within the inhomogeneous linewidth is noticeably larger than that at far detunings (
4
25 GHz) and the technical background
noise (grey area), confirming that they are caused by SFS of the ion spectral density. (
c
) Two traces of the transmitted intensities over the same 100 MHz
bandwidth near zero detuning at different times. The high degree of correlation confirms the static and repeatable nature of SFS.
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diffusions permit repeated optical addressing of the ions for 10 s
of
m
s (Supplementary Fig. 3 and Supplementary Note 6).
Dipole-induced transparency and statistical fine structure
.
QLMIs require efficient interactions between atoms and photons,
which is why quantum memories use long atomic clouds or
doped crystals to achieve large optical depth. One key advantage
provided by nanoresonators is that efficient atom–photon inter-
action can be achieved in a small volume with only a handful of
ions. This is readily observable in our system, where the Nd
3
þ
ions coherently interact with the intracavity field and control its
transmission via dipole-induced transparency
30
. With the cavity
tuned to 883 nm, the cavity transmission was probed using
broadband light and a dip was observed at resonance (Fig. 4a).
The depth of the dip depends on the collective coupling
cooperativity
Z
¼
4
N
g
2
=
k
G
h
ðÞ
, where
g
is the ensemble
averaged coupling strength,
k
is the cavity full linewidth,
G
h
is
the Nd
3
þ
homogeneous linewidth and
N
is the number of ions
per
G
h
. Considering an empirical collective dipole–cavity
coupling model, the normalized cavity transmission in the
presence of unsaturated resonant ions is,
T
¼
k
i
D
þ
k
þ
4
N
g
2
=
G
h
2
;
ð
1
Þ
which simplifies to
T
¼
(1
þ
Z
)
2
for zero detuning
31
. The cavity
transmission can be controlled by varying the probe light power
and observing the saturation of the ions at increasing intracavity
photon number (Supplementary Fig. 4 and Supplementary
Note 7). The saturation photon number in the nanocavity was
measured to be
h
n
cav
i¼
2
10
5
.
To better resolve the spectrum, a narrow (
B
20 kHz)
Ti:Sapphire laser was scanned across the resonance (see Methods)
to give the transmitted signals shown in Fig. 4b,c. A 75% decrease
in transmission was measured at zero detuning, which corre-
sponds to a collective cooperativity
Z
B
1.2. Fitting using a
Gaussian spectral density distribution (green line) with
measured parameters
g
¼
2
p
6 MHz,
G
h
¼
2
p
100 kHz and
G
inhom
¼
16.0 GHz gives a peak ion density of
N
E
53. Because of
the statistical fine structure (SFS) of the inhomogeneously
broadened line, a variation in the transmitted intensity
(
h
d
T
i
2
d
2
T
dN
2
h
d
N
i
2
), owing to
d
N
¼
ffiffiffiffi
N
p
fluctuations in the
ion spectral density is expected
32
. This expected variation is
represented in Fig. 4b by the green shaded region and shows good
agreement with that of the measured signal. This variation within
the inhomogeneously broadened line, on which the statistical
fluctuations of the ion spectral density are imprinted, is
significantly larger than the spectrometer technical noise (grey
area) and laser shot noise at far detunings (
4
25 GHz), thus
confirming that the static SFS in spectral density
N
(
D
l
) is probed.
Two traces of the laser scan over the same 100 MHz bandwidth
near zero detuning at different times are shown in Fig. 4c. The
high degree of correlation reflects the static and repeatable nature
of SFS. Notably, the current platform would allow detection and
control of a single ion coupled to the cavity if
N
o
o
1 and the laser
linewidth were narrower than
G
h
(Supplementary Fig. 5 and
Supplementary Note 8).
Discussion
The results reported in this paper (long optical coherence time,
small inhomogeneous broadening, enhanced coherent optical
control and resonant probing of cavity-coupled REIs) demon-
strate REI-based nanophotonics as a promising approach for
robust and scalable quantum photonic networks integrating
memories and single REI qubits. Single photon rates exceeding
1 MHz can be achieved with single REIs in nanocavities with
Q
/
V
B
10
4
–10
5
(
V
is normalized to (
l
/
n
)
3
) and the inhomoge-
neous broadening allows for frequency multiplexing of multiple
REIs. To use the interface as an optical quantum memory,
efficient optical pumping into the long-lived Zeeman level needs
to be demonstrated. Bulk REI quantum memories already boast
high storage efficiency
33
with multi-mode capacity
28
. Their
implementations in our nanophotonic platform open the
possibility of multiplexed systems for on-chip quantum
repeaters. For Nd, high-fidelity storage of entanglement based
on atomic frequency comb has been demonstrated
34,35
. With
cavity impedance matching
29
, unit storage efficiency is achievable
with a mesoscopic ensemble of cavity-coupled ions. Meanwhile,
long-lived nuclear spin coherence of 9 ms in
145
Nd (ref. 36) bodes
well for spin–wave quantum memories using our nanoresonators.
These devices can be further coupled to superconducting or
optomechanical devices, to enable hybrid quantum systems
4
.
Furthermore, the technology can be readily transferred to other
wavelengths, such as 1.5
m
m for telecom quantum memories
using Er
3
þ
:YSO or 580 nm for long-haul quantum hard drives
using Eu
3
þ
:YSO (ref. 16).
Methods
YSO nanoresonator design and fabrication
.
The nanobeam has an equilateral
triangular cross-section with each side of 780 nm. This geometry allows a circular
fundamental mode field that can be efficiently coupled with a free space laser beam.
The cavity is formed by 40 equally spaced grooves of lattice constant 340 nm on the
nanobeam, except for a defect introduced at the centre by perturbing the lattice
constant. The depth of the grooves is 65% of the beam height. The triangular
nanobeam resonator was fabricated using focused ion beam milling followed by
wet etching of Ga
þ
contaminated YSO in diluted (10%) hydrochloric acid. An ion
beam of 20 kV, 0.2 nA was used to fabricate the suspended nanobeam waveguide by
milling at 30
°
angle with respect to the crystal surface normal. A small ion beam of
23 pA was then used to accurately pattern the grooves on top of the nanobeam.
Limited by the finite width of the focused ion beam, the side walls of the grooves in
the actual device were not vertical, but had an angle of 6
°
. This leads to a degraded
theoretical
Q
of 5.0
10
4
. We were able to reproducibly fabricate arrays of
resonators (up to six) in a batch (Supplementary Fig. 1), with all the devices
measuring resonances close to 883 nm and quality factors varying from 1,100
to 10,000.
Experimental setup for the photon echo measurements
.
A 500-mT external
magnetic field was applied at
a
¼
135
°
relative to the crystal
D
1
axis using a pair of
permanent magnets (see Fig. 1b). The
p
/2 and
p
Gaussian pulses were generated by
amplitude-modulating the Ti:Sapphire laser with two acousto-optic modulators
(AOMs) in series, with each in a double-pass configuration. The two pulse widths
were 250 and 400 ns at a repetition rate of 1 kHz. The average (peak) power of the
excitation pulses was 210 nW (320
m
W) measured after the objective lens. The
extinction ratio between the on and off level of the pulses was
B
120 dB, ensuring
sufficient signal-to-noise ratio for detecting echo photons using a Si single-photon
counter (Perkin Elmer SPCM). A third shutter AOM in single-pass configuration
was inserted just before the photon counter to block the strong excitation pulses
from saturating the detector. The extinction ratio of this shutter AOM was 30 dB.
High-resolution laser spectroscopy on cavity-coupled Nd
3
þ
ions
.
For the
cavity transmission experiments, the Ti:Sapphire laser (M Squared SolsTiS)
was continuously scanned at a rate of 10 MHz per second. The high-sensitivity
charge-coupled device camera in the spectrometer (Princeton Instruments PIXIS)
registers the transmitted photon counts intermittently at an adjustable frame rate
(frames per second (fps)) with an exposure time 0.01 s for each frame. Therefore,
one exposure corresponds to a spectral width of 10 MHz
0.01
¼
100 kHz scanned
by the laser, which is equal to the homogeneous linewidth of the 0.2% doped
sample. The long-term drift of the laser is 10 MHz per hour, so the drift during
each exposure should be inconsequential. Each data point in Fig. 4b,c represents
the photon count collected in one camera exposure, corresponding to the signal
contributed by the ions within one homogeneous linewidth. The frame rate was
0.1 fps for the coarser scan in Fig. 4b, corresponding to a spectral interval of
100 MHz between two adjacent data points. The frame rate was 8.2 fps for the fine
scan in Fig. 4c, with a spectral interval
B
1 MHz. Each data point was obtained with
one scan. Several scans at different spectral regions were performed and stitched
together to cover the entire bandwidth in Fig. 4b.
Estimation of the branching ratio
.
The measured optical depth of a 15-
m
m-long
nanobeam resonator at 3.8 K was
d
¼
0.1, from which we deduce an oscillator
strength of
f
¼
6.5
10
7
and a spontaneous emission rate of this transition to be
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9206
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NATURE COMMUNICATIONS
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g
883
¼
1/
t
883
¼
1/5.6 ms (ref. 24). With a measured bulk medium lifetime
t
0
¼
250
m
s, the branching ratio was thus estimated to be
t
0
/
t
883
E
4.5%.
References
1. Kimble, H. J. The quantum internet.
Nature
453,
1023–1030 (2008).
2. Ko
́
ma
́
r, P.
et al.
A quantum network of clocks.
Nat. Phys.
10,
582–587 (2014).
3. Chen, W.
et al.
All-optical switch and transistor gated by one stored photon.
Science
314,
768–770 (2013).
4. Williamson, L. A., Chen, Y.-H. & Longdell, J. J. Magneto-optic modulator with
unit quantum efficiency.
Phys. Rev. Lett.
113,
203601 (2014).
5. Andrews, R. W.
et al.
Bidirectional and efficient conversion between microwave
and optical light.
Nat. Phys.
10,
321–326 (2014).
6. Michler, P. (ed.)
Single Quantum Dots
(Springer Berlin Heidelberg, 2009).
7. Aharonovich, I. & Neu, E. Diamond nanophotonics.
Adv. Optical Mater.
2,
911–928 (2014).
8. Bernien, H.
et al.
Heralded entanglement between solid-state qubits separated
by three metres.
Nature
497,
86–90 (2013).
9. Press, D., Ladd, T. D., Zhang, B. & Yamamoto, Y. Complete quantum control
of a single quantum dot spin using ultrafast optical pulses.
Nature
456,
218–221
(2008).
10. De Greve, K.
et al.
Quantum-dot spin-photon entanglement via frequency
downconversion to telecom wavelength.
Nature
491,
421–425 (2012).
11. Englund, D.
et al.
Controlling cavity reflectivity with a single quantum dot.
Nature
450,
857–861 (2007).
12. Faraon, A., Barclay, P. E., Santori, C., Fu, K. C. & Beausoleil, R. G. Resonant
enhancement of the zero-phonon emission from a colour centre in a diamond
cavity.
Nat. Photon.
5,
301–305 (2011).
13. Li, L.
et al.
Coherent spin control of a nanocavity-enhanced qubit in diamond.
Nat. Commun.
6,
6173 (2015).
14. Faraon, A., Santori, C., Huang, Z., Acosta, V. M. & Beausoleil, R. G. Coupling of
nitrogen-vacancy centers to photonic crystal cavities in monocrystalline
diamond.
Phys. Rev. Lett.
109,
033604 (2012).
15. Thiel, C., Bo
̈
ttger, T. & Cone, R. Rare-earth-doped materials for applications in
quantum information storage and signal processing.
J. Luminesc.
131,
353–361
(2001).
16. Zhong, M.
et al.
Optically addressable nuclear spins in a solid with a six-hour
coherence time.
Nature
517,
177–180 (2015).
17. Sun, Y., Thiel, C. W., Cone, R. L., Equall, R. W. & Hutcheson, R. L. Recent
progress in developing new rare earth materials for hole burning and coherent
transient applications.
J. Lumin.
98,
281–287 (2002).
18. Lvovsky, A. I., Sanders, B. C. & Tittel, W. Optical quantum memory.
Nat.
Photon.
3,
706–714 (2009).
19. Tittel, W.
et al.
Photon-echo quantum memory in solid state systems.
Laser
Photon. Rev.
4,
244–267 (2010).
20. Saglamyurek, E.
et al.
Broadband waveguide quantum memory for entangled
photons.
Nature
469,
512–515 (2011).
21. Marzban, S., Bartholomew, J. G., Madden, S., Vu, K. & Sellars, M. J.
Observation of photon echoes from evanescently coupled rare-earth ions in a
planar waveguide.
Phys. Rev. Lett.
115,
013601 (2015).
22. Kolesov, R.
et al.
Optical detection of a single rare-earth ion in a crystal.
Nat.
Commun.
3,
1029 (2012).
23. Utikal, T.
et al.
Spectroscopic detection and state preparation of a single
praseodymium ion in a crystal.
Nat. Commun.
5,
3627 (2014).
24. McAuslan, D. L. & Longdell, J. J. Cavity QED using rare-earth-metal-ion
dopants in monolithic resonators: what you can do with a weak oscillator.
Phys.
Rev. A
80,
062307 (2009).
25. Bayn, I., Meyler, B., Salzman, J. & Kalish, R. Triangular nanobeam photonic
cavities in single-crystal diamond.
N. J. Phys.
13,
025018 (2011).
26. Oskooi, A. F.
et al.
MEEP: a flexible free-software package for electromagnetic
simulations by the FDTD method.
Comput. Phys. Commun.
181,
687–702
(2010).
27. Purcell, E. M. Spontaneous emission probabilities at radio frequencies.
Phys.
Rev.
69,
681 (1946).
28. Usmani, I., Afzelius, M., de Riedmatten, H. & Gisin, N. Mapping multiple
photonic qubits into and out of one solid-state atomic ensemble.
Nat. Commun.
1,
12 (2010).
29. Afzelius, M. & Simon, C. Impedance-matched cavity quantum memory.
Phys.
Rev. A
82,
022310 (2010).
30. Waks, E. & Vuckovic
́
, J. Dipole induced transparency in drop-filter
cavity-waveguide systems.
Phys. Rev. Lett.
96,
153601 (2006).
31. Thompson, J. D.
et al.
Coupling a single trapped atom to a nanoscale optical
cavity.
Science
340,
1202–1205 (2013).
32. Moerner, W. E. & Carter, T. P. Statistical fine structure of inhomogeneously
broadened absorption lines.
Phys. Rev. Lett.
59,
2705 (1987).
33. Hedges, M. P., Longdell, J. J., Li, Y. & Sellars, M. J. Efficient quantum memory
for light.
Nature
465,
1052–1056 (2010).
34. Clausen, C.
et al.
Quantum storage of photonic entanglement in a crystal.
Nature
469,
508–511 (2011).
35. Bussie
`
res, F.
et al.
Quantum teleportation from a telecom-wavelength photon to
a solid-state quantum memory.
Nat. Photon.
8,
775–778 (2014).
36. Wolfowicz, G.
et al.
Coherent storage of microwave excitations in rare earth
nuclear spins.
Phys. Rev. Lett.
114,
170503 (2015).
Acknowledgements
We gratefully acknowledge the contributions of Alexander E. Hartz. This work was
funded by California Institute of Technology (Caltech) and National Science Foundation
(NSF) CAREER award number 1454607. Equipment funding was also provided by the
Institute of Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center
with support of the Moore Foundation. The device nanofabrication was performed in the
Kavli Nanoscience Institute at Caltech.
Author contributions
A.F. and T.Z. conceived the experiments. T.Z. and E.M. performed the simulations and
T.Z. fabricated the devices. T.Z. and J.M.K. performed the measurements and analysed
the data. T.Z. and A.F. wrote the manuscript with input from all authors.
Additional information
Supplementary Information
accompanies this paper at http://www.nature.com/
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Competing financial interests:
The authors declare no competing financial interests.
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How to cite this article:
Zhong, T.
et al.
Nanophotonic coherent light–matter interfaces
based on rare-earth-doped crystals.
Nat. Commun.
6:8206 doi: 10.1038/ncomms9206
(2015).
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| 6:8206 | DOI: 10.1038/ncomms9206 | www.nature.com/naturecommunications
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