of 6
Optically Addressing Single Rare-Earth Ions in a Nanophotonic Cavity
Tian Zhong,
1,2,3
,*
Jonathan M. Kindem,
1,2
John G. Bartholomew,
1,2
Jake Rochman,
1,2
Ioana Craiciu,
1,2
Varun Verma,
4
Sae Woo Nam,
4
Francesco Marsili,
5
Matthew D. Shaw,
5
Andrew D. Beyer,
5
and Andrei Faraon
1,2
,
1
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology,
Pasadena, California 91125, USA
2
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
3
Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
4
National Institute of Standards and Technology, 325 Broadway, MC 815.04, Boulder, Colorado 80305, USA
5
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA
(Received 20 March 2018; published 31 October 2018)
We demonstrate optical probing of spectrally resolved single Nd
3
þ
rare-earth ions in yttrium
orthovanadate. The ions are coupled to a photonic crystal resonator and show strong enhancement of
the optical emission rate via the Purcell effect, resulting in near radiatively limited single photon emission.
The measured high coupling cooperativity between a single photon and the ion allows for the observation
of coherent optical Rabi oscillations. This could enable optically controlled spin qubits, quantum logic
gates, and spin-photon interfaces for future quantum networks.
DOI:
10.1103/PhysRevLett.121.183603
Rare-earth dopants in solids exhibit long-lived coherence
in both the optical and spin degrees of freedom
[1,2]
. The
effective shielding of
4
f
electrons leads to optical and
radio frequency transitions with less sensitivity to noise in
their crystalline surroundings at cryogenic temperatures.
Significant progress in rare-earth-based quantum technol-
ogies has led to ensemble-based optical quantum memories
[3
6]
and coherent transducers
[7]
, with promising per-
formance as quantum light-matter interfaces for quantum
networks. On the other hand, addressing single ions has
remained an outstanding challenge, with the progress
hindered by the long optical lifetimes of rare-earth ions
and resultant faint photoluminescence (PL). So far, only a
few experiments have succeeded in isolating individual
praseodymium
[8
10]
, cerium
[11
13]
, and erbium
[14,15]
ions, though the majority of them did not probe ions via
their
4
f
-
4
f
optical transitions. Recently, several works
have demonstrated significant enhancement of spontaneous
emission of rare-earth emitters coupled to a nanophotonic
cavity
[6,15
17]
, among which
[6,16]
also showed negli-
gible detrimental effect on the coherence properties of ions
in nanodevices. These results point at a viable approach to
efficiently detect and coherently control individual ions in a
chip-scale architecture.
Here we demonstrate a nanophotonic platform based on a
yttrium orthovanadate (YVO
4
) photonic crystal nanobeam
resonator coupled to spectrally resolved individual neodym-
ium (Nd
3
þ
) ions. While the system acts as an ensemble
quantum memory when operating at the center of the
inhomogeneous line
[6]
, it also enables direct optical
addressing of single Nd
3
þ
in the tails of the inhomogeneous
distribution, which show strongly enhanced, near radiatively
limited, single photon emission. A measured vacuum Rabi
frequency of
2
π
×
28
.
5
MHz significantly exceeds the line-
width of a Nd
3
þ
ion, allowing for coherent manipulation of
spins with optical pulses. Unlike prior experiments
[8
13]
,
this techniquedoes not hinge on the spectroscopicdetails ofa
specific type of ion and can be readily extended to other rare
earths or defect centers. The technique opens up new
opportunities for spectroscopy on single ions that are distinct
from conventional ensemble measurements, which enables
probes for the local nanoscopic environment around indi-
vidual ions and may lead to new quantum information
processing, interconnect, and sensing devices.
Our experiment builds upon a triangular nanobeam
photonic crystal resonator
[16,18]
that was fabricated in
a nominally 50 ppm doped Nd
3
þ
YVO
4
crystal using
focused ion beam (FIB) milling
[18]
. The device is a one-
sided cavity, as the input [left mirror in Figs.
1(a)
and
1(b)
]
has a lower reflectivity. The optical coupling in and out of
the device was implemented via a 45°-angled coupler
[16]
.
An aspheric doublet mode matches the single-mode fiber to
the nanobeam waveguide [Fig.
1(a)
]. The coupling effi-
ciency was optimized to 19% (from fiber to waveguide)
using a three-axis nanopositioner. The nanocavity funda-
mental mode volume is
V
mode
¼
0
.
056
μ
m
3
(simulated)
with a measured quality factor
Q
¼
3900
(energy decay
rate
κ
¼
2
π
×
90
GHz). The waveguide-cavity coupling
κ
in
through the input mirror was 45% of
κ
. The device was
cooled to
20
mK base temperature in a dilution refrig-
erator, though the actual ensemble temperature was esti-
mated to be around 500 mK (by comparing the ground
Zeeman level populations from the PL spectra). The
elevated temperature was attributed to the very small
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=
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© 2018 American Physical Society
thermal conductance in the nanobeam. This limitation has
already manifested in previous sub-Kelvin bulk sample
measurements
[19]
and was even more demanding for
measuring nanodevices in the current case. The laser for
probing the ions was modulated by two double-pass
acousto-optic modulators and delivered to the sample via
a single-mode fiber. The reflected signal from the device
was sent via a circulator to a superconducting nanowire
single photon detector (SNSPD) that measured a 82%
detection efficiency at 880 nm and
<
2
Hz dark counts
[6]
.
The SNSPD was mounted in the same fridge at the 100 mK
stage. The overall photon detection efficiency including
transmission from the cavity to the detector and the detector
efficiency was 3.6% (see Supplemental Material
[20]
).
A typical cavity reflection spectrum when tuned nearly
on resonance with the Nd
3
þ
4
F
3
=
2
ð
Y
1
Þ
4
I
9
=
2
ð
Z
1
Þ
transi-
tion at 880 nm is shown in Fig.
1(c)
. A 390 mT magnetic
field was applied along the crystallographic
a
axis of
YVO
4
, giving rise to split Zeeman levels and four possible
optical transitions
[34]
(labeled 1
4) shown in the inset.
Symmetry considerations impose that the 2, 3 cross
transitions are forbidden and the 1, 4 transitions are close
to cyclic
[6,35]
. The PL spectrum (with a 200-ns pulsed
resonant excitation) is shown in the lower part of Fig.
1(c)
.
Two weak lines labeled 1
and 4
were identified as emis-
sions from Nd
3
þ
ions in the bulk substrate, which are red
detuned from ions coupled to the cavity by 2.5 GHz. This
shift is due to a static strain in the nanobeam, which makes
it easier to spectrally separate the ions in the cavity from
the bulk. For subsequent experiments, we focus on the
shorter wavelength tail of the inhomogeneous distribution.
Figure
1(d)
plots the resonant PL against detuning from the
peak of line 1 (340 703.0 GHz). The PL and thus the atomic
spectral density (
N
ions per excitation pulse bandwidth) fits
with a power law of
N
Δ
2
.
9
, where
Δ
is the detuning.
The 2.9 power exponent indicates an inhomogeneous
broadening mechanism due to strain by dislocation, accord-
ing to the asymptotic form in
[37]
. Statistical fine structure
(SFS)
[38]
was also evident. By fitting the SFS with the
projected shot noise of
N
(
ffiffiffiffi
N
p
indicated as the shaded
area), it is projected that discrete single ion spectra (
N<
1
)
emerge at a detuning
>
25
GHz.
To search for singles, we scanned the frequency of a 200-
ns resonant excitation pulse around
30
GHz blue detuning
from the peak of line 1 and measured the PL integrated over
5
μ
s after the excitation. The repetition rate of the excitation
pulses was 25 kHz, and the integration time was 20 s at each
frequency. The laser was frequency stabilized to a vacuum-
chamber reference cavity, attaining a narrowed linewidth of
<
5
kHz and a long-term drift
<
100
kHz
=
day. Figure
2(a)
shows the measured PL over a few gigahertz range.
A handful of peaks, such as the one with the close-up in
Fig.
2(c)
, were possible single Nd
3
þ
ions. The PL intensities
werehistogrammedinFig.
2(b)
toreveala distributionofion-
cavity coupling strengths, which is in good agreement with
that from the finite difference time domain (FDTD) simu-
lation (red). Thus, the PL intensity serves to correlate the
coupling strength of each ion with its spatial position relative
to the cavity antinodes: an ion located at the antinode would
have the strongest coupling and show the highest PL. The
linewidth of the peak in Fig.
2(c)
was broadened by the
excitation pulse. The actual linewidth of single ions was
-300
-200
-100
0
100
200
300
400
+340698 (GHz)
0
1
-60
-40
-20
0
20
40
GHz
10
15
20
25
30 35 40 45
+340703 (GHz)
10
2
10
3
PL counts
N
10
1
0.1
T = 20 mK
c
SNSPD
aspheric doublet
11
-
0
a
b
b
c
κ
sc
κ
in
690 nm
4
I
9/2
4
F
3/2
1
34
2
c axis
a
b
B = 390 mT
60
1
4
1’
4’
(b)
(a)
(c)
(d)
resolved singles
FIG. 1. (a) Schematics of the experiment in a dilution refrig-
erator. Scale bar is
1
μ
m. (b) SEM images of the one-sided
nanobeam photonic crystal cavity in YVO
4
fabricated using FIB.
The Lower part shows the simulated TM fundamental mode
profile, which has the polarization aligned to the dipoles of Nd
3
þ
along the crystallographic
c
axis. (c) Cavity reflection spectrum
(upper) and Nd
3
þ
photoluminescence spectrum (lower). (Insets)
Applied magnetic field and resulting Zeeman levels and tran-
sitions. PL from ions in the bulk substrate (1
and 4
) appear
redshifted from ions coupled to the cavity (1 and 4). (d) Atomic
spectra density versus detuning on the shorter wavelength tail of
the inhomogeneous distribution. The shaded area shows the
projected atomic shot noise.
PHYSICAL REVIEW LETTERS
121,
183603 (2018)
183603-2
expectedtobeconsiderably narrower.Withthelasertunedon
resonance with one of the peaks [marked with a red dot in
Fig.
2(a)
], the intensity autocorrelation measurement using a
single detector yielded a
g
ð
2
Þ
ð
0
Þ¼
0
.
09

0
.
013
[Fig.
2(e)
]
with
0
.
02
photons generated per pulse, which was nor-
malized to g
ð
2
Þ
(
t
)atlarge
τ
. The bunching behavior at
j
τ
j
<
600
μ
s was expected from a multilevel emitter
[39,40]
.The
imperfect antibunching was partlydue to a continuum ofions
thatisweaklycoupledtothecavity, resultinginabackground
in Fig.
2(e)
. This background was measured with the
excitation laser far detuned from the single ion resonance.
The optical
T
1
of this ion was
2
.
1

0
.
2
μ
s[Fig.
2(d)
], which
is strongly enhanced compared to the bulk
T
1
of
90
μ
s. The
lifetime enhancement corresponded to a Purcell factor of 111
of the probed
Y
1
-
Z
1
transition considering a branching ratio
of
β
¼
0
.
38
(the ground state splits into five Kramers
doublets
Z
1
-
Z
5
)
[20]
. The theoretically maximum Purcell
factor was
F
ð
3
=
4
π
2
χ
2
L
Þð
λ
=n
YVO
4
Þ
3
ð
Q=V
Þ¼
189
[26,41]
,
assuming a perfect alignment of the dipole with the cavity
mode and
χ
L
¼
3
n
2
YVO
4
=
ð
2
n
2
YVO
4
þ
1
Þ
is the local correction
to the electric field since the ion is less polarizable than the
bulk medium
[25]
, where we have used the real cavity
approximation (see Supplemental Material
[20]
). The dis-
crepancy is attributed to the nonoptimal position of the ion,
and the actual cavity mode volume being different from
simulation because of fabrication imperfections.
The small mode volume of the nanocavity results in a
significant enhancement of the coupling strength
g
0
.
Focusing on the ion in Fig.
2(c)
, Fig.
3(a)
plots the PL
excited by a square 250-ns resonant pulse with increasing
cavity mean photon number
̄
n
. The value of
̄
n
was
calculated from the input pulse energy, all losses in the
setup up to the device, and coupling rates of the photonic
crystal mirrors (see Supplemental Material
[20]
). The PL
shows Rabi oscillations similar to an optical nutation
[42]
.
The inset plots the extracted Rabi frequencies
Ω
versus
square root of
̄
n
from the peaks (corresponding to an
odd integer of
π
pulse areas) and valleys (even integer
of
π
pulses) of the Rabi oscillations. The fitted slope
corresponds to
g
0
¼
Ω
=
2
ffiffiffi
̄
n
p
¼
2
π
×
28
.
5

5
.
2
MHz. The
theoretical maximum
g
0
is
μ
=n
YVO
4
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ω
0
=
2
ε
0
V
p
¼
2
π
×
52
.
7
MHz
[26]
, where
μ
¼
1
.
59
×
10
31
C m is the tran-
sition dipole moment (see Supplemental Material
[20]
),
n
YVO
4
¼
2
.
1785
is the refractive index of YVO
4
,
ω
0
is
the transition frequency, and
ε
0
is the vacuum permittivity.
The measured
g
0
is orders of magnitude larger than the
linewidth of the emitter, which makes possible the use of
hard optical pulses
[43]
to coherently control each single
ion. Next, we applied two
π
=
2
pulses to measure the
Ramsey interference as shown in Fig.
3(b)
. The normalized
Ramsey fringes (subtracting a
T
1
decay background) reveal
a clear beating, which most likely corresponds to the
superhyperfine interactions between the Nd electron spins
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Frequency (+340732.0 GHz)
0
100
200
300
400
PL counts
0
150
300
Events
-50
-25
0
25
50
Frequency detuning (MHz)
0
50
100
150
200
250
300
PL counts
0
5
10
15
20
t (
s)
4.5
5
5.5
6
6.5
7
7.5
8
8.5
Log of PL counts
bulk
single Nd
3+
(c)
(d)
(e)
(a)
(b)
-800
-400
0
400
800
(
s)
0
1
g
(2)
(
)
FDTD
0
100
200
300
400
PL counts
FIG. 2. (a) Photoluminescence spectrum swept over 3 GHz around
Δ
30
GHz. Isolated peaks marked by filled circles correspond to
individual Nd
3
þ
ions. Each color represents a different laser scan. (b) Histogram of PL intensities from the ensemble of Nd
3
þ
. The red
curve is a FDTD simulation of the expected distribution given the different position of each ion inside the cavity. (c) PL spectrum of the
ion labeled with the red circle in Fig.
2(a)
. (d) PL decay of the ion (black) with a fitted
T
1
¼
2
.
1

0
.
2
μ
s (red) compared to
T
1
¼
90
μ
s
in bulk (gray). (e) Intensity autocorrelation measurement on the single Nd
3
þ
showing antibunching [
g
2
ð
0
Þ¼
0
.
09

0
.
013
]. The
background signal with an off-resonant excitation is in red.
PHYSICAL REVIEW LETTERS
121,
183603 (2018)
183603-3
and the nuclear spins of yttrium in YVO
4
[20]
. The measured
superhyperfine beating, confirmed by the two-pulse photon
echo measurement (see Supplemental Material
[20]
), was
740 kHz, which is consistent with the calculations based
on the gyromagnetic ratio of yttrium (
Y
) nuclear spins of
2
.
1
MHz
=
T
[20,30]
. At a relatively strong field of 390 mT,
the Nd-Y superhyperfine structure is dominated by the
yttrium nuclear magnetic moment (Supplemental Material
[20]
), as also observed in Nd
3
þ
Y
2
SiO
5
[29]
. The decay of
the Ramsey fringe envelope can be fitted empirically to
extract a
T

2
¼
4
.
0

0
.
2
μ
s. From that, the spectral indis-
tinguishabilityiscalculatedas
T
2
=
ð
2
T
1
Þ¼
0
.
952
,indicating
that the linewidth of this ion approaches the radiatively
limited regime.
The use of single rare-earth ions as spin-photon inter-
faces to entangle remote quantum nodes requires each
emitter
s linewidth to be radiatively limited. To further
characterize the coherence of the ions coupled to the cavity,
we performed additional ensemble two-pulse photon echo
measurements when the emitters have different detunings
from cavity resonance. The ensemble
T
2
times are plotted
against optical
T
1
in Fig.
4
, including the single ion
T

2
data
denoted by a square. The experimental data were fitted
with the relationship
1
=
ð
π
T
2
Þ¼
1
=
ð
2
π
T
1
Þþ
γ

, where
γ

is the pure dephasing rate. The fit (blue curve) gives a
γ

¼
9
.
7

0
.
6
kHz. While slow, this dephasing rate was
attributed to the superhyperfine interactions since it closely
matches the superhyperfine-limited
T
2
in Nd
3
þ
YVO
4
[2]
.
The contribution from Nd
3
þ
spin flip-flops are expected to
be small, because the measured
T
2
in an nominally
undoped YVO
4
crystal (residual doping estimated at
0.2 ppm) was comparable to that measured in the current
device (see Supplemental Material
[20]
).
The full radiatively limited
T
2
¼
2
T
1
is plotted in red.
With weak enhancement when the ions are detuned from
the cavity, the ions exhibit poor indistinguishabilities, as
indicated by the sizable gap between the red and blue
curves. Only when the ions are resonantly coupled to the
cavity do they become radiatively limited. A similar
approach has been used to improve the single photon
indistinguishabilities of quantum dots
[44]
. To increase the
indistinguishability, improving the cavity quality factor to
further reduce
T
1
would be a straightforward step, which
would also allow the device to operate at higher temper-
atures with stronger dephasing while still achieving radi-
atively limited emission. The current linewidth of the single
emitter was based on
T

2
values measured over a few
microseconds [Fig.
3(b)
]. For longer timescales (
100
μ
sto
0
0.02
0.04
0.06
0.08
0.1
0
200
400
600
800
1000
1200
PL counts
0
0.05
0.1
0.15
0
2
4
6
8
10
(2
MHz)
024681012
t (
s)
0
0.5
1
(a)
(b)
Normalized PL counts
exp(-t/T
2
)
*
t
n
n
fit
experiment
FIG. 3. (a) Rabi oscillations of PL following a pulsed resonant
excitation with increasing photon number
̄
n
. Black arrows point
to pulse areas that are integer multiples of
π
. (Inset) Extracted
Rabi frequencies against
ffiffiffi
̄
n
p
with a linear fit. (b) Normalized
Ramsey interference fringes. The beating at a frequency of
740 kHz is consistent with the superhyperfine coupling between
the Nd
3
þ
ion and surrounding
Y
.
0
5
10
15
20
25
T
1
cav
(
s)
0
5
10
15
20
25
30
35
40
T
2
cav
(
s)
fit to experiment
radiatively limited T
2
single ion T*
ensemble T
2
T
2
= 2T
1
1/(
π
T
2
)
= 1/(2
π
T
1
)+
γ
*
2
FIG. 4. Measured and theoretical optical coherences for Nd
3
þ
coupled to the cavity with varying detuning and Purcell enhance-
ment. The red line is the radiatively limited
T
2
time. The single
Nd
3
þ
on resonance with the cavity (square) exhibits a near
radiatively limited linewidth with a spectral indistinguishability
>
95%
.
PHYSICAL REVIEW LETTERS
121,
183603 (2018)
183603-4
ms), reducing the slow optical spectral diffusion could help
tomaintainahighindistinguishability,asdesiredbyquantum
memories for long-distance quantum network. In that regard,
using rare-earth emitters in hosts with weaker nuclear spin
baths or non-Kramers ions with weaker superhyperfine
couplings and operating at a zero-first-order-Zeeman point
[45]
may offer some advantages.
In conclusion, we have optically detected single Nd
3
þ
ions coupled to a nanophotonic cavity, which enhanced the
emitter spontaneous emission rate to the extent that the
linewidth of the emitter became radiatively limited. Optical
Rabi oscillations of the single Nd
3
þ
yielded a
g
0
¼
2
π
×
28
.
5
MHz and a linewidth of 12.5 kHz [
γ
h
¼
1
=
ð
π
T
2
Þ
],
where
T
2
¼
25
.
4
μ
s is the emitter homogeneous linewidth
without cavity enhancement (see Supplemental Material
[20]
). Given the cavity decay of
κ
¼
2
π
×
90
GHz, the
single ion cooperativity is
4
g
2
0
=
κγ
h
¼
2
.
9
. This value could
be improved significantly by using cavities with higher
Q
10
higher
Q
devices already demonstrated in
[18]
would
attain an indistinguishability
>
99
.
5%
and
C
30
), thus
making feasible the implementation of high-fidelity non-
destructive detection of optical photons with a single rare-
earth ion
[46]
. Nevertheless, questions remain regarding the
spin coherence and the qubit storage time of single ions
[47]
and spectral diffusion occurring at longer timescales.
When two spectrally resolved ions are nearby, their dipole-
dipole interaction can also be probed
[48]
. Single rare-earth
ions could be used to probe the field and temperature of its
nanoscopic surroundings. Finally, the large inhomogeneous
linewidth of the emitters may facilitate spectral multi-
plexing of individual quantum emitters for expanded
bandwidth of quantum communication networks.
This work was funded by a National Science Foundation
(NSF) Faculty Early Career Development Program
(CAREER) Grant (No. 1454607), the AFOSR Quantum
Transduction Multidisciplinary University Research
Initiative (FA9550-15-1-002), and the Defense Advanced
Research Projects Agency Quiness program (W31P4Q-15-
1-0012). Equipment funding was also provided by the
Institute of Quantum Information and Matter, an NSF
Physics Frontiers Center with support from the Moore
Foundation. The device nanofabrication was performed in
the Kavli Nanoscience Institute at the California Institute of
Technology. Part of the research was carried out at the Jet
Propulsion Laboratory, California Institute of Technology,
under a contract with the National Aeronautics and Space
Administration. The authors would like to acknowledge
Neil Sinclair, Ruffin Evans, Alp Sipahigil, Charles W.
Thiel, and Jeffrey Thompson for useful discussions.
*
tzh@uchicago.edu
faraon@caltech.edu
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