Coherent control and single-shot readout of a rare-earth ion embedded in a
nanophotonic cavity
Jonathan M. Kindem
1,2
, Andrei Ruskuc
1,2
, John G. Bartholomew
1,2
, Jake Rochman
1,2
, Yan Qi
Huan
1,2
, Andrei Faraon
1,2,
*
Affiliations:
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.
*Correspondence to: faraon@caltech.edu
Abstract:
Quantum networks based on optically addressable spin qubits promise to enable secure
communication, distributed quantum computing, and tests of fundamental physics. Scaling up
quantum networks based on solid-state luminescent centers requires coherent spin and optical
transitions coupled to photonic resonators. Here we investigate single Yb
!"!
#$
ions in yttrium
orthovanadate coupled to a nanophotonic cavity. These ions possess optical and spin transitions
that are first-order insensitive to magnetic field fluctuations, enabling optical linewidths less than
1 MHz and spin coherence times exceeding 30 ms for cavity-coupled ions. The cavity-enhanced
optical emission rate facilitates efficient spin initialization and conditional single-shot readout
with fidelity greater than 95%. These results showcase a solid-state platform based on single
coherent rare-earth ions for the future quantum internet.
Main text:
The distribution of entanglement over long distances using optical quantum networks is
an intriguing macroscopic quantum phenomenon with applications in quantum systems for
advanced computing and secure communication (1, 2). Solid-state emitters coupled to photonic
resonators (3) are promising candidates for implementing quantum light-matter interfaces
necessary for scalable quantum networks. A variety of systems have been investigated for this
purpose, including quantum dots and defects in diamond or silicon carbide (4–8). So far, the
ability to scale up these systems has remained elusive and motivates the development of
alternative platforms. A central challenge is identifying emitters that exhibit coherent optical and
spin transitions while coupled to photonic cavities that enhance the optical transitions and
arXiv:1907.12161v1 [quant-ph] 28 Jul 2019
channel emission into optical fibers. Ensembles of rare-earth ions (REIs) in crystals are known to
possess highly coherent 4f-4f optical and spin transitions (9, 10), but only recently have single
REIs been isolated (11, 12) and coupled to nanocavities (13, 14). The crucial next steps toward
using single REIs for quantum networks are demonstrating long spin coherence and single-shot
readout in photonic resonators.
Here we demonstrate spin initialization, coherent optical and spin manipulation, and
high-fidelity single-shot optical readout of the hyperfine spin state of single Yb
!"!
#$
%
ions
coupled to a nanophotonic cavity fabricated in an yttrium orthovanadate (YVO) host crystal. The
relevant energy level structure of
%
Yb
!"!
#$
in YVO is shown in Fig. 1A (see Fig. S2 and Ref.
(15) for additional details).
%
Yb
!"!
#$
directly substitutes for
&
#$
in a site that has non-polar
symmetry (D
2d
), which reduces the sensitivity to electric field fluctuations that can cause optical
decoherence. At zero applied magnetic field, the hyperfine interaction partially lifts the
degeneracy of the ground state
'
(
"
(
)
*
+
,
leading to coupled electron-nuclear spin states of the
form
-+
.
/
0
-
12
.
3%
-
45
.
6
7
8-9
.
/
0
-
12
.
:%
-
45
.
6
7
8;<=%%->?@
.
/
0
-
42
.
8
-
15
.
A%
Here we denote the electron spin as
-
4
.
0
B
C
D
0
!
(
E
8
-
1
.
0
B
C
D
0 3
!
(
E and the nuclear spin as
-
2
.
0
B
F
D
0
!
(
E
8
-
5
.
0
B
F
D
0 3
!
(
E
A
We use states
-+
.
/
and
-9
.
/
, which are separated by ~675 MHz,
to form the spin qubit. The
-+
.
/
and
-9
.
/
states have zero net magnetic moment and as a result
the
-+
.
/
G%-9
.
/
transition is first-order insensitive to magnetic fluctuations that induce
decoherence (10). The
-+
.
/
G -9
.
/
transition retains the strength of the electron spin transition,
which enables fast and efficient microwave manipulation.
A typical experimental sequence with spin initialization, control, and readout is shown in
Fig. 1B. The Yb
!"!
#$
ions are coupled to a photonic crystal cavity with small mode volume
H9
*
I J
KLM
N
,
#
%
and large quality factor
*
9O9+
P
,
%
(Fig 1C, D. See SI 1.1). This enhances the
emission rate, collection efficiency, and cyclicity of the optical transitions A and E via the
Purcell effect (16). The qubit is initialized into
-+
.
/
by optical and microwave pumping on F, A,
and f
e
to empty
->?@
.
/
and
-9
.
/
, followed by cavity-enhanced decay into
-+
.
/
via E (Fig. 1A). A
subsequent microwave
Q
pulse applied on
R
/
optionally initializes the ion into
-9
.
/
. The
%-9
.
/
state population is read out by exciting on A and collecting the resulting ion fluorescence.
Measurements are performed in a cryostat at 40 mK unless mentioned otherwise (See SI 6.5 for
discussion of sample temperature). The ions are optically addressed using two frequency-
stabilized continuous-wave lasers, while a microwave coplanar waveguide allows for driving of
the spin transitions (Fig. 1E).
The YVO material used has a ~20 ppb residual concentration of
171
Yb that is distributed
over an optical inhomogeneous linewidth of ~200 MHz in the device due to variations in the
local crystalline environment. This enables frequency isolation of single ions via pulsed resonant
photoluminescence excitation (PLE) spectroscopy on transition A. The PLE scan in Fig. 2A
shows peaks in fluorescence that are confirmed to originate from single
%
ions by measuring the
pulse-wise second-order photon correlation of the resonant emission (Fig. 2B). For ion X
(marked in Fig. 2A),
S
(
T
+
U
0 +A9VWX+A+99
. The observed bunching behavior for
Y Z +
is
expected for a multi-level system with long-lived shelving states (See SI 2.3). An optical lifetime
of
[
!
0 7A7W%\]
is measured for ion X (Fig. 2C), which is a reduction from the bulk lifetime
(
7^W%\]
) by
_'
`
0 99W
(with
%_ 0 +Aab%
the branching ratio for emission via A) and corresponds
to a single-photon coupling rate of
S% 0 %7 Q%O%7a
MHz. Similar measurements were performed
on ion marked as Y in Fig. 2A (See SI 2).
The cavity-enhanced optical transitions enable coherent optical control and efficient spin
initialization (Fig. S7). Measurements of the resonant PL with varying excitation pulse length
show optical Rabi oscillations (Fig. 2D), enabling calibration of
Q
and
Q
/2 pulses for optical
control and spin readout. An optical Ramsey measurement (Fig. 2E) gives a dephasing time of
[
(8c
d
0 aW+%
ns, a factor of 12 shorter than the lifetime-limited
[
(
0 7[
!
A
Further optical echo
measurements give
[
(8c
0 VA9%\]
(Fig. S8), which implies that
[
(8c
d
is limited by quasi-static
fluctuations of the transition frequency. We can extend the
[
(8c
d
beyond
9%\]
by using post-
selection to ensure the ion is on resonance with the readout sequence (Fig. S9). We measure the
long-term stability, or equivalently the spectral diffusion, of the ion using PLE readout over 6
hours (Fig. 2F) and observe a narrow integrated linewidth (FWHM) of 1.4 MHz.
We use this optical initialization and detection to demonstrate coherent spin manipulation
by driving Rabi oscillations on the
-+
.
/
G
-
9
.
/
qubit transition (Fig. 3A). We perform a spin
Ramsey measurement to extract a spin dephasing time of
[
(8e
d
0 fA7%\]%
(Fig. 3B)
A
The spin
coherence is further extended using dynamical decoupling sequences (17) to suppress quasi-
static contributions to dephasing. Fig. 3C shows the resulting coherence decay for increasing
numbers of
Q
pulses using a Carr-Purcell-Meiboom-Gill (CPMG) sequence (Fig. 3C inset). For a
single
Q
pulse, or spin echo sequence, we observe non-exponential behavior characteristic of a
spin coupled to a slowly-fluctuating dipolar spin-bath (18, 19) with
[
(8e
0 VaAb%\]
. This is
further evidenced by a measurement of the coherence time with N, the number of
Q
pulses,
which scales as
g
hA"hXhAh!
(Fig. S9). CPMG scans taken with finer temporal resolution reveal
periodic collapse and revivals of coherence indicative of coupling to nearby nuclear spins (Fig.
S10) that could potentially be used as local quantum registers.
We explore the limits of the spin coherence time by increasing the number of rephasing
pulses with a fixed pulse separation of 5.74
%\]
to avoid unwanted interactions with the nuclear
spin bath (20). This enables extension of the CPMG coherence time to 30 ms (Fig 3D). While the
CPMG sequence does not allow for preservation of arbitrary quantum states, we also
demonstrate coherence times longer than 4 ms using an XY-8 sequence (17) (Fig. S14) suitable
for use in long-range quantum networks (21). The measured qubit lifetime of 54 ms (Fig. S15)
indicates that the observed coherences are approaching the lifetime limit. We repeated these
measurements at cryostat temperatures up to 1.2 K (Fig. 3D) and observed minimal changes in
the spin coherence and lifetime, providing evidence that they are not limited by spin-lattice
relaxation (See SI 6.5).
To harness this long spin coherence lifetime for quantum networks, it is essential to read
out the qubit state in a single measurement. We achieve this with the scheme shown in Fig. 4A,
which consists of two consecutive optical read periods on transition A separated by a microwave
Q
pulse to invert the qubit population. This scheme was designed considering that in this device
direct resonant PL readout of the qubit state
%
can only be performed using a series of optical
Q
pulses on transition A (See SI 2.2). The Purcell-enhanced cyclicity of transition A (
_
i
Z jjA^k
,
see Fig. S6) allows for multiple photon emitting cycles before the ion is optically pumped out of
the qubit subspace into
->?@
.
/
(
-+
.
l
G
-
+
.
/
is forbidden at zero-field). Fig. 4B shows the
measured photon count distribution in the two readout sequences for the ion initialized in
-+
.
/
(blue) or
-9
.
/
(red). We assign the ion to
-9
.
/
if we measure
m 9
photons during the first readout
sequence and 0 photons during the second readout sequence, and vice versa for
-+
.
/
. This
discriminates between
-+
.
/
%
and
->?@
.
/
%
to ensure that the ion was in the qubit subspace during
the measurement. By implementing this scheme, we achieve an average readout fidelity of
95.3% (Fig. 4C).
These measurements showcase single
171
Yb
3+
in YVO as a promising system for solid
state quantum networking technologies. The measured spin coherence times correspond to light
propagation for thousands of kilometers in optical fibers, which is necessary for long-distance
quantum networks. Furthermore, the preservation of this coherence lifetime at temperatures of
1.2 K is promising for developing a viable technology with economical
4
He cryogenics. To
generate spin-spin entanglement with the current optical dephasing times will require a post-
selection protocol similar to what has already been developed for other quantum networks (22)
(Fig. S9). While the source of the optical dephasing is still under investigation, it will likely be
improved in higher purity samples (See SI 6.5). While not explored here, the high magnetic field
regime offers the possibility of longer optical and spin coherence times at the expense of weaker
spin transition strengths (15). The crucial next steps are increasing the cavity Q/V by an order of
magnitude and optimizing the collection efficiency, which should enable high rates of
indistinguishable photon emission. This could be achieved with the current device architecture,
or by using a hybrid platform where cavities are fabricated in a high-index material like GaAs
and bonded to the YVO substrate. Multi-qubit gates necessary to establish entanglement on
larger scale networks could be performed using the interaction with neighboring vanadium atoms
or other REIs (23). The technology demonstrated here with single REI qubits complements other
capabilities that could potentially be realized with Yb
!"!
#$
n&op8
including quantum memories
(24) for synchronizing photon traffic and quantum transducers (25) for coupling to qubits
operating at microwave frequencies, thus pointing to a unified platform for the future quantum
internet.
Acknowledgements: This work was funded by a National Science Foundation (NSF) Faculty
Early Career Development Program (CAREER) award (1454607), the AFOSR Quantum
Transduction Multidisciplinary University Research Initiative (FA9550-15-1-002), NSF
1820790, and the Institute of Quantum Information and Matter, an NSF Physics Frontiers Center
(PHY-1733907) with support from the Moore Foundation. The device nanofabrication was
performed in the Kavli Nanoscience Institute at the California Institute of Technology. J.G.B.
acknowledges the support from the American Australian Association’s Northrop Grumman
![Figure 2: Optical detection and coherent optical manipulation of single 171Yb3+ ions. A) Photoluminescence excitation (PLE) spectrum showing resolved peaks corresponding to single Yb!"! #$ ions. B) Pulsed autocorrelation measurement on ion X with 𝑔([0] = 0.147 ± 0.011. C) Normalized photoluminescence emission from ion X coupled to the cavity (red) compared to](/figures/figure-2-optical-detection-and-coherent-optical-manipulation-1qzwgb6n.webp)
