PHYSICAL REVIEW B
98
, 024404 (2018)
Editors’ Suggestion
Characterization of
171
Yb
3
+
:YVO
4
for photonic quantum technologies
Jonathan M. Kindem,
1
,
2
John G. Bartholomew,
1
,
2
Philip J. T. Woodburn,
3
Tian Zhong,
1
,
2
,
4
Ioana Craiciu,
1
,
2
Rufus L. Cone,
3
Charles W. Thiel,
3
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
Department of Physics, Montana State University, Bozeman, Montana 59717, USA
4
Institute of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
(Received 2 May 2018; published 5 July 2018)
Rare-earthionsincrystalsareaprovensolid-stateplatformforquantumtechnologiesintheensembleregimeand
attractive for new opportunities at the single-ion level. Among the trivalent rare earths,
171
Yb
3
+
is unique in that it
possesses a single 4
f
excited-state manifold and is the only paramagnetic isotope with a nuclear spin of 1
/
2. In this
work, we present measurements of the optical and spin properties of
171
Yb
3
+
:YVO
4
to assess whether this distinct
energy-level structure can be harnessed for quantum interfaces. The material was found to possess large optical
absorption compared to other rare-earth-doped crystals owing to the combination of narrow inhomogeneous
broadening and a large transition oscillator strength. In moderate magnetic fields, we measure optical linewidths
less than 3 kHz and nuclear spin linewidths less than 50 Hz. We characterize the excited-state hyperfine and
Zeeman interactions in this system, which enables the engineering of a
system and demonstration of all-
optical coherent control over the nuclear-spin ensemble. Given these properties,
171
Yb
3
+
:YVO
4
has significant
potential for building quantum interfaces such as ensemble-based memories, microwave-to-optical transducers,
and optically addressable single rare-earth-ion spin qubits.
DOI:
10.1103/PhysRevB.98.024404
I. INTRODUCTION
Future quantum networks will incorporate a number of
different quantum technologies, such as stationary qubits
for high-fidelity logic operations and quantum memories for
synchronization and long-term storage [
1
–
3
]. A successful
network will require robust interfaces to coherently map quan-
tum information between the best technologies, which may be
based on disparate physical systems. For example, quantum
transducers between the microwave and optical domains could
be used to interface superconducting processors over long
distances through optical networks [
4
].
Rare-earth ions (REIs) doped into crystalline hosts have
demonstrated significant progress in implementing solid-state
quantum technologies. REIs possess some of the longest opti-
cal and spin coherence lifetimes in the solid state [
5
–
8
], which
has provided the foundation for numerous demonstrations
of quantum memories and quantum interfaces [
9
–
14
]. For
interfaces involving both microwave and optical photons, REIs
with an odd number of electrons (i.e., Kramers ions), such
as erbium, neodymium, and ytterbium, are of interest due to
their electron-spin transitions. The large magnetic moments
of these ions allow for strong interactions with microwaves,
enabling fast operations and the potential for interfacing with
superconducting qubits. Isotopes of these ions with nonzero
nuclear spin also offer the possibility of long-term quantum
storage[
8
].Thiscombinationofpropertiescreatesthepotential
*
faraon@caltech.edu
for building interfaces between microwave photons, optical
photons, and long-lived nuclear spins.
Among the Kramers ions, ytterbium is an attractive choice
due to its simple level structure consisting of only two elec-
tronic multiplets. The optical transition between the lowest
energy levels of these multiplets occurs around 980 nm, which
is readily accessible by standard diode lasers. Furthermore,
the
171
Yb
3
+
isotope is unique among the trivalent REIs
as the only Kramers ion with a nuclear spin of 1
/
2. This
gives the simplest possible hyperfine energy structure allowing
for both electron- and nuclear-spin degrees of freedom, reduc-
ing the complexity of optical preparation and manipulation
of spin states [
15
,
16
]. Recent work in
171
Yb
3
+
:Y
2
SiO
5
[
17
–
20
], Yb
3
+
:LiNbO
3
[
21
], and Yb
3
+
:YAG [
22
] highlights the
interest in this ion. In this work, we investigate
171
Yb
3
+
doped
into the host crystal YVO
4
.YVO
4
is an attractive choice for
implementing quantum interfaces [
23
,
24
] due to the ability to
fabricate nanoscale devices [
25
] and high site symmetry in this
material. Furthermore, previous work points to the potential for
high oscillator strength transitions for Yb
3
+
doped into YVO
4
[
26
].
We present an initial survey of the properties of optical
and nuclear-spin transitions in
171
Yb
3
+
:YVO
4
at cryogenic
temperatures. To determine whether this material can be
used for efficient interactions with light, we characterized the
strength and inhomogeneity of the optical transitions using
high-resolution optical spectroscopy. Large hyperfine cou-
plings and narrow optical inhomogeneous lines in this material
result in resolved optical transitions between the hyperfine
states, which allowed for characterization of the excited-state
2469-9950/2018/98(2)/024404(10)
024404-1
©2018 American Physical Society
JONATHAN M. KINDEM
et al.
PHYSICAL REVIEW B
98
, 024404 (2018)
spin Hamiltonian directly from absorption measurements in
an applied magnetic field. Knowledge of the spin Hamiltonian
enables the identification of magnetic-field orientations that
create strongly spin-conserving transitions (for cyclic transi-
tions) or strongly spin-mixing optical transitions (allowing for
efficient lambda systems). To assess the possibility of storage
and manipulation of quantum information in this material, we
measured the coherence properties of the optical and nuclear-
spin transitions as a function of applied magnetic field. To
demonstrate the potential for all-optical control of the nuclear
spin states, we also measured spin echoes using bichromatic
Raman pulses.
This paper is organized as follows: Section
II
presents the
materialpropertiesofthesamplesusedinthisworkandthespin
Hamiltonian used to model this system. Section
III
describes
the experimental methods and apparatus. Section
IV
presents
the experimental results and discussion. This section is further
divided into subsections: A (optical-absorption spectroscopy),
B (optical transition strengths), C (excited-state lifetime), D
(optical coherence measurements), E (nuclear-spin measure-
ments), and F (all-optical spin coherence measurements).
II. BACKGROUND
A. Material properties
YVO
4
(also called yttrium orthovanadate or YVO) forms a
zircon tetragonal crystal with
D
4
h
symmetry [
27
]. Ytterbium
substitutes for yttrium in sites of local
D
2
d
point-group symme-
try. The
z
axis of the site coincides with the crystalline fourfold
axis (the
c
axis of the crystal). The uniaxial nature of this site
reduces the number of parameters needed to characterize the
system compared to a lower symmetry crystal such as Y
2
SiO
5
[
17
,
18
].
The majority of measurements presented in this paper
were performed in samples cut from a boule of YVO
4
doped
with isotopically enriched
171
Yb
3
+
custom grown by Gamdan
Optics. The concentration of
171
Yb was measured to be 100
ppm using secondary ion mass spectrometry (SIMS). The
samples were cut and polished to various thicknesses appropri-
ate to each measurement. Fluorescence lifetime measurements
were performed using a nominally undoped sample of YVO
4
(Gamdan Optics), which was measured using SIMS to have a
residual
171
Yb
3
+
concentration of approximately 2 ppm.
B. Spin Hamiltonian
The 4
f
13
configuration of Yb
3
+
consists of two electronic
multiplets:
2
F
7
/
2
and
2
F
5
/
2
. In the crystal field of YVO
4
,the
ground-state multiplet (
2
F
7
/
2
) splits into four Kramers doublets
and the excited-state multiplet (
2
F
5
/
2
) splits into three Kramers
doublets. The energies of these crystal-field levels have been
measured previously [
28
] and are shown in Fig.
1(a)
.At
liquid-helium temperatures, only the lowest energy doublet of
the ground state is thermally occupied. The optical transition
of interest for quantum interfaces is between the lowest energy
doublets of the ground state and excited state [
2
F
7
/
2
(0)
→
2
F
5
/
2
(0)]. This transition occurs at approximately 984.5 nm
for Yb
3
+
doped into YVO
4
.
In this work, we focus on the
171
Yb isotope, which has
a nuclear spin
I
=
1
/
2. Treating the Kramers doublets as
effective spins with
S
=
1
/
2, we can describe the system with
the following spin Hamiltonian [
29
]:
H
eff
=
μ
B
B
·
g
·
S
+
I
·
A
·
S
−
μ
n
B
·
g
n
·
I
.
(1)
The first term is due to the electronic Zeeman interaction,
where
μ
B
is the Bohr magneton,
B
is the applied magnetic
field,
g
is the electronic Zeeman tensor, and
S
is the spin-1
/
2
operator. The second term describes the coupling between the
electron spin and nuclear spin via the hyperfine interaction,
where
I
is the nuclear-spin operator and
A
is the hyperfine
interactiontensor.ThelasttermarisesfromthenuclearZeeman
interaction, where
μ
n
is the nuclear magneton and
g
n
is the
nuclear Zeeman tensor. For
171
Yb in YVO
4
, the nonzero
components of
g
n
will be of the order of the gyromagnetic
moment of the free nucleus
g
n
=
0
.
987, which leads to a
nuclear Zeeman interaction
∼
2000 times smaller than the
electronic Zeeman term. For the magnetic-field values used
in this work, we treat this interaction by incorporating it into
the electronic Zeeman tensor.
The energy structure in the absence of an external magnetic
field (
B
=
0) is determined by the hyperfine interaction
I
·
A
·
S
. In the site symmetry of YVO
4
, the degeneracy of these
levels is partially lifted and the Hamiltonian has the follow-
ing eigenvalues at zero field:
E
=
A
4
,
A
4
,
−
A
+
2
A
⊥
4
,
−
A
−
2
A
⊥
4
,
where
A
⊥
and
A
are the components of the hyperfine tensor
A
perpendicular and parallel to the crystal symmetry axis (the
c
axis) [
29
]. The order of the energies is determined by the signs
of these components, which we have determined to be
A
g
<
0 and
A
g
⊥
,A
e
,A
e
⊥
>
0 (see Sec.
IVA
) with the superscript
g
(
e
) denoting the ground (excited) state. The corresponding
eigenstates numbered from lowest to highest energy are
|
1
g
=|↑⇑
g
,
|
1
e
=
1
√
2
(
|↑⇓
e
−|↓⇑
e
)
,
(2)
|
2
g
=|↓⇓
g
,
|
2
e
=
1
√
2
(
|↑⇓
e
+|↓⇑
e
)
,
(3)
|
3
g
=
1
√
2
(
|↑⇓
g
−|↓⇑
g
)
,
|
3
e
=|↑⇑
e
,
(4)
|
4
g
=
1
√
2
(
|↑⇓
g
+|↓⇑
g
)
,
|
4
e
=|↓⇓
e
.
(5)
We denote the electron-spin components as
|↑ ≡ |
S
z
=
1
2
,
|↓ ≡ |
S
z
=−
1
2
and the nuclear-spin components as
|⇑ ≡
|
I
z
=
1
2
,
|⇓ ≡ |
I
z
=−
1
2
.
For high magnetic fields applied along the
c
axis, the
electronic Zeeman interaction dominates over the hyperfine
interaction. In this regime, mixing between the electron and
nuclear spin is greatly reduced and the states effectively
become
|
1
g
≈|↑⇑
,
|
1
e
≈|↓⇑
,
(6)
|
2
g
≈|↑⇓
,
|
2
e
≈|↓⇓
,
(7)
|
3
g
≈|↓⇓
,
|
3
e
≈|↑⇓
,
(8)
|
4
g
≈|↓⇑
,
|
4
e
≈|↑⇑
.
(9)
024404-2
CHARACTERIZATION OF
171
Yb
3
+
:YVO
4
FOR ...
PHYSICAL REVIEW B
98
, 024404 (2018)
FIG. 1. Energy-level diagram for
171
Yb
3
+
:YVO
4
. (a) Crystal-field splittings of
171
Yb
3
+
:YVO
4
reproduced from [
28
]. (b) Zero-field energy-
level diagram for the
2
F
7
/
2
(0)
→
2
F
5
/
2
(0) transition of
171
Yb
3
+
:YVO
4
at 984.5 nm studied in this paper. Energy splittings in the ground and
excited state are extracted from the excited-state hyperfine tensor determined in this work and previous measurements of the ground-state
hyperfine tensor [
30
]. The transitions corresponding to the observed absorption spectrum in Fig.
2
for
E
c
(
E
⊥
c
) are shown in solid blue
(dashed red). The dotted grey lines correspond to transitions that are forbidden by symmetry. (c) Energy-level diagram for the linear Zeeman
regime with
B
c
with arrows denoting the transitions studied in this work.
We have again numbered the states from lowest to highest
energy using the fact that
g
<
0 for the ground state and
g
>
0 for the excited state (see Sec.
IVA
). The prime is
used to distinguish between the high-field and zero-field state
labels. In this work, we focus on the coherence properties of
the optical and nuclear-spin transitions in the regime where the
linear Zeeman interaction is dominant.
III. EXPERIMENTAL METHODS
High-resolution laser absorption scans with a home-built
external-cavity diode laser (ECDL) using the design from [
31
]
were performed to measure the inhomogeneous linewidth and
absorption of the
2
F
7
/
2
(0)
→
2
F
5
/
2
(0) transition. The energies
of the optical transitions were extracted from absorption scans
taken with magnetic fields applied along the crystal symmetry
axes and used to determine the excited-state spin Hamiltonian.
For this purpose, we used a 90-
μ
m-thick
a
-cut sample of
171
Yb
3
+
:YVO
4
. Thisthicknesswaschosensuchthatthesample
was not overabsorbing at 2 K. The sample was mounted
in a custom sample mount and masked to avoid spurious
light leakage around the crystal that could lead to inaccurate
measurements of the optical depth. For the data presented here,
the probe light propagated parallel to the
a
axis of the crystal
and perpendicular to the applied magnetic field (
k
⊥
B
,c
). Ad-
ditional axial spectra (
k
c
) were taken to confirm the electric
dipole nature of the optical transitions [
32
]. The absorption
was determined by measuring the transmission of the ECDL
on a photodetector (New Focus 2031) as the frequency of the
laser was scanned across resonance. The center frequency of
the scan was calibrated with a wave meter (Burleigh WA-1500)
and the frequency detuning of the scan was calibrated using a
Fabry-Perot reference cavity. The absorption experiments were
performed in an Oxford Spectromag cryostat at a temperature
of 2 K with an applied magnetic field of up to 6 T.
For measurements of the excited state, optical coherence,
and spin coherence lifetimes, the optical transitions were ad-
dressed using a single frequency Ti:sapphire laser (M-Squared
Solstis) that was gated by an 80-MHz acousto-optic modulator
in a double-pass configuration to create the required pulse
sequence. For measurements of the coherence properties and
inhomogeneity of the nuclear-spin transition, the nuclear-spin
transition was addressed directly using a coaxial transmission
line mounted directly next to the sample.
The excited-state lifetime was measured from the time-
resolved fluorescence decay. We performed pulsed excitation
on the
2
F
7
/
2
(0)
→
2
F
5
/
2
(0) transition and collected the re-
sulting fluorescence to the upper crystal-field levels of the
ground state [i.e.,
2
F
5
/
2
(0)
→
2
F
7
/
2
(1
−
3)] using a 1000-nm
long-pass filter. The fluorescence counts as a function of
time were recorded using a silicon avalanche photodiode
(Perkin-Elmer). Fluorescence measurements were performed
in a 500-
μ
m-thick sample that was nominally undoped (resid-
ual
171
Yb
3
+
concentration of
∼
2 ppm) and a 200-
μ
m-thick
100-ppm sample of
171
Yb
3
+
:YVO
4
. These measurements were
performed at 4 K with zero applied magnetic field in a Montana
Instruments cryostat using a home-built confocal microscope
setup.
The coherence properties of the optical transition were
investigated using two-pulse photon echo decays as a function
of magnetic field strength. For this purpose, two-pulse photon
echoes on the
|
1
g
→|
1
e
transition were measured using
heterodyne detection. During the echo sequence, a fiber-based
phase modulator EOM (IXBlue NIR-MPX-LN-20) was driven
by a microwave source (Windfreak Synth HD) at 500 MHz to
create an optical sideband resonant with the optical transition.
The resulting echo was detected as a beat at the sideband
024404-3
JONATHAN M. KINDEM
et al.
PHYSICAL REVIEW B
98
, 024404 (2018)
frequency using an InGaAs photodiode (Thorlabs DET08CFC,
5GHzbandwidth). Typical
π
pulsesforthismeasurementwere
4
μ
s long.
Optical coherence measurements were performed with the
sample mounted on the still plate of a Bluefors dilution
refrigerator at a temperature of 650 mK. These measurements
used a 500-
μ
m-thick
c
-cut 100-ppm sample with
k
c
.The
light entered the refrigerator via single-mode optical fiber and
was focused onto the back surface of the sample, which was
coated in gold to enhance reflection. The reflected light was
coupled back into the fiber and directed to the photodetector
with a fiber beam splitter. A variable magnetic field of up to
1.5 T was applied along the crystal
c
axis using a home-built
superconducting solenoid.
The inhomogeneous linewidth of the nuclear-spin transi-
tion was measured using continuous-wave Raman heterodyne
detection [
33
]. Frequency-swept microwave tones from a
tracking generator (Anritsu) were amplified and applied to the
sample. The coherence generated on the
|
1
g
→|
2
g
nuclear-
spin transition was mapped to an optical coherence by applying
a continuous-wave laser to the
|
2
g
→|
1
e
optical transition
at frequency
ν
0
, which resulted in coherent Raman scattering
on the
|
1
g
→|
1
e
optical transition at
ν
r
. This signal was
detected on the transmitted optical beam as a beat at the
microwave transition frequency (
ν
0
−
ν
r
) using an InGaAs
photodiode.
The nuclear-spin coherence was measured using two-pulse
spin echoes. Coherent manipulation on the nuclear-spin state
was performed with both direct microwave excitation and all-
optical excitation with bichromatic Raman pulses [
34
–
37
]. The
ionswerefirstinitializedintothe
|
1
g
stateviaopticalpumping
on the
|
2
g
→|
1
e
transition. For direct manipulation, the
echo sequence was performed using tones generated by a
microwave source tuned to the
|
1
g
→|
2
g
nuclear spin
transition. Pulses were generated using microwave switches
(Minicircuits ZASWA-2-50DR+) with typical
π
pulse lengths
of 100
μ
s. For all-optical spin echoes, the nuclear-spin tran-
sition was coherently manipulated via the shared excited state
|
1
e
by applying bichromatic pulses to the
|
2
g
→|
1
e
and
|
1
g
→|
1
e
transitions as depicted in Fig.
1(c)
. Typical
spin
π
pulses for the all-optical sequence were 8
μ
s. The
two optical frequencies were generated by driving a fiber-
based phase modulator with a microwave source tuned to the
nuclear-spin transition frequency. The relative power of the
two optical frequencies was chosen to maximize the echo
signal. The resulting spin echo was optically detected via
Raman heterodyne scattering by applying a readout pulse to
the
|
2
g
→|
1
e
transition at the time of the echo. The signal
was detected as a beat on the probe laser at the nuclear-spin
transition frequency.
Nuclear-spin coherence measurements were performed at
approximately 700 mK. These measurements were done in
transmission through a 2-mm-thick
a
-cut sample with
k
⊥
c,
B
. The polarization of the input light was set using a
fiber polarization controller to maximize the echo signal. A
variable magnetic field was applied to the crystal using a set of
home-built superconducting Helmholtz coils. For the direct
microwave measurements, the magnetic field was applied
alongthe
c
axis.Fortheall-opticalmeasurements,themagnetic
field was applied
∼
20
◦
from the
c
axis. As described in Sec.
IV
,
FIG. 2. Optical-absorption spectra of the
2
F
7
/
2
(0)
→
2
F
5
/
2
(0)
transition of
171
Yb
3
+
:YVO
4
at 2 K and zero applied magnetic field for
light polarized parallel (solid blue) and perpendicular (dashed red) to
the crystal
c
axis.
this was done to help equalize the strengths of the optical
transitions used in the measurement.
IV. OPTICAL AND SPIN PROPERTIES OF
171
Yb:YVO
4
A. Optical-absorption spectroscopy
The zero-field absorption spectra for the
2
F
7
/
2
(0)
→
2
F
5
/
2
(0) transition of
171
Yb
3
+
:YVO
4
at2KisshowninFig.
2
.
We observed narrow inhomogeneous linewidths [the average
full width at half maximum (FWHM) is 275 MHz], which
allowed us to resolve and address individual optical-hyperfine
transitions. For
E
c
, we observed three resolved transitions
with a peak absorption coefficient for the strongest transition
of 450 cm
−
1
.For
E
⊥
c
, we observed four resolved transi-
tions with a peak absorption of 50 cm
−
1
. The corresponding
transitions on the energy diagram are labeled in Fig.
1(b)
.
The strong polarization selection rules between the optical
hyperfine transitions observed in Fig.
2
are consistent with
those derived for electric-dipole transitions based on the site’s
point-group symmetry [
38
].
We observed a peak at zero detuning, which corresponds
to the presence of zero-spin isotope in the sample (measured
to be
<
10 ppm from SIMS). We also noted the presence of
additional satellite lines due to the 173 isotope.
The ground-state Zeeman and hyperfine tensors of
171
Yb
3
+
:YVO
4
have been determined using electron para-
magnetic resonance [
30
], so a description of the system
requires finding the corresponding values for the excited state.
For a uniaxial crystal, this reduces to four parameters: the
components of
g
and
A
, parallel and perpendicular to the
crystal symmetry axis. The values for
A
can be determined by
the energy-level structure in the absence of a magnetic field,
while
g
can be determined from the energy-level structure as
magnetic fields are applied parallel and perpendicular to the
crystal’s
c
axis.
Fitting to the energy-level splittings extracted from the ab-
sorption spectra, we find agreement with previously published
024404-4
CHARACTERIZATION OF
171
Yb
3
+
:YVO
4
FOR ...
PHYSICAL REVIEW B
98
, 024404 (2018)
FIG. 3. (a) Typical high-resolution absorption spectra for a mag-
netic field ramp with
B,
k
⊥
c
and
E
⊥
c
showing resolved optical
hyperfine transitions. Darker regions correspond to higher absorption.
(b) Simulated absorption spectra using the experimentally determined
spin Hamiltonian for magnetic field ramp with
B,
k
⊥
c
and
E
⊥
c
.
The simulated absorption spectra take into account a slight misalign-
ment (
∼
1
◦
) between the crystal
a
axis and the applied magnetic field.
data for the ground-state
A
tensor [
30
](
A
g
/h
=−
4
.
82 GHz,
A
g
⊥
/h
=
0
.
675 GHz) and we determine the principal values
of the excited-state hyperfine tensor to be
A
e
/h
=
4
.
86
±
0
.
05 GHz and
A
e
⊥
/h
=
3
.
37
±
0
.
05 GHz.
The excited-state
g
tensor was determined by measuring
the frequency of the optical transitions with magnetic fields
applied parallel and perpendicular to the crystal’s
c
axis.
Figure
3(a)
shows an example of one such measurement
in which the absorption was recorded while the magnetic
field perpendicular to the crystal
c
axis was continuously
ramped. By fitting to the energy levels extracted from this
spectra and similar measurements for other field orientations,
we determine
g
e,
=
2
.
51
±
0
.
1 and
g
e,
⊥
=
1
.
7
±
0
.
1. Figure
3(b)
shows the absorption spectra expected from the spin
Hamiltonian, which we see enables accurate predictions of
the energy-level splittings and relative transition absorption
oscillator strengths in this case.
B. Optical transition strengths
The strength of the optical transitions can be characterized
by assigning an oscillator strength to each individual transition.
The absorption oscillator strength for a transition
|
i
→|
j
for
a polarized spectrum is given by [
39
,
40
]
f
ij
=
4
π
0
m
e
c
πe
2
1
N
∑
i
9
n
i
(
n
2
i
+
2
)
2
∫
α
i
(
ν
)
dν,
(10)
where
0
is the vacuum permittivity,
m
e
is the mass of the
electron,
e
is the charge on the electron,
c
is the speed of
TABLE I. Absorption properties of the
171
Yb
3
+
:YVO
4
transitions
as labeled in Fig.
2
, including the transition polarization [
38
],
integrated absorption coefficient, oscillator strength, and radiative
decay rate at zero magnetic field.
Trans. Pol.
∫
α
(
ν
)
dν
(GHz
/
cm)
f
(10
−
6
)1
/τ
rad
(kHz)
A
π
97.3
5.4
1.3
C
σ
16.4
1.0
0.3
E
π
102.7
5.5
1.4
F
σ
17.4
1.1
0.4
G
σ
20.2
2.6
0.2
H
σ
19.9
2.6
0.2
I
π
189.7
4.9
1.2
light,
N
is the number density, and the summation is over the
three orthogonal polarizations states with
α
i
and
n
i
absorption
coefficient and index of refraction, respectively. For YVO
4
,
n
=
2
.
17 and
n
⊥
=
1
.
96 at 984 nm [
41
].
Assuming a doping density of 100 ppm, the number density
of Yb
3
+
in YVO
4
is calculated to be
N
=
1
.
24
×
10
18
cm
−
3
,
which is distributed between the four ground-state levels
according to Boltzmann statistics at 2 K. The integrated ab-
sorption coefficient and corresponding oscillator strengths for
theobservedtransitionsaresummarizedinTable
I
.Wemeasure
an average oscillator strength of 5
.
3
×
10
−
6
for transitions
allowed for
E
c
(transitions A, E, I in Fig.
2
) and 1
.
8
×
10
−
6
for transitions allowed for
E
⊥
c
(transitions C, F, G, H in
Fig.
2
).
The radiative lifetime for the
2
F
5
/
2
(0)
→
2
F
7
/
2
(0) transi-
tions can be determined from the absorption measurements.
The radiative lifetime for a transition
|
j
→|
i
is related to
the oscillator strength by [
39
,
40
]
1
τ
rad
=
2
πe
2
0
m
e
c
(
n
2
+
2)
2
9
n
n
2
λ
2
0
f
ji
3
,
(11)
where
n
is the index of refraction,
λ
0
is the wavelength in
vacuum, and
f
ji
is the emission oscillator strength. The emis-
sion oscillator strength is related to the absorption oscillator
strength
f
ij
by
f
ji
=
g
i
g
j
f
ij
, where
g
i
(
g
j
) is the degeneracy of
state
|
i
(
|
j
). The calculated emission rates for the observed
transitions are included in Table
I
. From these rates, we
obtain an average radiative rate of 1
/τ
rad
=
1
/
(590
μ
s) for the
2
F
5
/
2
(0)
→
2
F
7
/
2
(0) transitions.
C. Excited-state lifetimes
The excited-state lifetime is important for optical prepara-
tion of population among the spin states and sets the upper
limit on the optical coherence time. The measured excited-
state lifetime allow us to determine the optical branching
ratio between the crystal-field levels, which is important in
the context of Purcell enhancement in nanophotonic cavities
[
42
]. Here, we measure the excited-state lifetime through
fluorescence decay.
To avoid the problem of radiation trapping [
43
] ob-
served in previous measurements of excited-state lifetimes in
Yb-doped materials [
22
,
26
,
44
], the excited-state lifetime was
measured in a nominally undoped sample of YVO
4
, which had
024404-5
JONATHAN M. KINDEM
et al.
PHYSICAL REVIEW B
98
, 024404 (2018)
FIG. 4. Excited-state lifetime measurement via fluorescence de-
cay. An exponential fit (dashed line) gives
τ
f
=
267
±
1
μ
s.
a residual
171
Yb
3
+
concentration of approximately 2 ppm. In
this sample, we did not see variations in the optical lifetime
within the inhomogeneous line or other signs of radiation
trapping. A typical fluorescence decay in this sample is shown
in Fig.
4
. Fitting to a single exponential gives a fluorescence
lifetime of
τ
f
=
267
±
1
μ
s. The branching ratio back to the
same crystal-field level [
2
F
5
/
2
(0)
→
2
F
7
/
2
(0)] is then given
by
β
=
τ
f
/τ
rad
, where
τ
f
and
τ
rad
are the fluorescence and
radiative lifetimes. Using the radiative lifetime obtained from
the absorption measurements, we determine the branching
ratio to be
β
=
0
.
45.
We also note that in a 200-
μ
m-thick 100-ppm sample we
observed lifetimes longer than 500
μ
s in the center of the
inhomogeneous distribution that decreased to less than 300
μ
s
when the excitation pulse was detuned by 200 MHz from
the center of the line. This behavior is attributed to radiation
trapping due to the high optical depth and strong transition
strengths of these ions.
D. Optical coherence measurements
To assess the ability to store quantum states in the material,
we first investigate the coherence of the optical transition using
two-pulsephotonechoes(2PPEs).ForKramersions,weexpect
a dominant source of decoherence to be magnetic fluctuations
due to magnetic dipole-dipole interactions between Yb ions
[
45
]. One way to minimize this source of decoherence is
to freeze-out the electron spins by achieving a ground-state
splitting much larger than
k
b
T
[
45
]. For
171
Yb
3
+
:YVO
4
,the
energy-level splitting is maximized for a magnetic field along
the crystal
c
axis. Here, we present measurements of the optical
coherence in the linear Zeeman regime with the magnetic field
along the
c
axis. While a comprehensive study is warranted to
fully understand the decoherence mechanisms in this system,
a large magnetic field applied parallel to
c
provides insight on
the maximum achievable coherence times in this material and
the dominant decoherence mechanisms.
Figure
5(a)
shows typical photon echo decays for magnetic
fields ranging from 340 mT to 1.36 T along the crystal
c
axis. We observed strong nonexponential decays, which can
be attributed to spectral diffusion and described by a Mims
decay [
46
]. For heterodyne detection, the decay of the echo
field is given by [
46
]
E
(
t
12
)
=
E
0
e
−
(2
t
12
/T
m
)
x
,
(12)
where
t
12
is the delay between the two pulses used in the
photon echo experiment,
x
is the Mims parameter describing
the spectral diffusion, and
T
m
is phase memory time (the time
at which the echo field amplitude decays to
e
−
1
of its initial
value). Fits to the Mims decay are shown as solid lines in
Fig.
5(a)
.From
T
m
, we can extract an effective homogeneous
linewidth as
h,eff
=
(
πT
m
)
−
1
. The effective linewidth as a
function of applied magnetic field along the
c
axis is shown in
Fig.
5(b)
.
We observed a decrease in the linewidth with applied
magnetic field from
∼
5
.
5 kHz at 340 mT to
∼
3kHz at
1.5 T, which was the maximum magnetic field achievable for
this measurement. The reduction in linewidth for increasing
magnetic field is expected for dephasing dominated by Yb-
Yb spin flips and similar to that observed in other Kramers
ions [
45
,
47
]. At the highest magnetic fields, we saw that
the coherence no longer increased with applied field. The
nonexponential decay and saturation of coherence time in the
high-field limit are typical signs of the superhyperfine limit
[
48
]. In this limit, magnetic fluctuations due to the electron
spins are effectively frozen out and the main contribution to
dephasing is interactions with the nuclei of the host material.
We note that recent work in
171
Yb
3
+
:Y
2
SiO
5
[
20
] and
167
Er
3
+
:Y
2
SiO
5
[
49
] demonstrated an increase in coherence
time due to reduced sensitivity to magnetic fluctuations at zero
first-order Zeeman (ZEFOZ) points at
B
=
0. While we did not
explore the low-field regime in this work, Eq. (
1
) predicts sim-
ilar zero-field ZEFOZ transitions in
171
Yb
3
+
:YVO
4
between
levels
|
3
g
and
|
4
g
of the ground state and
|
1
e
and
|
2
e
of the
excited state.
E. Nuclear-spin measurements
The coherence times of the
2
F
7
/
2
(0) nuclear-spin transitions
will determine the feasibility of long-term quantum infor-
mation storage in this system. In this section, we present
measurements on the inhomogeneous linewidth and coherence
properties of the
|
1
g
→|
2
g
nuclear-spin transition in the
linear Zeeman regime.
The inhomogeneous broadening of the nuclear-spin transi-
tion was measured using continuous-wave Raman heterodyne
spectroscopy [
33
]. Figure
6
shows a typical trace of the
normalized Raman heterodyne signal power as the microwave
frequency is swept across the resonance. Fitting this peak
to a Lorentzian gives a FWHM of 250 kHz, which serves
as an upper bound on the inhomogeneous broadening of the
spin transition since the width of the observed signal can
be power broadened by the Rabi frequencies of the optical
and microwave fields used in the measurement [
50
]. The
inhomogeneity of the nuclear-spin transition can be attributed
to variations in the crystal field due to strain and defects in the
crystal and variations in the local magnetic field arising from
spin-spin interactions [
51
], as well as inhomogeneity of the
applied magnetic field along the beam path. This measurement
024404-6
CHARACTERIZATION OF
171
Yb
3
+
:YVO
4
FOR ...
PHYSICAL REVIEW B
98
, 024404 (2018)
FIG. 5. (a) Typical photon echo decays for
B
c
showing an increase of coherence time and strong nonexponential decays with increasing
magnetic field. Fits to a Mims decay are shown for each field value as a solid line (see main text for details). (b) Effective linewidth extracted
from the fits to the photon echo decays for
B
c
.
was done with a field of 440 mT along
c
, but is typical of what
was obtained for other magnetic field amplitudes applied along
this direction.
The nuclear-spin coherence was measured by spin-echo
decays with direct microwave manipulation of the
|
1
g
→
|
2
g
spin transition and optical detection via coherent Raman
scattering. Figure
7
shows typical nuclear-spin echo decays
for increasing magnetic fields along the
c
axis. For the higher
field decays, we observed nonexponential decays resulting
from time-varying dephasing mechanisms that can again be
described by the Mims decay using Eq. (
12
). We measured
coherence times of 250
μ
s at 60 mT that increased up to
6.6 ms at a field of 440 mT, which was the maximum achievable
magnetic field for the experimental configuration at the time of
the measurement. Time-resolved measurements of the decay
of the area of spectral holes prepared in the inhomogeneous
line [
51
] gave spin-relaxation times longer than 200 ms in this
field configuration, indicating that these coherence times are
not lifetime limited.
FIG. 6. Continuous-wave Raman heterodyne measurement of the
nuclear-spin inhomogeneity with
B
=
440 mT parallel to the
c
axis.
A Lorentzian fit gives a FWHM of 250 kHz.
F. All-optical spin coherence measurements
In addition to direct microwave excitation of the nuclear
spins, we are interested in performing coherent all-optical con-
trol on the nuclear spins. All-optical control allows us to take
advantage of relatively strong optical transitions to perform
faster manipulations on the spin. This approach also removes
the need for a microwave circuit to be incorporated next to
the sample, which reduces the complexity of the experimental
setup and prevents additional heating of the sample through
the microwave excitation. As an initial demonstration of the
potential for all-optical control in this system, we use an all-
optical Raman echo technique [
52
] to measure the coherence
of the nuclear-spin transition. The
|
1
g
→|
2
g
transition is
addressedbyapplyingbichromaticpulsestothelambdasystem
formed by the
|
2
g
→|
1
e
and
|
1
g
→|
1
e
optical transi-
tions. Efficient rephasing of coherence on the spin transition
using bichromatic pulses in this fashion requires that the Rabi
frequencies of the two transitions of the lambda system are
FIG. 7. Typical nuclear-spin echo decays for increasing applied
magnetic field along the
c
axis. The echo sequence is performed with
direct microwave excitation and read out optically.
024404-7