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# Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

Nithya Arunkumar  Department of Physics, Harvard University, Cambridge,
Massachusetts 02138, USA  John A. Paulson School of Engineering and Applied
Sciences, Harvard University, Cambridge, Massachusetts 02138, USA  Quantum
Technology Center, University of Maryland, College Park, Maryland 20742, USA
Kevin S. Olsson  Quantum Technology Center, University of Maryland, College
Park, Maryland 20742, USA  Department of Electrical and Computer Engineering,
University of Maryland, College Park, Maryland 20742, USA  Intelligence
Community Postdoctoral Research Fellowship Program, University of Maryland,
College Park, Maryland 20742, USA  Jner Tzern Oon  Quantum Technology Center,
University of Maryland, College Park, Maryland 20742, USA  Department of
Physics, University of Maryland, College Park, Maryland 20742, USA  Connor
Hart  Quantum Technology Center, University of Maryland, College Park,
Maryland 20742, USA  Department of Electrical and Computer Engineering,
University of Maryland, College Park, Maryland 20742, USA  Dominik B. Bucher
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
Department of Chemistry, Technical University of Munich, Germany  David Glenn
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
Mikhail D. Lukin  Department of Physics, Harvard University, Cambridge,
Massachusetts 02138, USA  Hongkun Park  Department of Physics, Harvard
University, Cambridge, Massachusetts 02138, USA  Department of Chemistry and
Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
Donhee Ham  John A. Paulson School of Engineering and Applied Sciences,
Harvard University, Cambridge, Massachusetts 02138, USA  Ronald L. Walsworth
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
Quantum Technology Center, University of Maryland, College Park, Maryland
20742, USA  Department of Electrical and Computer Engineering, University of
Maryland, College Park, Maryland 20742, USA  Department of Physics, University
of Maryland, College Park, Maryland 20742, USA

###### Abstract

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble
of solid-state, hybrid two-qubit sensors. We achieve a factor of 30
improvement in signal-to-noise ratio, translating to a sensitivity enhancement
exceeding an order of magnitude. Using the electronic spins of nitrogen
vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen
nuclear spins of the NV centers as memory qubits, in combination with
homogeneous bias and control fields, ensuring that all of the ${\sim}10^{9}$
two-qubit sensors are sufficiently identical to permit global control of the
NV ensemble spin states. We find quantum logic sensitivity enhancement for
multiple measurement protocols with varying optimal sensing intervals,
including XY8 dynamical decoupling and correlation spectroscopy, using a
synthetic AC magnetic field. The results are independent of the nature of the
target signal and broadly applicable to metrology using NV centers and other
solid-state ensembles. This work provides a benchmark for macroscopic
ensembles of quantum sensors that employ quantum logic or quantum error
correction algorithms for enhanced sensitivity.

Quantum technologies for information processing, networking, and metrology
increasingly employ hybrid architectures leveraging the advantageous
properties of multiple physical qubit types. In platforms for quantum
computing, this approach enables increased system sizes, while maintaining
high fidelity and low cross-talk [1, 2, 3, 4]. For timekeeping applications,
ion clocks using two species, one ‘clock’ ion with a stable transition and a
second ‘logic’ ion for preparation and readout, have demonstrated exceptional
performance [5, 6, 7, 8].

Analogous multi-qubit strategies are similarly compelling for quantum sensors.
In particular, the use of additional memory qubits in support of sensing
qubits presents an attractive avenue towards entanglement-enhanced performance
[9, 10]. Among leading quantum sensing platforms, defect centers in solid-
state systems are naturally amenable to quantum logic assisted protocols since
they commonly consist of multiple individually controllable spin degrees of
freedom localized within or near a defect.

An early demonstration of entanglement-enhanced sensing was by Jiang et al.
[11], who performed repetitive, quantum non-demolition readout of a single-
negatively charged nitrogen-vacancy (NV) center spin state coupled to nearby
13C nuclear spins. The technique circumvents the poor optical readout fidelity
of NV centers by mapping the NV electronic spin state onto the longer-lived
nuclear memory qubit. The nuclear spin state can then be interrogated
repeatedly by re-entangling the NV electronic and 13C nuclear spins between
each optical readout.

Subsequent work with single NV centers improved upon this protocol by using
the nitrogen nuclear spin inherent to the NV center as a memory qubit, instead
of the 13C nuclear spin [12, 13]. In contrast to 13C nuclear spins, which are
randomly distributed within the diamond lattice, the on-site nitrogen nuclear
spin has a well-determined hyperfine coupling with the NV electronic spin.
This homogeneous coupling makes it particularly suitable for translation to
ensembles of NV centers, as reported here.

By spatially averaging over many NV centers, ensemble measurements trade
nanometer-scale spatial resolution for dramatically improved sensitivity [9],
which has enabled a wide range of applications across the physical and life
sciences, including by nuclear magnetic resonance (NMR) [14], magnetic
microscopy [15], crystal stress and pressure spectroscopy [16, 17], and
thermometry [18, 19]. However, in nearly all such experiments, only global
control of the NV ensemble is available. Therefore, the useful realization of
quantum logic protocols with NV ensembles demands each constituent multi-qubit
sensor system be nearly identical, for both interactions within the NV center
and diamond lattice, as well as its response to external fields.

In this Letter, we demonstrate quantum logic enhanced (QLE) sensing with a
macroscopic ensemble of two-qubit sensors, each consisting of an NV electronic
spin and an on-site 15N nuclear spin. Interrogating a
$($10$\times$10$\times$10$)\,$µm3 volume of diamond containing ${\sim}10^{9}$
of these two-qubit sensors, the QLE protocol increases the effective readout
fidelity of each constituent NV, achieving a nominal $33\times$ improvement in
signal-to-noise ratio (SNR) compared to measurements using only the NV
electronic spins.

We also show that the observed SNR improvement translates to enhancements in
magnetic field sensitivity, which can exceed an order-of-magnitude.
Importantly, the present approach is universally applicable (independent of
the sensing protocol or target signal), and thus provides a benchmark for
quantum sensing using quantum logic architectures, both for ensembles of NV
centers and other platforms.

Figure 1: NV ensemble sensor integrated with quantum logic [20]. (a) A 532 nm
optical beam illuminates the diamond chip with a spot diameter of $\sim$15 µm,
using a total internal reflection configuration. A single-loop coil antenna
above the $10\,$µm-thick NV layer drives both the microwave transition of the
NV electronic spin states and the radio frequency transition of the 15N
nuclear spins. The magnified view depicts the multi-qubit NV spin system. A
multi-loop coil provides the synthetic AC magnetic field measured in this
study, which can be substituted with a relevant target signal, such as those
originating, e.g., from NMR, integrated circuits, materials science, and
thermometry applications. (b) NV energy levels allow optical initialization
and readout of the electronic spin states. The expanded view of the ground
state triplet energy levels shows splittings due to Zeeman and hyperfine
interactions.

Figure 1(a) illustrates the experimental setup (refer to the supplement for
further detail [20]), which operates at ambient laboratory conditions and
probes a (2$\times$2$\times$0.5) mm3 diamond chip containing an ensemble of NV
centers at a concentration of [NV] ${\approx}\,2.3$ ppm ([N]$\,{\approx}\,14$
ppm) [21]. Each near-identical two-qubit system consists of the NV electronic
‘sensor’ spin ($S=1$) and the nuclear ‘memory’ spin ($I=1/2$) of the
associated 15N nucleus. By applying a bias magnetic field along the NV
symmetry axis, the NV ground state spin sublevels are non-degenerate (Fig.
1(b)), allowing them to be individually addressed using microwave fields. We
employ the electronic spin states $m_{s}\\!=\\!0$ and $m_{s}\\!=\\!\text{-}1$
as an effective two-level system, with representative qubit states
$|\downarrow_{e}\rangle$ and $|\uparrow_{e}\rangle$, respectively. The two
nuclear spin states $m_{I}=-\frac{1}{2},\frac{1}{2}$ are represented by
$|\downarrow_{n}\rangle$ and $|\uparrow_{e}\rangle$. The eigenstates of the
composite electron-nuclear system are denoted by
$|\\{\uparrow_{e},\downarrow_{e}\\};\\{\uparrow_{n},\downarrow_{n}\\}\rangle$.

We first demonstrate control of the NV nuclear spin (memory qubit) using the
NV electronic spin (sensor qubit) via quantum logic protocol. To entangle the
NV sensor and memory qubits, two controlled NOT (CNOT) gates are applied in
succession, forming a SWAP operation. Fig. 2(a) and the top panel of Fig. 3
(excluding the sensing sequence) illustrate this procedure, which begins with
a selective microwave (MW) $\pi$ pulse that exchanges the spin populations of
the states $|\downarrow_{e};\uparrow_{n}\rangle$ and
$|\uparrow_{e};\uparrow_{n}\rangle$. This pulse acts as a CNOT operation on
the electronic spin, conditioned on the nuclear spin state (CNOTe|n). Next, a
radio frequency (RF) $\pi$ pulse is applied, resulting in a CNOTn|e gate that
exchanges the populations of $|\uparrow_{e};\uparrow_{n}\rangle$ and
$|\uparrow_{e};\downarrow_{n}\rangle$. As a result, the electronic spin
population is mapped to that of the nuclear spin, effectively encoding the
information measured by the sensor spins onto the memory spins.

To evaluate the efficacy of the SWAP operation, we perform optically detected
magnetic resonance (ODMR) measurements on the NV ensemble. After applying an
initial 532 nm laser pulse to polarize the electronic spin states to
$|\downarrow_{e}\rangle$, the ODMR spectra with and without the SWAP operation
is measured, as shown in Figure 2(b). A clear transfer of polarization from
the electronic sensor spins to the nuclear memory spins is observed when the
SWAP operation is applied, with an estimated fidelity of $93\%$.

After encoding the sensor spin population onto the memory spins using the SWAP
gate, the electronic spin states are reset using an optical polarization
pulse. With successive $N$ applications of a CNOTe|n gate followed by an
optical readout pulse, the information stored in the nuclear memory spins is
then repeatedly mapped back onto the electronic spins and measured optically.
This procedure provides many readouts within a duration limited by the nuclear
spin lifetime $T_{1}$, thereby enhancing the overall readout fidelity. The
large number of NVs probed allows a high-precision ensemble average
measurement of the sensor spin state with one execution of this repetitive
readout protocol.

Flip-flop transitions between the electronic and nuclear spins present the
dominant $T_{1}$ relaxation channel, and are increasingly suppressed at higher
bias magnetic fields. Using the pulse sequence shown in Fig. 2(c), we present
measurements of $T_{1}$ in Fig. 2(d) for magnetic fields up to 4000 G,
generated by a feedback-stabilized electromagnet [14]. At each magnetic field,
the NV fluorescence signal contrast is measured as a function of optical pulse
duration ($T_{\text{op}}$), which is applied after the SWAP operation and
electronic spin reset, as described above, and before a single application of
the CNOTe|n gate. The contrast decay curves are fit to a stretched exponential
function to extract $T_{1}$, with examples at the magnetic fields 200 G, 1700
G, and 3700 G shown in the inset of Fig. 2(d). The intensity of the laser
pulse also affects the nuclear $T_{1}$ (see [20]), and is kept fixed. The
$T_{1}$ values are fit to a power law function, yielding a power law exponent
of 1.8(2) in agreement with an expected quadratic dependence [12]. The
measurements presented in the remainder of this paper are performed at a bias
magnetic field of 3700 G, with a corresponding 15N nuclear spin $T_{1}$ of
3.44(12) ms.

Figure 2:  Nuclear spin control with quantum logic. (a) The energy levels of
the two-qubit system are formed by the NV electronic spin and its on-site 15N
nuclear spin. A selective MW pulse exchanges the spin population between
$|\downarrow_{e};\uparrow_{n}\rangle$ and $|\uparrow_{e};\uparrow_{n}\rangle$,
acting as a CNOTe|n gate. An RF pulse implements a CNOTn|e gate, exchanging
the populations of $|\uparrow_{e};\uparrow_{n}\rangle$ and
$|\uparrow_{e};\downarrow_{n}\rangle$. Applying the CNOTe|n and CNOTn|e gates
in succession contitutes a SWAP operation. (b) Measured NV ensemble ODMR
spectra with and without the SWAP operation. (c) Experimental pulse sequence
used to measure the nuclear spin lifetime $T_{1}$ under optical illumination.
(d) Measured 15N ensemble nuclear spin lifetime $T_{1}$ (white circles) at
bias magnetic fields up to $3700$ G, fit to a power law function.  Figure 3:
Quantum logic enhanced (QLE) sensing protocol. After a sensing sequence with a
duration $T_{\text{sense}}$, the electronic spin state is encoded onto the
nuclear spin for each NV in the ensemble, through the application of CNOTe|n
and CNOTn|e gates. After a subsequent optical pulse polarizes the electronic
spins, the readout sequence consisting of a CNOTe|n gate and a repolarization
pulse is repeated $N$ times. The duration of each individual quantum logic
readout sequence, $T_{\text{QLR}}$, is limited by the time required to
repolarize the electronic spins. Example AC magnetic field sensing sequences
are shown in the magnified view of $T_{\text{sense}}$.  Figure 4:  Quantum
logic enhanced (QLE) readout demonstrated with correlation spectroscopy. (a)
Example measured NV correlation spectroscopy time trace of the three-tone test
signal, without the QLE protocol. (b) Power spectra of the correlation
spectroscopy signal with and without QLE protocol. The power spectrum in the
absence of quantum logic is scaled $200\times$ for visibility. (c) Signal-to-
noise ratio (SNR) of the measured test signal as a function of the number of
quantum logic readout (QLR) cycles, $N$, compared to the reference SNR of
conventional readout, i.e., a single readout sequence without the QLE
protocol. Inset shows the decreasing signal amplitude from conventional
readout (lightest) compared to the $n$-th QLR cycle, with $n$ = 1, 600, 1300,
and 2000 (darkest).

We apply the above repetitive readout technique to demonstrate quantum logic
enhanced (QLE) AC magnetic field sensing using an ensemble of NV centers. We
first use correlation spectroscopy to measure a three-tone test signal at
about 1 MHz, generated by an RF synthesizer and communicated to the NV
ensemble via a multi-loop coil (see Fig. 1, [20]).

Correlation spectroscopy is a popular NV $T_{1}$-limited technique for AC
magnetometry in which the time delay between two dynamical decoupling
sequences ($T_{\text{corr}}$) is varied, see Fig. 3, with optical readout
applied only after the second decoupling sequence [22, 23, 24, 25, 26]. Our
correlation spectroscopy measurement employs two XY8-6 sequences [27, 28]. As
shown in Fig. 3, the sensing interval $T_{\text{sense}}$ is followed by a SWAP
operation with duration $T_{\text{SWAP}}$ and $N$ quantum logic readout cycles
(each with duration $T_{\text{QLR}}$).

Figure 4(a) depicts the NV ensemble fluorescence signal when measuring the
test signal using correlation spectroscopy and conventional readout, which
consists of a single optical readout pulse and omits other aspects of the QLE
protocol. The corresponding power spectrum, with the three tones well-
resolved, is shown in Fig. 4(b), scaled up by a factor of 200.

For the quantum logic enhanced (QLE) sensing protocol applied to measurements
of the test signal, we determine a series of power spectra from the
correlation time series acquired for each of the $N$ readout cycles. As
apparent in the inset of Fig. 4(c), the power spectrum signal amplitudes,
$A_{n}$, decay with increasing readout cycle index $n$ due to 15N nuclear spin
$T_{1}$ relaxation. To optimize the signal-to-noise ratio SNR($N$) after $N$
readouts [11], the signal amplitude for the $n$-th readout is weighted by
$A_{n}/\sigma_{n}^{2}$, where $\sigma_{n}$ is the standard deviation of the
noise at the $n$-th readout. Fig. 4(b) compares the power spectrum of a
weighted signal after $N=2000$ quantum logic readout (QLR) cycles to the
reference signal obtained using conventional readout.

The resulting QLE SNR($N$) is given by
$\sqrt{\sum_{n=1}^{N}A_{n}^{2}/\sigma_{n}^{2}}.$ We normalize SNR($N$) by
SNR(Ref), the SNR of the conventional NV electronic spin readout (without
quantum logic), measured under the same experimental conditions. The SNR
enhancement realized with quantum logic is shown in Fig. 4(c). For example,
with 2000 QLR cycles, we achieve a 33.3(9)$\times$ enhancement.

However, improvements in SNR do not necessarily translate into enhanced
sensitivity, since SNR does not consider the impact on the measurement
timescale (and hence bandwidth) of an extended readout interval. We first
describe quantum logic sensitivity enhancement for AC magnetometry experiments
using only a single dynamical decoupling sequence, and then address
correlation spectroscopy experiments with varying $T_{\text{sense}}$. For non-
correlation spectroscopy experiments, $A_{n}$ corresponds to the maximum
signal amplitude as the magnitude of a single-tone, 1 MHz test signal is
varied.

Accounting for the overhead time associated with the SWAP operation
($T_{\text{SWAP}}=16.5\,$µs) and each readout cycle ($T_{\text{QLR}}=3\,$µs),
the sensitivity enhancement obtained using the QLE protocol can be estimated
from our measurements using,

$\widetilde{\eta}_{\text{QLE}}\approx\dfrac{\text{SNR}(N)}{\text{SNR(Ref)}}\dfrac{\sqrt{T_{\text{sense}}+T_{\text{QLR}}}}{\sqrt{T_{\text{sense}}+T_{\text{SWAP}}+(N\times
T_{\text{QLR}}})},$ (1)

where we have assumed the duration of a conventional readout is approximately
$T_{\text{QLR}}$.

Figure 5:  Quantum logic enhanced (QLE) sensitivity. (a) Experimentally
determined QLE sensitivity factor ($\widetilde{\eta}_{\text{QLE}}$) as a
function of the number $N$ of quantum logic readouts, for the three types of
sensing sequences used in the present work. (b) Calculated QLE sensitivity
factor ($\widetilde{\eta}_{\text{QLE}}$), given by color bar, as a function of
the number of readouts $N$ and sensing duration $T_{\text{sense}}$.
Calculations use Eq. 1 and the conditions of the present experiment. Dashed
lines indicate the $T_{\text{sense}}$ values of the three sensing measurements
reported in (a).

As shown in Fig. 5(a) for an XY8:6 (six repetitions of an XY8) dynamical
decoupling sequence with an optimal $T_{\text{sense}}=24\,$µs, the quantum
logic protocol achieves up to $\widetilde{\eta}_{\text{QLE}}=2.4(3)$ for
$N\approx 150$, compared to the same sensing sequence with conventional
readout. For the diamond sample used here, the optimal $T_{\text{sense}}$
under XY8 decoupling is constrained by the NV electronic spin coherence time
$T_{2}\approx 28\,$µs, which, in turn, is limited by NV-NV dipolar
interactions [20].

To surpass this interaction limit, we employ the DROID-60 decoupling sequence
introduced in Refs. [29, 30] and thereby extend the optimal $T_{\text{sense}}$
to $144\,$µs [20]. As anticipated from Eq. (1), when the sensing duration
becomes long compared to the additional overhead time for quantum logic
readout, larger sensitivity enhancements are attained. From our measurements
we find up to $\widetilde{\eta}_{\text{QLE}}=5.6(3)$ for DROID-60:6 using
quantum logic and $N\approx 400$, compared to conventional readout, as shown
in Fig. 5(a).

For AC magnetometry using the correlation spectroscopy sequence described
earlier, $T_{\text{sense}}$ varies with $T_{\text{corr}}$. To account for this
dynamic $T_{\text{sense}}$ when acquiring correlation spectroscopy signals, we
compare measurements using quantum logic with $N$ readouts to conventional
measurements repeated $M$ times, where the total acquisition time for both
experiments is equivalent. In Fig. 5(a), the number of conventional
measurements $M$ used to calculate the reference sensitivity for correlation
spectroscopy scales with $N$ to maintain:
$M\,\times\,(T_{\text{sense}}+T_{\text{QLR}})\,=\,T_{\text{sense}}+T_{\text{SWAP}}+(N\times
T_{\text{QLR}}$). For $T_{\text{corr}}$ ranging from $0\,\text{--}\,1.5\,$ms
in our experiments, we find a quantum logic sensitivity enhancement of up to
$\widetilde{\eta}_{\text{QLE}}=11.3(3)$ for $N\approx 1000$. More intuitively,
if we use the average value of $T_{\text{corr}}$ (0.75 ms) when calculating
$\widetilde{\eta}_{\text{QLE}}$ via Eq. (1), we estimate a similar QLE
sensitivity factor of $\widetilde{\eta}_{\text{QLE}}\approx 11$.

To highlight the versatility of the QLE technique, Fig. 5(b) provides
estimates of quantum logic enhancement for a range of sensing durations
T${}_{\text{sense}}$, given our experimental conditions. Applying an
arbitrarily large amount of readouts is not favorable. In 5(b)
$\widetilde{\eta}_{\text{QLE}}$ is reduced as $N$ increases, most visible at
$T_{\text{sense}}\sim 200-600$ µs for the ranges used in the plot. An
improvement in sensitivity ($\widetilde{\eta}_{\text{QLE}}\\!>\\!1$) is
readily achieved when $T_{\text{sense}}$ exceeds $T_{\text{SWAP}}$, applicable
to a wide range of sensing sequences (and diamond materials) commonly used in
NV-ensemble metrology and, in principle, for other solid-state spin systems.

In summary, we leveraged quantum logic using a macroscopic ensemble of solid-
state, hybrid two-qubit sensors – each consisting of an NV electronic spin and
the on-site 15N nuclear spin in diamond – to realize a factor of 30
improvement in spin state readout SNR, which in turn enables significant
improvement in AC magnetic field sensitivity. The observed sensitivity
enhancements can exceed an order of magnitude under favorable conditions (i.e,
sensing interval $\sim 1$ ms) using only global control of the NV ensemble.

Over a range of nitrogen doping concentrations (0.5–20 ppm), it is reasonable
to tune the optimal sensing duration by decreasing the total nitrogen density
in the material, which increases the NV electronic coherence time ($T_{2}$)
proportionally [31], without impacting the photon-shot-noise-limited
sensitivity (assuming a constant N-NV conversion efficiency). For example,
exchanging the sample used here ([N${}_{\text{tot}}$]$\,\approx$ 14 ppm) for
another with [N${}_{\text{tot}}$]$\,\approx$ 0.8 ppm in future work, we
anticipate an 18-fold increase in the optimal XY8 sensing duration, sufficient
to provide an order-of-magnitude improvement in quantum logic enhanced
sensitivity (QLE) for the conditions otherwise used in the present
experiments.

Furthermore, the current approach is agnostic to the target signal and,
therefore, broadly applicable to sensing a variety of physical quantities. In
the context of NV ensemble magnetometry, the QLE protocol is naturally
amenable to NMR spectroscopy given that both favor strong, uniform bias
magnetic fields. Using a diamond with reduced [N] (and [NV]) to extend the NV
ensemble coherence time, the QLE protocol provides a path towards order-of-
magnitude improvements in the sensitivity of micron-scale NV-NMR with high
spectral resolution [14]. Additionally, the improvements realized here are
compatible with the growing collection of techniques for NV -NMR sample
hyperpolarization [32, 33].

Beyond magnetometry, NV-diamond dynamical decoupling protocols sensitive to
crystal stress, pressure, and temperature have attained sensing durations of
tens of microseconds or longer. For example, such sequences were recently
employed in path-finding experiments for diamond-based dark matter searches
[16]. With further development, the key metric of
$T_{\text{sense}}>T_{\text{SWAP}}$ may be realized for these alternative
sensing applications, enabling quantum logic enhanced sensitivity.

Integrating additional quantum degrees of freedom, e.g., defects with
couplings to multiple nuclear spins, is another promising direction for
further progress in QLE sensing [34, 35, 36, 37]. Similarly, solutions to
address the random distribution of host lattice nuclear spins, such as
manipulating the collective modes of a spin bath [38], may prove advantageous
when exploring more advanced quantum logic or error correction algorithms [39]
for further sensing enhancements.

###### Acknowledgements.

This work was supported by, or in part by, the U.S. Army Research Laboratory
under Grant No. W911NF1510548; the U.S. Army Research Office under Grant No.
W911NF1920181; the Moore Foundation; the DARPA DRINQS program under Grant No.
D18AC00033; and the University of Maryland Quantum Technology Center. D.B.B.
was partially sup- ported by the German Research Foundation (BU 3257/ 1-1).
K.S.O. acknowledges support through an appointment to the Intelligence
Community Postdoctoral Research Fellowship Program at the University of
Maryland, administered by Oak Ridge Institute for Science and Education
through an interagency agreement between the U.S. Department of Energy and the
Office of the Director of National Intelligence.

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