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United States Patent Application 
20170138735

Kind Code

A1

Cappellaro; Paola
; et al.

May 18, 2017

STABLE THREEAXIS NUCLEAR SPIN GYROSCOPE
Abstract
An nNVbased gyroscope is provided that includes a diamond structure
implanted with a plurality of NV centers, whose nuclear spins form a spin
gyroscope. A number of radiofrequency (rf) coils and microwave (.mu.w)
coplanar waveguides are fabricated on the diamond structure to provide a
sensitive and stable threeaxis gyroscope in the solid state while
achieving gyroscopic sensitivity by exploiting the coherence time of the
.sup.14N nuclear spin associated with the NV centers in the diamond
structure combined with the efficient optical polarization and
measurement of electronic spin.
Inventors: 
Cappellaro; Paola; (Somerville, MA)
; Ajoy; Ashok; (Cambridge, MA)

Applicant:  Name  City  State  Country  Type  MASSACHUSETTS INSTITUTE OF TECHNOLOGY  Cambridge  MA  US   
Assignee: 
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Cambridge
MA

Family ID:

1000002425617

Appl. No.:

15/218401

Filed:

July 25, 2016 
Related U.S. Patent Documents
       
 Application Number  Filing Date  Patent Number 

 13874718  May 1, 2013  9417068 
 15218401   

Current U.S. Class: 
1/1 
Current CPC Class: 
G01N 24/08 20130101; G01C 19/62 20130101 
International Class: 
G01C 19/62 20060101 G01C019/62; G01N 24/08 20060101 G01N024/08 
Goverment Interests
SPONSORSHIP INFORMATION
[0001] This invention was made with government support under Contract No.
W911NF1110400 awarded by the Army Research Office. The government has
certain rights in the invention
Claims
1. An nNVbased gyroscope comprising: a diamond structure implanted with
a plurality of NV centers, whose nuclear spins form a spin gyroscope; and
a plurality of radiofrequency (rf) coils and microwave (.mu.w) coplanar
waveguides being fabricated on the diamond structure to provide a
sensitive and stable threeaxis gyroscope in the solid state while
achieving gyroscopic sensitivity by exploiting the coherence time of the
nuclear spin associated with the NV centers in the diamond structure
combined with the efficient optical polarization and measurement of
electronic spin.
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Description
BACKGROUND OF THE INVENTION
[0002] The invention related to the field of gyroscopes, and in particular
a quantumbased gyroscope that provides a sensitive and stable threeaxis
gyroscope in the solid state.
[0003] Conventional commercial gyroscopes are built using
microelectromechanical systems (MEMS) technology that allows for
sensitivities exceeding 3 (mdeg s.sup.1)/ {square root over (Hz)} in a
hundreds of micronsized footprint. Despite several advantagesincluding
low current drives (.about.100 .mu.A) and large bandwidths (200
deg/s)that have allowed MEMS gyroscopes to gain ubiquitous usage, they
suffer from one critical drawback: The sensitivity drifts after a few
minutes of operation, making them unattractive for geodetic applications.
The intrinsic reason for these drifts formation of charged asperities at
the surface of the capacitive transduction mechanism is endemic to MEMS
but does not occur in other systems used as gyroscopes, such as atom
interferometers or nuclear spins. However, to achieve sensitivities
comparable to MEMS, these systems require large volumes
(.about.cm.sup.3), long startup times, and large power and space
overheads for excitation and detection.
SUMMARY OF THE INVENTION
[0004] According to one aspect of the invention, there is provided an
nNVbased gyroscope. The nNVbased gyroscope includes a diamond
structure implanted with a plurality of NitrogenVacancy defect color
centers in diamond (NV centers), whose nuclear spins form a spin
gyroscope. A number of radiofrequency (rf) coils and microwave (.mu.w)
coplanar waveguides are fabricated on the diamond structure to provide a
sensitive and stable threeaxis gyroscope in the solid state while
achieving gyroscopic sensitivity by exploiting the coherence time of the
.sup.14N nuclear spin associated with the NV centers in the diamond
structure combined with the efficient optical polarization and
measurement of electronic spin.
[0005] According to another aspect of the invention, there is provided a
method of implementing a quantum sensor. The method includes implanting a
plurality of NV centers in a diamond structure, whose nuclear spins form
a spin gyroscope. Moreover, the method includes fabricating a plurality
of radiofrequency (rf) coils and microwave (.mu.w) coplanar waveguides
on the diamond structure to provide a sensitive and stable threeaxis
gyroscope in the solid state while achieving gyroscopic sensitivity by
exploiting the coherence time of the .sup.14N nuclear spin associated
with the NV centers in the diamond structure combined with the efficient
optical polarization and measurement of electronic spin.
[0006] According to another aspect of the invention, there is provided a
quantum sensor. The quantum sensor includes a diamond structure implanted
with a plurality of NV centers, whose nuclear spins form a spin
gyroscope. A number of radiofrequency (rf) coils and microwave (.mu.w)
coplanar waveguides are fabricated on the diamond structure to provide a
sensitive and stable threeaxis gyroscope in the solid state while
achieving gyroscopic sensitivity by exploiting the coherence time of the
.sup.14N nuclear spin associated with the NV centers in the diamond
structure combined with the efficient optical polarization and
measurement of electronic spin.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIG. 1 is a schematic diagram illustrating an nNV gyroscope formed
in accordance with the invention;
[0008] FIG. 2 is a graph illustrating an nNVgyroscope control sequence;
[0009] FIG. 3 is a graph illustrating an nNVgyroscope sensitivity
[0010] FIG. 4 is a graph illustrating the signal S.sub.c from the four
classes of NV centers; and
[0011] FIGS. 5A5B are schematic diagrams illustrating an integrated
nNVMEMS gyroscope.
DETAILED DESCRIPTION OF THE INVENTION
[0012] The invention overcomes the drawbacks of current gyroscopes by
using a solidstate spin associated with the nuclear spin of
nitrogenvacancy (NV) centers in diamond as a gyroscope (referred herein
as nNV gyro). The nNV gyro combines the efficient optical
initialization and measurement offered by the NVelectronic spin with the
stability and long coherence time of the nuclear spin, which is preserved
even at high densities.
[0013] FIG. 1 is a schematic diagram illustrating a nNV gyro 2 formed in
accordance with the invention. A slab of diamond 4 of dimensions
(2.5.times.2.5) mm2.times.150 .mu.m is anchored to the device body 6.
Radiofrequency (rf) coils and microwave (.mu.w) coplanar waveguides 8
are fabricated on the diamond 4 for fast control. NV centers are
polarized by a green laser (532 nm) 10, and state dependent fluorescence
intensity (637 nm) is collected employing a sidecollection technique. A
second set of rf coils 12 rotate with respect to the diamondchip frame,
for example, by being attached to one or more rings 14 in a mechanical
gimbal gyroscope. The .sup.14N nuclear spins are used as probes of the
relative rotation between the diamond frame and the external rfcoil
frame.
[0014] The operating principles are based on the detection of the phase
that the nitrogen14 nuclear spin 1 (.sup.14N) acquires when it rotates
around its symmetry axis. Consider an isolated spin 1 with Hamiltonian
H.sub.0=QI.sup.2+.gamma..sub.NbI.sub.Z, where Q is the intrinsic
quadrupolar interaction (Q=4.95 MHz for the NV center's .sup.14N), b is
a small magnetic field, .gamma.Nb<<Q, and .gamma.N=2.pi..times.3.1
MHz/T is the .sup.14N gyromagnetic ratio. The spin is subject to rf
fields in the transverse plane at frequency Q and with a (gated)
amplitude 2.omega..sub.rf(t). The diamond rotates around the
spinsymmetry axis (z axis) at a rate .OMEGA. with respect to the frame
in which the rf field is applied. Thus, the driving field is described by
the Hamiltonian H.sub.rf=2.omega..sub.rf(t)cos(Qt).left brktbot.I.sub.x
cos (.OMEGA.t)I.sub.y sin(.OMEGA.t).right brktbot.. One can describe
the spin evolution in the interaction frame set by
(QI.sub.z.sup.2.omega.I.sub.Z). The second term (e.sup.i.OMEGA.I.sup.z)
transforms H.sub.rf to
2.omega..sub.rf cos(Qt)I.sub.x=.omega..sub.rf.left
brktbot.e.sup.iQI.sup.z.sup.2.sup.tI.sub.xe.sup.iQI.sup.z.sup.2.sub.t+e
.sup.iQI.sup.z.sup.2.sup.tI.sub.xe.sup.iQI.sup.z.sup.2.sup.t.right
brktbot. (1)
[0015] In a Ramsey sequence shown in FIG. 2, the spin acquires a phase
.phi.=(.gamma..sub.Nb+.OMEGA.)t from which one can extract the rotation
rate. Although the nNVgyro operating principles are somewhat similar to
NVbased magnetometers and NMR gyroscopes, some critical differences lead
to its outstanding performance. In contrast to magnetometry, the
sensitivity to rotation rates is independent of the spin's gyromagnetic
ratio. Thus, one can exploit the .sup.14N nuclear spin as a sensor,
leading to a much improved performance because of the isolation of
nuclear spins from noise sources. However, this also requires new
strategies for the polarization and readout of the nuclear spin. There
are two critical advantages of the nNV gyro with respect to NMR gyros.
[0016] Although certain NMRgyroscope designs use optical pumping for spin
polarization the nNV gyro exploits the unique properties of the NV
electron spin for optical polarization and readout of the nuclear spins,
achieving far better efficiencies, close to 100%. Furthermore, using a
solidstate system allows the application of control fields in the same
reference frame of the sensor spins, which, as shown below, decouple the
spins from lowfrequency noise sources, such as temperature fluctuations,
stray magnetic fields, and strains. Stated equivalently, whereas NMR
gyros are limited by the dephasing time T.sub.2* of the spins, the nNV
gyro is limited by the much longer coherence time T.sub.2.
[0017] Consider first the operation of a oneaxis nNV gyro. The nuclear
spin is first initialized by polarization transfer from the electronic NV
spin. Under optical excitation, the electronic ms=.+.1 levels follow a
nonspinpreserving transition through metastable levels down to the ms=0
ground state, yielding high polarization of the electronic spin. The
polarization can be transferred to the nuclear spin exploiting the
hyperfine coupling A=2.2 MHz in the electronnuclearspin Hamiltonian,
H.sub.en=.DELTA.S.sub.z.sup.2+.gamma..sub.ebS.sub.z+QI.sub.z.sup.2+(.OME
GA.+.gamma..sub.Nb)I.sub.z+A{right arrow over (S)}{right arrow over (I)}
(2)
where .gamma..sub.e=2.8 MHz/G is the electronic gyromagnetic ratio and
.DELTA.=2.87 GHz is the zerofield splitting.
[0018] Several techniques for polarization transfer have been implemented
experimentally, including measurement post selection and exploiting a
level anticrossing in the orbital excited state at b.about.500 G (using
an adiabatic passage or the resonance between the nuclear and the
electronic spins). Unfortunately, all these techniques have drawbacks
that make them unsuitable for purposes of the invention. The first
technique is too lengthy, whereas the second prevents the use of repeated
readouts and requires precise alignment of a large static magnetic field.
At low field, polarization transfer between the electronic and the
nuclear spins is complicated by the fact that both are spin 1.
[0019] Unlike for spin 1/2, polarization transfer in the rotating frame
(under the HartmannHahnmatching condition) does not lead to perfect
polarization, unless the electronic spin is reduced to an effective spin
1/2. Instead, the invention proposes using forbidden twophoton
transitions to achieve population transfer. Driving the NVelectronic
spin at the .DELTA..+..gamma..sub.eb+Q transitions with a field along
its longitudinal (z) axis modulates its resonance frequency, thus, making
energy exchange with the nuclear spin possible.
[0020] Although the transition rates are usually small, the ability to
drive the NVelectronic spin with very high fields makes the polarization
time
t = .pi. .DELTA. + .gamma. e b + Q A .OMEGA. R
##EQU00001##
short. For a Rabi frequency=500 MHz and a field b=20 G, the time required
is only 1.3 .mu.s. This initialization time is far shorter than for other
gyroscope types, including the few tens of milliseconds of startup time
required for MEMS gyroscopes.
[0021] For ease of operation, one can assume that the rf and .mu.w pulses
used for initialization and readout can be delivered by an onchip
circuit, integrated with the diamond. After preparation, the
NVelectronic spin is left in the 0state, which does not couple to the
.sup.14N nuclear spin nor to the spin bath. A Ramsey sequence is applied
using the offchip rf driving, thus, inducing accumulation of a
rotationdependent phase [Eq. (1)]. A 2.pi. pulse at the center of the
sequence, applied with the onchip rf field, refocuses the effects of
stray magnetic fields and provides decoupling from the spin bath. The
sensor spin coherence time is limited by T.sub.2 (and not by the shorter
dephasing time T.sub.2*), which can be exceptionally long for nuclear
spins. Thus, the additional pulse, made possible by working with a
solidstate device, is critical in making the nNV gyro immune to a host
of lowfrequency drifts that limit the operational time of other
gyroscope types.
[0022] Moreover, since the echo refocuses the coupling to other electronic
spins, the nNV gyro can operate at very high densities of the sensor
spins. Ion implantation can reach an NV density of nNV.about.10.sup.18
cm.sup.3. Even assuming a density of residual singlenitrogen defects
(P1 centers) n.sub.P1.apprxeq.10nNV.about.10.sup.19 cm.sup.3, the N
T.sub.2 time is not appreciably affected by the P1 bath. Indeed, while at
these densities, the dipoledipole interaction
d ab = .mu. 0 4 .pi. 2 .pi. .gamma. a
.gamma. b r ab 3 ##EQU00002##
among P1 centers is large (d.sub.P1,P1.about.3 MHz with
.gamma..sub.Pt.gamma..sub.e), and the coupling to the nuclear spin is
still small, d.sub.P1,N.about.345 Hz (where the meanspinspin distance
is estimated as
r = ln ( 8 ) / ( 4 .pi. n p 1 ) 3 ) .
##EQU00003##
This leads to motional narrowing and a very slow exponential decay as
confirmed by simulations.
[0023] The N coherence time is also affected by the interaction with the
closeby NV center, which induces dephasing when undergoing relaxation
with T.sub.1.about.26 ms at room temperature and low field. Whereas, in
highpurity diamonds, the dephasing time T.sub.2* can be as long as 7 ms,
in the proposed conditions of operation, one can conservatively estimate
the coherence time of the nuclear spin to be T.sub.2=1 ms. The echo
sequence has the added benefit to make the measurement insensitive to
many other imperfections, such as temperature variation, strain,
background stray fields, variation in the quadrupolar interaction, and
instability in the applied bias magnetic field. Thus, this scheme yields
a solidstate gyroscope with stability comparable to that achieved in
atomic systems.
[0024] After the sensing sequence, the .sup.14N spin is left in the state,
.psi. n = sin ( .OMEGA. t ) 2 (
+ .OMEGA. t  1   .OMEGA. t
+ 1 )  cos ( .OMEGA. t ) 0 ( 3 )
##EQU00004##
which can be mapped into a population difference between the NV levels
thanks to the hyperfine coupling (here, one only considers the
longitudinal component of the isotropic hyperfine interaction
AI.sub.ZS.sub.Z because of the large zerofield splitting .DELTA.).
[0025] The readout sequence, as shown in FIG. 2, with pulses on resonance
to both 0.+.1 transitions, generates the state,
.psi. en = 1 2 sin ( .OMEGA. t ) [
.OMEGA. t (  1 ,  1 + + 1 ,  1
) +  .OMEGA. t ( + 1 , + 1 +  1
, + 1 )  cos ( .OMEGA. t ) 0 , 0 ]
( 4 ) ##EQU00005##
where m.sub.z.sup.S,m.sub.z.sup.I indicates an eigenstate of S.sub.Z and
I.sub.Z for the electronic and nuclear spins, respectively. The time
required to map the state onto the NV center is t.sub.map=230 ns, which
is close to the T.sub.2* time for the NV at high densities, thus, one can
expect a reduction in contrast. Indeed, it is the NV dephasing time that
ultimately limits the allowed spin densities. A possible solution would
be to perform a spin echo on both nuclear and electronic spins to extend
the coherence time.
[0026] Optical readout extracts the information about the rotation
.OMEGA.. The measurement step can be repeated to improve the contrast.
Although, at low field, the nuclearspin relaxation time under optical
illumination is relatively short, thus, limiting the number of repeated
readouts when combined with a sidecollection scheme giving high
collection efficiency .eta..sub.m.apprxeq.1, one can still achieve a
detection efficiency of C.about.0.25 for nr=100 repetitions and a total
readout time of t.sub.m.apprxeq.150 .mu.s. The higher detection
efficiency will also allow a large dynamic range by exploiting adaptive
phaseestimation schemes.
[0027] One can now consider the performance of the nNVgyroscope design
with respect to sensitivity and stability and its potential advantages
over competing technologies.
[0028] The sensitivity per unit time .eta. is ideally shotnoise limited:
.eta..varies.1/ {square root over (tN)}, where N is the number of
nitrogen nuclear spins associated with NV centers in the diamond chip.
The expected sensitivity can be estimated by limiting the interrogation
time t to T.sub.2 and taking into consideration the preparation and
readout dead times td=t.sub.pol+t.sub.ro and the detection efficiency C,
.eta. = T 2 + t d CT 2 N ( 5 ) ##EQU00006##
[0029] For a volume V=1 mm.sup.3, containing
N=nNVV/4.apprxeq.2.5.times.10.sup.14 sensor spins along the rotation
axis, the estimated sensitivity for the nNV gyro is then
.eta..apprxeq.0.5 (mdegs.sup.1)/ {square root over (Hz)}, better than
the current MEMS gyroscopes, although in a slightly larger volume, as
shown in FIG. 3.
[0030] More importantly, the stability of the nNV gyro can be much higher
than for MEMS and can be comparable to atomic gyroscopes, shown in FIG.
4. Indeed, the echobased scheme makes the nNV gyro insensitive to
drifts due to strain, temperature, and stray fields. In addition, the NV
spin is a sensitive probe of these effects, capable of measuring magnetic
and electric fields as well as frequency and temperature shifts. Because
of almost 4 orders of magnitude larger sensitivity of the NV spin than
the .sup.14N spin (given by the ratio .gamma..sub.e/.gamma..sub.N), the
NV can be used to monitor such drifts and to correct them via a feedback
mechanism.
[0031] The NV center in diamond includes a substitutional nitrogen
adjacent to a vacancy in the lattice. The nitrogen tovacancy axis sets
the direction of the electronic zerofield splitting and nuclear
quadrupolar interaction. The axis can be along any of the four
tetrahedral 1,1,1 crystallographic directions of the diamond lattice.
This intrinsic symmetry can be exploited to operate the nNV gyro as a
threeaxis gyroscope, extracting information about the rotation rate as
well as its direction.
[0032] Although the maximum sensitivity is achieved for rotations aligned
with the symmetry axis, if the rotation is about an axis forming an angle
{.theta.,.phi.} with respect to the NV axis, the .sup.14N still undergoes
a complex evolution that depends on {right arrow over (.OMEGA.)}. The two
rf pulses in the Ramsey interferometry scheme differ not only by their
phase .psi..sub.1,2 in the NV xy plane, but also by their flip angle
.alpha..sub.1,2. If one can assume the first pulse to be along the x axis
for the first NV class, the second rf pulse is rotated by an angle
.psi..sub.1,2=.psi.(.theta.,.phi.,.OMEGA.t) in the NV xy plane with
tan ( .PSI. 2 1 ) = sin 2 ( .theta. ) sin (
2 .phi. ) sin 2 ( .OMEGA. t / 2 ) + cos
( .theta. ) sin ( .OMEGA. t ) cos ( .OMEGA.
t )  sin 2 ( .theta. ) cos 2 ( .phi. )
cos ( .OMEGA. t ) + sin 2 ( .theta. ) cos 2
( .phi. ) ( 6 ) ##EQU00007##
The flip angle .alpha..sub.1,2=.alpha.(.theta.,.phi.,.OMEGA.t) is also
reduced with respect to the nominal angle .pi.,
[0033] The state at the end of the Ramsey sequence is then given by
.psi. n =  .psi. 2 [ sin ( .psi. 2 )
 cos ( .alpha. 2 2 ) cos ( .psi. 2 ) ] 2
+ 1  sin ( .alpha. 2 2 ) cos ( .psi. 2 )
0  .psi. 2 [ sin ( .psi. 2 ) + cos (
.alpha. 2 2 ) cos ( .psi. 2 ) ] 2  :
( 7 ) ##EQU00008##
from which one can extract information about the rotation rate .OMEGA..
Similar expressions hold for the other NV classes if it is possible to
drive excitation fields in the transverse plane of each family. Then, the
angles .alpha..sub.2.sup.c, .psi..sub.2.sup.c are different for each
family of NVs, and measuring the signal from three families allows
extracting information about {right arrow over (.OMEGA.)}.
[0034] Assuming that the driving field is applied only along one direction
for all the four NV classes, even the first excitation pulse angles
{.psi..sub.1.sup.c, .alpha..sub.1.sup.c} differ for each class, whereas,
for the second pulse, {.psi..sub.2.sup.c, .alpha..sub.2.sup.c} depend not
only on the class, but also on the rotation vector {right arrow over
(.OMEGA.)} via simple trigonometric relationships. The signal for each
class is defined as,
S.sup.c=[cos(.alpha..sub.1.sup.c/2)cos(.alpha..sub.2.sup.c/2)sin(.alpha
..sub.1.sup.c/2)sin(.alpha..sub.2.sup.c/2)cos(.psi..sub.1.sup.c.psi..sub.
2.sup.c)].sup.2 (8)
which is shown in FIG. 4. The signal can be measured by sequentially
mapping the nuclearspin state onto the corresponding electronic spin via
on resonance microwave pulses (a bias field of 1020 G is sufficient to
lift the frequency degeneracy among the four classes). A more efficient
scheme would take advantage of repeated readouts and long relaxation
times of the nuclear spins to measure the signal from three NV classes
without the need to repeat the preparation and echo sequences. Although a
driving field along a single direction makes the deconvolution algorithm
more complex, the signal arising from three classes of NV centers is
still enough to reconstruct the rotation rate and its direction.
[0035] The invention proposes a solidstate device able to measure
rotation rates with a resolution of .eta..apprxeq.0.5 (mdegs.sup.1)/
{square root over (Hz)} in a 1mm.sup.3 package while providing great
stability. The device performance compares favorably with respect to
other current. Even smaller deviceson the micron scalecould be useful
by exploiting this longtime stability to improve the performance of the
MEMS gyroscope in a combinatoric device, as shown in FIGS. 5A5B.
[0036] In particular, FIG. 5A shows an integrated nNVMEMS gyroscope 22,
comprising a bulk acoustic wave (BAW) singleaxis MEMS gyroscope 20 in an
800.mu.m diamond disk 24 implanted with NV centers, whose nuclear spins
form a spin gyroscope. The spins implanted in the disk are polarized by a
laser 26. The electrodes 30 surrounding the disk 24 are silvered to allow
for total internal reflection, and fluorescence is side collected by
replacing one of them by an onchip optical waveguide 32 at 638 nm. Strip
lines 38 for rf or .mu.w control are fabricated on the disk. FIG. 5B
shows the operation of the BAW mechanical gyroscope 20. The BAW 20 is
electrostatically driven in the second elliptic mode by a .about.10kHz
sinusoidal signal from the drive electrodes 28.
[0037] A rotation out of the plane causes a decrease in the gap near the
sense electrodes 36, leading to a capacitive measurement of the rotation.
Combinatoric filtering with the nNV measurement leads to noise rejection
and improved stability. Highperformance MEMS gyroscopes can be
fabricated in diamond using reactive ionetching tools. While the
substrate itself acts as a mechanical gyroscope, the nuclear spins inside
it act as a spin gyroscope. These two gyroscopes, employing complementary
physical effects, are sensitive to different sources of noise, which can
be corrected by Kalmanfilter techniques. The integrated device would
offer both stability and sensitivity in a small package.
[0038] The invention introduces a quantum sensor that provides a sensitive
and stable threeaxis gyroscope in the solid state. One can achieve high
sensitivity by exploiting the long coherence time of the .sup.14N nuclear
spin associated with the nitrogenvacancy center in diamond, combined
with the efficient polarization and measurement of its electronic spin.
Although the gyroscope is based on a simple Ramsey interferometry scheme,
one can use coherent control of the quantum sensor to improve its
coherence time and robustness against longtime drifts. Such a sensor can
achieve a sensitivity of .eta..about.0.5 (mdeg s.sup.1)/ {square root
over (Hzmm.sup.3)} while offering enhanced stability in a small
footprint. In addition, we exploit the four axes of delocalization of the
nitrogenvacancy center to measure not only the rate of rotation, but
also its direction, thus obtaining a compact threeaxis gyroscope.
[0039] Although the present invention has been shown and described with
respect to several preferred embodiments thereof, Various changes,
omissions and additions to the form and detail thereof, may be made
therein, without departing from the spirit and scope of the invention.
* * * * *