U.S. patent application number 16/421521 was filed with the patent office on 2019-12-26 for method for the hyperpolarisation of nuclear spin in a diamond via a long-range interaction.
This patent application is currently assigned to Universitaet Ulm. The applicant listed for this patent is Universitaet Ulm. Invention is credited to Jianming CAI, Fedor JELEZKO, Boris NAYDENOV, Martin PLENIO, Alex RETZKER, Ilai SCHWARZ.
Application Number | 20190391216 16/421521 |
Document ID | / |
Family ID | 48143072 |
Filed Date | 2019-12-26 |
![](/patent/app/20190391216/US20190391216A1-20191226-D00000.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00001.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00002.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00003.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00004.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00005.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00006.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00007.png)
![](/patent/app/20190391216/US20190391216A1-20191226-D00008.png)
![](/patent/app/20190391216/US20190391216A1-20191226-M00001.png)
![](/patent/app/20190391216/US20190391216A1-20191226-P00001.png)
United States Patent
Application |
20190391216 |
Kind Code |
A1 |
JELEZKO; Fedor ; et
al. |
December 26, 2019 |
METHOD FOR THE HYPERPOLARISATION OF NUCLEAR SPIN IN A DIAMOND VIA A
LONG-RANGE INTERACTION
Abstract
The invention concerns a method for the hyperpolarisation of
.sup.13C nuclear spin in a diamond, comprising an optical pumping
step, in which colour centre electron spins in the diamond are
optically pumped. The method further comprises a transfer step in
which the polarisation of a long-lived state of the colour centre
electron spins is transferred to .sup.13C nuclear spins in the
diamond via a long-range interaction.
Inventors: |
JELEZKO; Fedor; (Ulm,
DE) ; CAI; Jianming; (Neu-Ulm, DE) ; PLENIO;
Martin; (Ulm, DE) ; RETZKER; Alex; (Ulm,
DE) ; NAYDENOV; Boris; (Ulm, DE) ; SCHWARZ;
Ilai; (Tel Aviv, IL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Universitaet Ulm |
Ulm |
|
DE |
|
|
Assignee: |
Universitaet Ulm
Ulm
DE
|
Family ID: |
48143072 |
Appl. No.: |
16/421521 |
Filed: |
May 24, 2019 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
14783262 |
Oct 8, 2015 |
10345400 |
|
|
PCT/EP2014/056958 |
Apr 7, 2014 |
|
|
|
16421521 |
|
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01N 24/006 20130101;
G06N 10/00 20190101; G01R 33/5601 20130101; B82Y 10/00 20130101;
G01R 33/62 20130101; G01N 24/12 20130101; G01R 33/282 20130101 |
International
Class: |
G01R 33/28 20060101
G01R033/28; G01R 33/62 20060101 G01R033/62; G01N 24/00 20060101
G01N024/00; G01R 33/56 20060101 G01R033/56; G01N 24/12 20060101
G01N024/12; B82Y 10/00 20060101 B82Y010/00; G06N 10/00 20060101
G06N010/00 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 8, 2013 |
EP |
13162810.9 |
Claims
1.-20. (canceled)
21. A method for hyperpolarizing a sample, comprising: a. placing
the sample near or in contact with a diamond or a plurality of
diamond particles having color centers; b. optically polarizing the
color centers; c. transferring the polarization from the color
centers to .sup.13C nuclear spins in the diamond or plurality of
diamond particles; d. propagating the polarization from the
.sup.13C nuclear spins to .sup.13C nuclear spins in the sample;
wherein the method is performed at temperatures higher than or
equal to 77K and lower than about 298K.
22. The method according to claim 21, wherein the sample is placed
in contact with the diamond or a plurality of diamond particles
after the .sup.13C nuclear spins are already hyperpolarized.
23. The method according to claim 21, wherein the sample is placed
in contact with the diamond or plurality of diamond particles
before the polarization of the .sup.13C nuclear spins.
24. The method according to claim 21, wherein transferring the
polarization from the color centers to the .sup.13C nuclear spins
in the diamond or the plurality of diamond particles includes
applying at least one of a microwave field or a radio frequency
(RF) field.
25. The method according to claim 24, wherein at least one of the
microwave field or the RF field applied is pulsed.
26. The method according to claim 21, wherein the polarization from
the color centers is transferred to the .sup.13C nuclear spins in
the diamond or the plurality of diamond particles via a long-range
interaction while fulfilling the Harman-Hahn condition.
27. The method according to claim 26, wherein the Hartmann-Hahn
condition is achieved by a microwave field, and wherein an
intensity of the microwave field is chosen to match an energy
difference between dressed color center electronic spin eigenstates
and the .sup.13C nuclear spins in an external magnetic field.
28. The method according to claim 27, wherein a magnetic flux
density of the external magnetic field is smaller than 3 T.
29. The method according to claim 21, wherein the color centers
include nitrogen vacancy (NV) centers.
30. The method according to claim 21, wherein the optical
polarizing step and the transferring step are repeated
cyclically.
31. A system for hyperpolarizing a sample, comprising: a diamond or
a plurality of diamond particles having color centers, wherein a
sample is placed near or in contact with the diamond or the
plurality of diamond particles; a magnet configured to generate a
magnetic field about the diamond or the plurality of diamond
particles having color centers; a laser configured to optically
polarize the color centers; and a microwave source configured to
facilitate transfer of the polarization from the color centers to
.sup.13C nuclear spins in the diamond or the plurality of diamond
particles at a temperature higher than or equal to 77K and lower
than about 298K, wherein the polarization is propagated from the
.sup.13C nuclear spins to .sup.13C nuclear spins in the sample at
the temperature.
32. The system according to claim 31, wherein the magnet further
includes at least one of a permanent magnet or an
electromagnet.
33. The system according to claim 31, wherein the sample is placed
in contact with the diamond or the plurality of diamond particles
after the .sup.13C nuclear spins are already hyperpolarized.
34. The system according to claim 31, wherein the sample is placed
in contact with the diamond or plurality of diamond particles
before the polarization of the .sup.13C nuclear spins.
35. The system according to claim 31, wherein the microwave source
is configured to apply at least one of a microwave field or a radio
frequency (RF) field.
36. The system according to claim 35, wherein at least one of the
microwave field or the RF field applied is pulsed.
37. The system according to claim 31, wherein the polarization from
the color centers is transferred to the .sup.13C nuclear spins in
the diamond or the plurality of diamond particles via a long-range
interaction while fulfilling the Harman-Hahn condition.
38. The system according to claim 37, wherein the Hartmann-Hahn
condition is achieved by a microwave field, and wherein an
intensity of the microwave field is chosen to match an energy
difference between dressed color center electronic spin eigenstates
and the .sup.13C nuclear spins in an external magnetic field.
39. The system according to claim 38, wherein a magnetic flux
density of the external magnetic field is smaller than 3 T.
40. The system according to claim 31, wherein the color centers
include nitrogen vacancy (NV) centers.
Description
FIELD OF THE INVENTION
[0001] The invention concerns a method for the hyperpolarisation of
13C nuclear spin in a diamond. The invention further comprises a
method for the nuclear spin hyperpolarisation of 13C in a molecule
and a method for producing an imaging agent. Additionally, a
diamond and uses for such a diamond form part of the invention.
PRIOR ART
[0002] In a diamond, electron spins in a particular kind of colour
centre, a nitrogen vacancy centre, can be polarised optically.
[0003] In "Dressed-State Polarization Transfer between Bright &
Dark Spins in Diamond", arXiv:1211,2749v1 [quant-ph], 12 Nov. 2012,
C. Belthangady et al. report the polarisation of electron spins in
a nitrogen vacancy centre in diamond by optical pumping. The
polarisation of the nitrogen centre electron spins can then be
transferred to substitutional nitrogen electron spins by applying
electromagnetic fields analogous to the Hartmann-Hahn matching
condition. In this publication, polarisations are exclusively
transferred between electrons and not from electrons to nuclei or
between nuclei.
[0004] Methods for the hyperpolarisation of .sup.13C nuclear spin
in a diamond are known in the art. In "Optical polarization of
nuclear ensembles in diamond", arXiv:1202.1072v3 [quant-ph], R.
Fischer et al. report the polarisation of a dense nuclear spin
ensemble in diamond. Their method is based on the transfer of
electron spin polarisation of negatively charged nitrogen vacancy
colour centres to the nuclear spins via the excited-state level
anti-crossing of the centre. Fischer et al. have adapted the method
to polarise single nuclear spins in diamond based on optical
pumping of a single nitrogen vacancy centre defect, which had
already been described by V. Jacques et al. in "Dynamic
Polarization of Single Nuclear Spins by Optical Pumping of
Nitrogen-Vacancy Color Centers in Diamond at Room Temperature",
Phys. Rev. Lett., volume 102, issue 5, pages 057403-1 to 057403-4.
Both Fischer et al. and Jacques et al. use short-lived states of
the colour centre spins, which are not suitable for directly
polarising via long-range interactions nuclear spins far away from
the colour centre.
[0005] In "Sensitive magnetic control of ensemble nuclear spin
hyperpolarization in diamond", Nature communication 4 (2013)
Hai-Jing Wang et al. show polarisation of nuclear spins in contact
interaction with a nitrogen vacancy colour centre in a diamond
using the ground state level anti-crossing of the centre. While the
colour centre state is long-lived, the experiment demonstrates
polarisation of nuclear spins only via then short range contact
interaction, which does not diffuse to nuclei further away.
Moreover, for the specific polarisation method described in the
text, the T.sub.2 time of the colour centres in the diamond used
correspond to a very short coherence time and is too short for
polarising nuclear spins via long ranged interactions.
[0006] Eduard C. Reynhardt et al. describe the polarisation of
.sup.13C nuclei by means of nuclear orientation via electron
spin-locking (Hartmann-Hahn cross-polarisation between paramagnetic
electrons and .sup.13C nuclei) in a suite of natural diamonds in
"Dynamic nuclear polarization of diamond. II. Nuclear orientation
via electron spin-locking", J. Chem. Phys. volume 109, number 10,
pages 4100 to 4106. Reynhardt et al., however, do not exploit the
electron spin of nitrogen vacancy centres and are thus not able to
use optical polarisation of the electron spin.
[0007] In magnetic resonance applications, it is desirable to reach
a higher degree of polarisation of .sup.13C nuclei throughout a
diamond than has hitherto been accomplished.
SUMMARY OF THE INVENTION
Problem According of the Invention
[0008] The problem to be solved by the invention is to provide a
better method for the hyperpolarisation of nuclear spin in a
diamond, to supply a diamond with hyperpolarised .sup.13C nuclei
and create a use for such a diamond. In addition to this, an
improved method for the nuclear spin hyperpolarisation of .sup.13C
in a molecule and an improved method for the production of an
imaging agent is sought.
Solution According to the Invention
[0009] The invention solves the problem according to the invention
by a method for the hyperpolarisation of .sup.13C nuclear spin in a
diamond, which comprises an optical pumping step and a transfer
step. In the optical pumping step, colour centre electron spins in
the diamond are optically pumped. In the transfer step, the
polarisation of a long-lived state of the colour centre electron
spins is transferred to .sup.13C nuclear spins in the diamond via a
long-range interaction.
[0010] In the context of the present invention, a long-range
interaction is defined as an interaction which decays according to
a power law with the distance of the .sup.13C nuclear spins from
the colour centre. Examples are a coherent dipolar interaction,
which decays as the distance cubed, and the case of the incoherent
dipolar interaction, which decays as the distance to the power of
six.
[0011] A long-lived colour centre spin state is defined as a state
in which the coupling strength of the colour centre spin and
nuclear spins is larger than the decay rate of the colour centre
spin state for nuclear spins at least 0.5 nm distanced from the
colour centre spin.
[0012] Furthermore, the problem is solved by a method for the
nuclear spin hyperpolarisation of .sup.13C nuclear spins in a
molecule, wherein the molecule is brought near or into contact with
a diamond and prior to, during or after that, the diamond is
hyperpolarised in the method according to claim 1. In this context,
"near" means that the diamond and the molecule are close enough to
each other to allow propagation of a nuclear spin's polarisation
from a .sup.13C nucleus of the diamond to a nucleus of the
molecule.
[0013] Another solution to the problem consists in a method for the
production of an imaging agent, wherein a diamond is coupled to a
molecule and prior to or after the coupling, the diamond is
hyperpolarised in the method according to claim 1. The problem is
further solved by the use of a hyperpolarised diamond according to
claim 1 in medical or cell based imaging, in a quantum information
processor or a quantum sensor based on spin degrees of freedom.
Moreover, a diamond with a volume of above 1 .mu.m.sup.3, in some
embodiments of above 1 .mu.m.sup.3, in which diamond the .sup.13C
nuclear spins in the entire diamond are hyperpolarised to at least
0.001% polarization solves the problem according to the
invention.
[0014] In the context of the present invention, polarization is
defined according to the standard definition: the number of
.sup.13C nuclear spins in the preferred direction minus the number
in the opposite direction, divided by the total number of .sup.13C
nuclear spins.
[0015] Point defects in a diamond lattice, in which a vacancy is
filled by one or more electrons, are termed colour centres. The
electron spins at a suitable colour centre can be polarised by
optical pumping. Optically polarised colour centre electron spins
can be transferred to surrounding .sup.13C nuclear spins to create
nuclear polarisation.
[0016] A diamond according to the invention can be a synthetic
diamond or a naturally occurring diamond. The diamond according to
the invention possesses at least one colour centre. Synthetic
diamonds according to the invention can be produced, e.g., by
chemical vapour deposition (CVD), using detonation or milling of
large scale, high pressure, high temperature crystals. High
.sup.13C nuclear spin polarisation densities can be achieved in
diamond as the nuclear density of diamond is higher than in most
other available materials. In CVD, advantageously, diamonds
enriched for .sup.13C can be produced such that an even higher
.sup.13C nuclear spin polarisation density is achievable.
[0017] An imaging agent can be produced by coupling the diamond to
a molecule and prior to, during or after the coupling, the diamond
is hyperpolarised according to the method described in claim 1.
Preferably, the molecule is a biological molecule, such as a
protein, and/or a molecule with a high affinity to a biological
molecule, such as a drug. Preferably, such imaging agents can bind
to specific structures in individual cells or to defined sites in
the body of an animal or human. The specific structures of defined
sites can then by located by locating the hyperpolarised diamond
using MRI. Advantageously, the imaging agent can aid the detection
and tracking of specific structures in vivo.
[0018] The hyperpolarised diamond according to the invention can be
used in medical or cell based imaging. Even though diamond is a
chemically inert material, biological molecules can be linked to
the surface of diamonds. In particular, it has been demonstrated in
"Dynamics of Diamond Nanoparticles in Solution and Cells", Felix
Neugart et al., Nano Letters, 2007, volume 7, issue 12, pages 3588
to 3591 (the corresponding portion of which is incorporated into
the present disclosure by way of reference) that diamond
nanoparticles can be conjugated with biotin, to which streptavidin
is able to bind. As many streptavidin-linked biological molecules,
in particular proteins, are already commercially available,
biotinylated diamond nanoparticles can easily be conjugated to bind
specifically to a variety of proteins and cells. As cryogenic
temperatures can be avoided, the loss in polarisation during the
transfer of the hyperpolarised diamond from the site of
polarisation to the MRI scanner can be reduced. Due to the high
density of .sup.13C nuclei, a much higher signal density can be
achieved in diamond than in other hyperpolarised materials.
[0019] A hyperpolarised diamond according to the invention can be
used in a quantum information processor or a quantum sensor based
on spin degrees of freedom. Polarisation of nuclear spin
environments reduces the noise that the nuclear environment exerts
on the electronic spin degree of freedom. Thus, the invention can
allow for improving the coherence times of quantum information
processors and quantum sensors based on spin degrees of
freedom.
[0020] The volume of the diamond is preferably greater than 1
nm.sup.3, more preferably greater than 10 nm.sup.3, even though
diamonds with a volume greater than 1000 nm.sup.3 or even greater
than 1 .mu.m.sup.3 or even greater than 10 .mu.m or even greater
than 1000 .mu.m.sup.3 are also possible. A preferred diamond has a
volume of less than 1000 nm.sup.3 more preferably less than 100
nm.sup.3. In principle a diamond with an arbitrary size can be
polarised with the method according to the invention as long as the
concentration of the colour centres is high enough. An attainable
advantage of the method according to the invention is that it can
be applied at any magnetic field. The methods described in the
prior art work only for a particular magnetic field, namely at the
level anti-crossing of the NV centre's spin levels.
[0021] The use of the dipolar long-range interactions between the
colour centre and .sup.13C nuclear spins can greatly increase the
speed of the polarisation process, as a much larger number of
nuclear spins can be polarised directly by the colour centre spin,
and the final bulk polarisation achieved. Accordingly, with the
invention it is achievable to hyperpolarise nuclear spins in a
diamond faster and/or to attain higher overall polarisation.
[0022] The invention makes it possible to produce diamond
nanoparticles that are hyperpolarised through their entire volume.
Such hyperpolarised diamond nanoparticles can lead to large signal
to noise ratios in NMR and MRI and can thus increase resolutions,
lower the detection threshold and permit faster and dynamic scans.
Cells and processes in the body can be imaged with the aid of
hyperpolarised diamonds attached to proteins. Advantageously, the
method according to the invention can be performed at room
temperature; cryogenic temperatures are no longer needed.
Furthermore, the method only requires a relatively low magnetic
field, which enables the hyperpolarised diamonds to be produced
inexpensively, on a large scale and in a relatively simple setup.
Such simple setups can be incorporated into a hospital environment
more easily, which may lead to a reduction in implementation costs.
Additionally, the very long relaxation time of .sup.13C nuclear
spins in diamond nanoparticles can allow for a long period of time
to pass between the polarisation process and the imaging. The
duration of this period of time in some embodiments of the
invention is greater than 1 minute, in some embodiments even
greater than 10 minutes, in some embodiments even greater than 30
minutes. Thus, the polarisation process can be performed in a
different location from the imaging, potentially even in a central
location for a few hospitals, and can be used for imaging processes
in the body with a longer timescale.
Preferred Embodiments According to the Invention
[0023] Examples of long-lived colour centre spin states that are
suitable for practicing the present invention include the ground
state of an NV centre spin in a diamond. The preferred diamond is
of high purity, i.e. at most 200 ppm nitrogen nuclei (also referred
to as "P1 centres"), more preferably less than 5 ppm nitrogen
nuclei. In some embodiments, the invention is practiced a low
temperature, e.g. liquid nitrogen temperature (77 K).
[0024] In some embodiments, the polarisation of a long-lived
excited triplet state, for example in an oxygen-vacancy (2.818 eV),
is transferred to the .sup.13C nuclear spins.
[0025] In preferred methods according to the invention, the
long-lived colour centre spin state is a state in which the
coupling strength of the colour centre spin and nuclear spins is
larger than the decay rate of the colour centre spin state for
nuclear spins at least 3 nm, more preferably 5 nm distanced from
the colour centre spin. With such very long-lived colour centre
spin states, a high hyperpolarisation can be achieved particularly
fast.
[0026] In preferred methods according to the invention, an external
microwave field or radio frequency (RF) field is applied. The
external microwave field or radio frequency (RF) field may be
continuous or pulsed. The application of the microwave field
preferably serves to tune the coupling between the colour centre
electron spins and the surrounding .sup.13C nuclear spins. Another
purpose of the microwave field is, preferably, to narrow the line
width of the electron and thus make the transfer of the
polarisation of the electron spins to the nuclear spins more
efficient. Applying the microwave field in this manner, it is
preferably achievable to completely polarise the .sup.13C nuclei
close to the colour centre. It is an achievable advantage of these
embodiments of the invention that the spin polarisation transfer
from the colour centres to the .sup.13C nuclear spins can be
accelerated. Many DNP protocols as discussed below involve the
application of an external microwave field or a radio frequency
(RF) field.
[0027] According to some embodiments of the invention, the long
range interaction is achieved by using dipolar interaction between
the colour centre electron spin and the .sup.13C nuclear spins.
According to some embodiments, the polarisation is transferred by a
standard dynamic nuclear polarisation (DNP) protocol for using
dipolar interactions to transfer electron polarisation to
surrounding nuclear spins. In the context of the present invention,
DNP protocols are defined as protocols for transferring the
polarization from an electron spin is to the .sup.13C nuclei by
microwave or RF irradiation of the sample. Advantageously, by means
of a DNP the transfer of the polarisation from the electron spins
to the surrounding nuclear spins can be accelerated.
[0028] Examples for suitable DNP protocols include the solid
effect, the cross effect, thermal mixing, and pulsed DNP methods
such as the NOVEL sequence or dressed-state solid effect. A review
of many current DNP protocols can be found in Maly, Thorsten, et
al. "Dynamic nuclear polarization at high magnetic fields." J Chem
Phys. 2008; 128(5): 052211 (see section II. "Polarizing mechanisms
in DNP experiments"). Most DNP protocols involve either
interactions between electron spins or are based on two underlying
physical mechanisms: fulfilling the Hartmann-Hahn condition and
excitation of selective transitions (i.e. irradiation at a
frequency matching the energy gap between two quantum states). The
DNP protocols differ in the configurations for achieving these
conditions and by the usage of microwave pulses or continuous
microwave radiation.
[0029] According to the invention, the DNP protocols can be used
for fulfilling the Hartmann-Hahn condition between the colour
centre spin and the .sup.13C nuclear spins or for excitation of
selective transitions caused by the dipolar interaction of .sup.13C
nuclear spin states with the colour centre spin. The general
concept of Hartmann-Hahn double resonance as described in Hartmann,
S. R. and Hahn, E. L., "Nuclear Double Resonance in the Rotating
Frame", Physical Review, 1962, vol. 128, Issue 5, pp. 2042-2053,
relevant portions of which are incorporated into the present
disclosure by way of reference.
[0030] According to some DNP protocols, the Hartmann-Hahn condition
is achieved. This condition requires that the Rabi frequency of the
electron spin be equal to the Larmor frequency of the .sup.13C
nuclear spins in some reference frame (both the Rabi frequency and
Larmor frequency can be between dressed or bare eigenstates). In
this case mutual spin flip-flops are allowed and the high electron
spin polarisation can be transferred to the nuclear spins. Thus,
transferring of the polarisation of the colour centre electron
spins to the .sup.13C nuclear spins can be achieved. Preferably,
the DNP method termed NOVEL is used to transfer spins from the
colour centre electrons to the .sup.13C nuclei. In NOVEL,
preferably, a pi/2 rotation is carried out, followed by spin
locking for an adequate time for the transfer of the colour centre
electron spin to the .sup.13C nuclear spin to occur. After the
Hartmann-Hahn condition has been achieved, it is also possible to
not use spin locking and simply wait for a spin flip-flop between
the electron and the nuclear spin to occur, which can also lead to
the polarisation transfer from the colour centre electrons to the
surrounding .sup.13C nuclei. Preferably, the Hartmann-Hahn
condition is achieved by a microwave field or a radio frequency
field, the intensity of the field being chosen to match the energy
difference between dressed colour centre electron spin eigenstates
and the .sup.13C nuclear spins in an external magnetic field.
[0031] Alternatively, the Hartmann-Hahn condition between NV-centre
electron spin and external nuclear spins can also be achieved by
means of optical Raman fields at low temperatures, preferably below
10 K, which couple the electronic spin states via an optically
excited state obtained by tuning a magnetic field to an excited
state anti-crossing to enable individual addressing. For other
solid state based systems such as chromium in ruby the use of
optical Raman fields is possible at room temperature.
[0032] The magnetic flux density of the external magnetic field is
smaller than 3 T. The method according to the invention allows for
the use of external magnetic fields with a low magnetic flux
density, preferably below 2 T, more preferably below 1 T and most
preferably below 0.5 T. Advantageously, these magnetic flux
densities can be achieved by a permanent magnet or an
electromagnet, which does not rely on liquid cooling.
[0033] Another preferred method for using the long-ranged
interaction, according to some embodiments, involves excitation of
selective transitions caused by the dipolar interaction of .sup.13C
nuclear spin states with the colour centre spin. Focusing on a two
particle system of the colour centre spin and a .sup.13C nuclear
spin, the dipolar interaction causes a shift in the energy level of
the combined two-spin quantum system. This shift induces different
energy gaps between the two spin system states, meaning that each
transition between states has a unique energy gap. This allows for
external excitation of only one selected transition using pulses or
continuous waves in a specific frequency tuned to the energy gap of
that particular transition. Excitation of the transition between
the state where the colour centre spin is polarised and the
.sup.13C nuclear spin is not polarised to the opposite state
(polarised .sup.13C nuclear spin, non-polarised colour centre spin)
induces a polarisation transfer, used in the solid effect DNP
protocol.
[0034] In some methods according to the invention the transfer step
is performed by interaction involving at least two colour centre
spins and a nuclear spin. This mechanism (used in the cross effect
and thermal mixing DNP protocols) is based on allowed transitions
of several electron spins and a nuclear spin involving a
homogeneously or inhomogeneously broadened EPR line. The broadening
of the EPR lines allow a simultaneous flip of two or more electron
spins and a nuclear spin to be energy conserving and enables
transfer of the electron spins' polarization to the nuclear spins
with the correct microwave irradiation.
[0035] The colour centres in diamond used in the method according
to the invention can achieve a much higher electron spin
polarisation compared with the nitrogen spins used in previous
studies.
[0036] Preferably, in the methods according to the invention the
diamond's .sup.13C nuclear spin polarisation is far above thermal
equilibrium conditions. Preferably, the diamond's .sup.13C nuclear
spin polarisation is by a factor of at least 10.sup.3, more
preferably at least 10.sup.4 and most preferably at least a factor
of 10.sup.5 above thermal equilibrium conditions. Due to such
hyperpolarisation, such diamonds can easily be detected in nuclear
magnetic resonance (NMR) and magnetic resonance imaging (MRI). The
above is particular in contrast to prior art methods in which only
nuclear spins in .sup.13C nuclei very close to the colour centre
can be polarized, leading to a considerably lower polarization of
the diamond as a whole.
[0037] In preferred embodiments of the invention the .sup.13C
nuclear spin polarisation in the diamond is greater than 1%. For
example, a nano-diamond with 100 .sup.13C spins with 51 in the
preferred direction and 49 in the opposite direction would have a
polarization of 2%. Preferably the .sup.13C nuclear spin
polarisation is greater than 7%, more preferably greater than 10%,
more preferably greater than 15%, more preferably greater than 20%,
more preferably greater than 30%, more preferably greater than 50%,
and most preferably greater than 70%.
[0038] Preferably the colour centre, in which the electron spins
are optically pumped, is a nitrogen vacancy (NV) centre. One common
colour centre in diamond is known as an NV centre, in which a
nitrogen atom substitutes a carbon atom leading to a vacancy in the
lattice. An NV centre is especially suited for the optical pumping
of its electron spins. Yet, atom substitutes other than nitrogen
are also possible for forming a colour centre, e.g. Silicon.
[0039] Preferably, the optical pumping step and the transfer step
are repeated cyclically. After the optical pumping of the NV centre
electrons, the electron spins can be transferred to the surrounding
.sup.13C nuclei. By repeating the optical pumping step and the
transfer step, it is achievable to polarise most, preferably all
.sup.13C nuclear spins in close proximity to the NV centre.
Preferably, a pause after each cycle allows for the .sup.13C
nuclear spin polarisation to spread from .sup.13C atoms adjacent to
the NV centre throughout the diamond. The propagation of the
.sup.13C nuclear spins may occur spontaneously. Advantageously, no
application of alternating electromagnetic fields may be required
during the diffusion of nuclear spin from .sup.13C nuclei close to
the NV centre to .sup.13C nuclei further away. By cyclically
repeating the optical pumping step, transfer step and pause, the
invention permits the polarisation of preferably more than 10%,
more preferably more than 50%, more preferably more than 80%, more
preferably more than 90%, more preferably more than 95% and most
preferably all of the .sup.13C nuclei within the diamond.
[0040] Preferably, the method is carried out for less than 10
minutes, more preferably, less than 5 minutes, more preferably less
than 1 minute, most preferably less than 10 seconds are required to
achieve hyperpolarisation in the entire diamond. Preferably, in
this method, the diamond has a volume of at least 1 nm.sup.3, more
preferably at least 10 nm.sup.3, even though diamonds with a volume
of at least 1000 nm.sup.3 or even at least 1 .mu.m.sup.3 or even at
least 10 .mu.m or even at least 1000 .mu.m.sup.3 are also possible.
Advantageously, applying the method according to the invention,
hyperpolarisation can be achieved rapidly, even in a large diamond.
Small diamonds can easily be adapted to medical purposes, in
particular as medical imaging agents for MRI. Furthermore,
nanoscale diamonds can be taken up into cells by endocytosis, which
permits cell based imaging.
[0041] Preferably, the optical pumping is performed with a least
one laser pulse. A laser is the preferred light source for carrying
out the electron spin polarisation of the colour centres. Using a
laser, the optical pumping can be achieved efficiently.
[0042] Preferably, the method according to the invention is carried
out at a temperature above 10 K. More preferably, the method is
performed at a temperature greater than 80 K, more preferably
greater than 200 K, more preferably greater than 273 K and most
preferably at a temperature above 288 K. Preferably, cryogenic
temperatures are not needed to polarise a diamond according to the
invention. After transfer of the electron spin to the .sup.13C
nuclear spin, the colour centre electron spins can be polarised
again by optical pumping. In this way, the colour centre electron
spin can preferably serve as a near-zero temperature electron bath,
allowing the bulk diamond to be kept at a higher temperature,
preferably room temperature.
[0043] The preferred diamond according to the invention is a
synthetic diamond. Synthetic diamonds can be enriched for .sup.13C
to allow for even larger polarisations to be created. Furthermore,
synthetic diamond material can be synthesised inexpensively in a
variety of shapes and sizes, including the deposition of diamond on
the surface of other materials, e.g., by CVD. At least 1% of the
carbon atoms in the diamond are preferably .sup.13C. More
preferably, the diamond is enriched for a .sup.13C isotope
concentration between 5% and 20%, more preferably between 10% and
15%, even though much higher concentrations of .sup.13C isotopes
are possible.
[0044] In one preferred embodiment according to the invention, the
diamond is coated with a nondiamond material. The coating can take
place before or after the hyperpolarisation. A preferred coating
yields a higher biocompatibility of the diamond when injected into
the bloodstream.
[0045] In method for the nuclear spin hyperpolarisation of nuclear
spins in a molecule according to the invention, the molecule is
brought near or into contact with a diamond comprising one or more
colour centre(s).
[0046] The nuclear spins of the molecule can then be polarised. In
a preferred method of polarising the nuclear spins in a molecule
the .sup.13C nuclear polarisation is allowed to propagate from the
diamond to the molecule. For this, preferably, the molecule is
attached to the diamond; more preferably, the molecule is
covalently attached to the diamond. The diamond's .sup.13C nuclear
spin may be hyperpolarised according to the invention with the
molecule already near or in contact with the diamond, the molecule
may be put near or in contact with the diamond .sup.13C nuclear
spin already hyperpolarised according to the invention, and/or the
diamond and the molecule are brought near or in contact during
hyperpolarisation of the diamond's .sup.13C nuclear spin. The spin
diffusion is made possible by the dipolar coupling between the
.sup.13C nuclear spins in the diamond and the non-zero nuclear
spins in the molecule. Preferably, for the propagation of the
nuclear spin polarisation from the diamond's .sup.13C nuclei to the
molecule's nuclei to be efficient, the diamond and the molecule are
closer than 1 nm to each other. Possibly, the molecules can then be
separated from the diamond. Preferably, after transfer of
polarisation to the molecule, the molecule can be scanned in an NMR
or MRI scanner. In this way, even small amounts of the molecule can
be detected.
[0047] Thus, the invention offers a better method for the
hyperpolarisation of nuclear spin in a diamond and, furthermore,
supplies a diamond with hyperpolarised .sup.13C nuclei. Moreover,
uses for such a diamond and improved methods for nuclear
hyperpolarisation in a molecule and for the production of an
imaging agent are provided.
BRIEF DESCRIPTION OF THE DRAWINGS
[0048] FIG. 1A shows the experimental setup in one conceptual
representation.
[0049] FIG. 1B shows the experimental setup in another conceptual
representation.
[0050] FIG. 2 shows at the top an optical microscope picture of the
fabricated structure on glass used in magnetic resonance
experiments. At the bottom, a picture of the holder with the strip
line structure is displayed.
[0051] FIG. 3 shows a confocal map of single NV centres adjusted to
a microwave stripline.
[0052] FIG. 4 shows a photo of the magnet stage with a cylindrical
magnet attached.
[0053] FIG. 5 shows a graphical representation of the polarisation
transfer protocol using the solid state effect.
[0054] FIG. 6A shows a difference in nuclear polarisation build-up
depending in the ESR line width compared to the Larmor
frequency.
[0055] FIG. 6B shows another difference in nuclear polarisation
build-up depending in the ESR line width compared to the Larmor
frequency.
[0056] FIG. 7A shows the process of microwave driven polarisation
transfer based on the cross effect.
[0057] FIG. 7B depicts the new population distribution under
microwave irradiation of frequency.
[0058] FIG. 7C depicts positive nuclear polarisation due to
microwave irradiation of frequency.
[0059] FIG. 8A displays the pulse sequence that was used to
polarise nuclear spins.
[0060] FIG. 8B shows the low frequency components in the
spin-locking signal on the x-axis for various microwave driving
fields with the corresponding Rabi frequency on the y-axis.
DESCRIPTION OF THE EMBODIMENTS
Experimental Setup
[0061] FIG. 1A conceptually details the experimental setup with a
diamond 1 placed in the magnetic field of a permanent magnet 2. The
diamond 1 contains a colour centre 3, which is an NV centre. A
laser 4 serves to excite a colour centre 3 electron. In order to
move the diamond 1 into the focus of the laser 4, the diamond 1 is
mounted on a piezo stage (not shown). The magnet 2 is mounted on
rotation/translation stages 5 (not shown) to be able to align the
magnetic field with the crystallographic axis of the colour centre
3. A microwave source 6 allows facilitation of polarisation
transfer from electron to .sup.13C nucleus. In the conceptual
representation of the experimental setup in FIG. 1B, the diamond 1
is placed between the permanent magnet 2 and the microwave source
6, which allows for the Hartmann-Hahn double resonance to be
generated in the diamond 1. The optical path 8 of the laser 4 (not
shown) is directed through a glass coverslip 7 and focussed into
the diamond 1 in order to polarise the electrons in an NV
centre.
Diamond Material
[0062] The following experiments were performed in a synthetic
diamond layer formed by CVD doped with NV centres during growth.
The sample used in these experiments possesses two layers with
different properties, the substrate and a CVD grown layer. The
substrate is a type IIa diamond 1 with a (111) cut and a natural
abundance of .sup.13C. The CVD grown layer is also a (111) cut with
a natural abundance of .sup.13C and a 1 ppm concentration of
phosphorus donors. The donors were added to stabilise the charge
state of the NV centre. For some of the dynamic nuclear
polarisation protocols a different donor concentration is
preferable, and will be mentioned in the description.
[0063] For the direct polarisation of external spins via NV
centres, ultra-small nanodiamonds, i.e. diamonds with volume
between 1 nm.sup.3 and 1000 nm.sup.3, are preferable. Polarisation
transfer will be enabled by dipolar interactions between NV centre
spins and external nuclear spins. In addition, it is possible to
use other electron spins as mediators for spin polarisation.
Alternatively, nitrogen (P1 centre) present in 100 ppm or higher
concentration in synthetic high pressure high temperature diamond
can be used for this purpose.
Confocal Microscopy of Single NV Centres
[0064] Single NV centres were detected using a confocal microscopy
technique. A laser beam diode pumped solid state laser 4 operating
at 532 nm was focussed onto a diffraction limited spot using a high
numerical aperture microscope objective (Olympus UPLAPO 60x). The
sample was scanned using a piezo driven stage (nPoint, Inc.).
Fluorescence was collected by the same microscope objective and
focussed on avalanche photodiodes with single photon sensitivity
(SPCM-AQRH, Excelitas). By observation of photon-antibunching, it
could be detected that an individual NV centre was in focus.
Fluorescence detection of magnetic resonance on single electron
spin is based on optical contrast of spin states associated with NV
centres.
Microwave Excitation
[0065] In order to excite microwave transitions of single colour
centres 3 in diamond 1, the sample was placed on a home built
microwave strip line providing efficient excitation of the diamond
1. At the top in FIG. 2, an optical microscopic picture of the
structure is shown, which was fabricated on a glass cover slip by
conventional photolithography and was used in the magnetic
resonance experiments. The width and gap of each microstrip is 20
.mu.m. At the bottom in FIG. 2, a picture of the holder with the
strip line structure can be seen. The signal is applied via coaxial
cables connected to SMA connectors and matched to the two coplanar
microstrips.
[0066] A commercial microwave source 6 (Anritsu MG 37020A) was used
in the experiments. In order to achieve Rabi frequencies of a few
MHz, the source was amplified using a commercial high power
microwave amplifier (10 W, Gigatronics GT 1000A). Phase control of
microwave fields was achieved using commercially available phase
shifters (Narda, Inc.). Microwave pulses were formed using
commercial microwave switches (General Microwave, F9914). The
strength of the microwave drive was controlled by the output level
of the microwave source 6.
[0067] In FIG. 3, the fluorescence image of a diamond 1 sample on
top of the 4-strip microstructure is shown. On the top and the
bottom of the image, one strip is displayed each. Between the
strips, the diamond area can be seen. Bright spots correspond to
the fluorescence emissions of NV centres.
Magnetic Field Control
[0068] Experiments were performed in a magnetic field on the order
of 0.4 T generated by a permanent magnet 2 (magnets4you GmbH)
located about 100 .mu.m from the diamond face. In order to align
the magnetic field with the crystallographic axis (z-axis) of the
NV defect, the magnet 2 was moved using rotation and translation
stages 5 (Micos GmbH), as shown in FIG. 4. For ensemble experiments
aiming to polarise large samples, magnetic field need to be
homogeneous enough to fulfil resonance conditions for the whole
sample. Permanent magnet arrangements or electromagnets can be used
for this purpose.
Time Resolved Measurements
[0069] Optical pulses for optical spin polarisation and time
resolved detection of magnetic resonance were produced using
acousto-optical modulators (Crystal Technology). Microwave, optical
pulses, sample scanning and data acquisition were synchronised by a
computer controlled pulse generator (Tektronix, DTG) connected to
drivers of acousto-optical modulators, microwave switches and a
fast photon counter (FastComtec, P7998).
[0070] The optical detection of magnetic resonance was carried out
in accordance with the scientific publications Jelezko, F. et al.,
"Single defect centres in diamond: A review." Physica Status Solidi
(a) Applications and Materials Science, 2006. 203(13): pages 3207
to 3225, Jelezko, F. et al., "Read-out of single spins by optical
spectroscopy.", Journal of Physics-Condensed Matter, 2004. 16(30):
pages R1089 to R1104 and Jelezko, F., et al., "Observation of
coherent oscillations in a single electron spin", Physical Review
Letters, 2004. 92(7), the relevant portions of which are
incorporated into the present disclosure by way of reference.
Polarisation of Electron Spin
[0071] Electron spins associated with NV centres were polarised by
the application of a short (300 ns) laser 4 pulse. Optical pumping
was achieved by excitation of the NV centre into an excited
electronic state. The decay of this state occurs predominantly into
one of the spin sublevels of the ground state.
Dynamical Polarisation Transfer from Electron Spin to Nuclear
Spin
[0072] Exchange of polarisation between optically pumped electron
spin of NV centre and nuclear spins can be performed using several
established dynamic nuclear polarisation protocols, e.g. the solid
effect, the cross effect, thermal mixing, the NOVEL sequence and
more. Most of these protocols either involve interactions between
electron spins or are based on two underlying physical mechanisms:
fulfilling the Hartmann-Hahn condition and excitation of selective
transitions. The DNP protocols differ in the configurations for
achieving these conditions and by the usage of pulses or continuous
waves.
[0073] For the above DNP protocols, the experimental setup is
similar, with the difference in the microwave frequency, pulse
sequence and/or magnetic field strength. We used the same equipment
for all three protocol examples detailed below, as all three
protocols are in the regime of our equipment.
[0074] The solid effect (excitation of forbidden transition
involving double, electron nuclear spin flips using microwave
driving) followed by electron spin relaxation is known to induce
efficient polarisation transfer. Notably, the weak electron spin
relaxation process can be significantly enhanced by optical pumping
of NV centre.
[0075] A rigorous theoretical treatment of the solid effect has
been performed in numerous papers, e.g. Abragam A, Goldman M. Rep
Prog Phys 1978; 41:395, W. T. Wenckebach Applied Magnetic Resonance
2008, 34, 227-235. A graphical representation of the polarisation
transfer protocol using the solid state effect is shown in FIG.
5.
[0076] At the first stage the laser polarises the NV centre by
optical pumping, as described above. Next, via the forbidden
transition a microwave excitation excites simultaneously the NV
spin and the nuclear spin which results in nuclear polarisation.
The NV spin is then re-polarised via optical pumping.
[0077] The rate of polarisation transfer is maximal for microwave
frequencies corresponding to the energy levels of the forbidden
transitions .omega..sub.+.apprxeq..omega..sub.NV-.omega..sub.I for
positive nuclear polarisation and
.omega..sub.-.apprxeq..omega..sub.NV+.omega..sub.I for negative
nuclear polarisation, where .omega..sub.0S denotes the NV spin Rabi
frequency and .omega..sub.I the nuclear spin Larmor frequency in
the lab frame. As the polarisation rate is a function of the NV
centre spin ESR line shape, effective polarisation transfer is
achieved when the ESR line is narrow compared with the nuclear
spins Larmor frequency (or the longitudinal hyperfine component of
the interaction with the NV centre spin). The difference in nuclear
polarisation build-up depending in the ESR line width compared to
the Larmor frequency is depicted in FIGS. 6A-6B. FIG. 6A depicts
the nuclear polarisation as a function of the microwave frequency
for the case where the nuclear Larmor frequency (.omega..sub.I) is
larger than the NV centre ESR line. This case is known as the "well
resolved solid effect". FIG. 6B depicts the nuclear polarisation
for the case where the ESR line is not narrow compared to the
nuclear Larmor frequency, which is known as the "differential solid
effect". In this case, the effects for positive nuclear
polarisation and negative nuclear polarisation--depicted in dashed
lines in FIG. 6B--overlap, reducing the overall polarisation
reached (solid line).
[0078] Larmor frequencies of .sup.13C nuclear spins were
approximately 5 MHz for magnetic fields used in our experiments,
though stronger magnetic fields can be used for larger Larmor
frequencies. For narrow NV centre ESR lines, diamonds with a small
concentration of P1 (Nitrogen) donors (less than 10 ppm) are
preferable. For instance, CVD grown diamonds with 10 ppm P1 donor
will result in NV centre ESR line width which is only limited by
13C, thus enabling efficient polarisation. Polarisation transfer is
then enabled by continuous laser 4 optical pumping combined by
resonant microwave 6 irradiation.
[0079] An alternative method for transferring the NV centre spin
polarisation to the nuclear spins is the so-called cross
polarisation effect, involving two electron spins and one nuclear
spin. This effect is particularly interesting for samples having
high concentration of NV centres with strongly dipolar coupled
electron spins. The basis for the cross effect are two dipolar
coupled electron spins under the condition that the resonance
frequency the electrons is separated by the nuclear Larmor
frequency. Thus, the cross-effect can only occur if the
inhomogeneously broadened ESR lineshape has a linewidth broader
than the nuclear Larmor frequency, contrary to the condition for
effective polarisation via the solid effect. An additional
condition for the cross effect is that the homogeneously broadened
ESR linewidth is narrower than the nuclear Larmor frequency.
[0080] The cross effect was first discovered in the 1960s by
Kessenikh et al. In Kessenikh et al. Phys Solid State 1963; 5:321,
and later by Wollan DS. Phys Rev B 1976; 13:3671. In the last few
years, it has again aroused interest after experiments which have
shown a large DNP enhancement to the NMR signal in high magnetic
fields (e.g. Hall et al. Science 1997; 276:930, Song et al. J Am
Chem Soc 2006; 128:11385).
[0081] The cross effect is based on a three spin interaction (two
electron spins and a nuclear spin) satisfying the relation:
.omega..sub.S2-.omega..sub.S1=.omega..sub.I, (1)
[0082] with .omega..sub.S1(2) denoting the EPR frequency of
electron 1(2) and .omega..sub.I denoting again the Larmor frequency
of the nuclear spin.
[0083] For driving the polarisation transfer, a microwave
irradiation is added of frequency .omega..sub.S1(2), leading to a
negative(positive) nuclear polarisation. The polarisation process
is depicted in FIGS. 7A-7C. FIG. 7A depicts the population
distribution at thermal equilibrium for a general three spin system
(two electron spins and a nuclear spin) in an external magnetic
field. In FIGS. 7B and 7C, the energy level have been set such that
condition 1 is met. FIG. 7B depicts the new population distribution
under microwave irradiation of frequency .omega..sub.S1, which
leads to a saturation of the allowed EPR transitions. As can be
seen, this corresponds with negative nuclear polarisation.
Microwave irradiation of frequency .omega..sub.S2 leads to positive
nuclear polarisation, see FIG. 7C.
[0084] For a typical diamond with 100 ppm P1 donors, the homogeneus
broadening could be .about.100 KHz, and the inhomogeneus broadening
is typically in the MHz range, but can be made larger by growing
the diamond with intrinsic strain along some axis, or by increasing
the 13C concentration in the diamond. Additionally, one could
imagine using the P1 donors' electron spin as a pair for the
dipolar coupling in the cross effect with the NV centre spins.
[0085] Another proposed experimental realization of a DNP protocol
for the polarisation transfer is achieved by establishing a
Hartmann-Hahn condition between the electron and nuclear spin This
is achieved by driving the electron spin transitions between ms=0
and ms=-1 state by means of a microwave field whose intensity is
chosen to match the energy difference between dressed electronic
spin eigenstates and the nuclear spins in an external magnetic
field.
[0086] The dynamics of the NV electronic spin and an additional
nuclear spin, in the presence of a continuous driving microwave
field have been theoretically analysed in Cai, J. M. et al.,
"Diamond based single molecule magnetic resonance spectroscopy",
New Journal of Physics, 2013, 15, 013020,
http://arxiv.org/abs/arXiv: 1112.5502 and the article's
supplementary information; the relevant portions of the publication
and the supplementary information are incorporated into the present
disclosure by way of reference. The Hamiltonian describing the NV
centre electronic ms=0, -1 states and an additional 13C nuclear
spin, in the presence of an external magnetic field B and a
resonant microwave field is
H=.OMEGA..sigma..sub.z.sym.1+.gamma..sub.N1
.sym.|B.sub.eff|.sigma..sub.z+.gamma..sub.NA.sub.hyp.sigma..sub.xo(sin
.theta..sigma..sub.x+cos .theta..sigma..sub.z) (1)
[0087] where .OMEGA. is the Rabi frequency of the driving field and
a are the spin-1/2 operators, defined in the microwave-dressed
basis
.+-. = 1 2 ( 0 .+-. - 1 ) ##EQU00001##
for the electronic basis, and in the (|.dwnarw.z.sup.r,
|.gradient.z.sub.r basis for the nuclear spins, where z' is defined
along the direction of B.sub.eff. B.sub.eff is an effective
magnetic field and is given by B.sub.eff=B-(1/2) A.sub.hyp, where
A.sub.hyp is the hyperfine vector which characterises the coupling
between the two spins. In equation (1), .gamma..sub.N is the
gyromagnetic ratio of the nuclear spin and cos .theta.=h{circumflex
over (b)}, where h and {circumflex over (b)} are the directions of
the hyperfine vector A.sub.hyp and the effective magnetic field
B.sub.eff, respectively. The first two terms in the Hamiltonian
form the energy ladder of the system (.OMEGA. for the dressed NV
spin, and .gamma..sub.N|B.sub.eff| for the Larmor frequency of the
nuclear spin), whereas the last two terms are responsible for
electron-nuclear spin interaction. Here, the former represents
mutual spin-flips, or coherent evolution of the electron-nuclear
pair, and the latter is the nuclear spin dephasing caused by
electron flips. When the driving field is adjusted properly, an
energy matching condition (known as the "Hartmann-Hahn condition")
given by
.OMEGA.=.gamma..sub.N|B.sub.eff|=.gamma..sub.N|B-(1/2)A.sub.hyp|,
(2)
[0088] can be engineered, equalising the first two terms in
Hamiltonian (1). Then, the coupling term in the Hamiltonian becomes
dominant, and the time evolution of the system is a coherent joint
evolution of the electron nuclear pair. For instance, starting in
the |+, .dwnarw. state, the system evolves according to |.PSI.=|+,
.dwnarw. cos (Jt).sup.+ |-, .gradient. sin (Jt), with J given
by
J=1/4.gamma..sub.N|A.sub.hyp| sin .theta.. (3)
[0089] Thus, at time t=.pi./2J the two spins become maximally
entangled, and after a t=.pi./J a full population transfer occurs
and the states of the two spins are in effect `swapped`.
[0090] Larmor frequencies of .sup.13C nuclear spins were
approximately 5 MHz for magnetic fields used in our experiments. In
order to transfer the electron spin to the nuclei, we applied a
sequence, in which a short laser 4 pulse (300 ns) is used for the
polarisation of the electron spin in the ground state of the NV
centre and for readout of the population via spin-dependent
fluorescence. The microwave manipulation is the alternating spin
locking sequence for 8 .mu.s as shown in FIG. 8A. A sweep of the
source power through the Hartmann-Hahn double resonance while
counting all the photons yielded the trace shown in FIG. 8B. The
low frequency components in the spin-locking signal for various
microwave driving fields is shown on the x-axis, the corresponding
Rabi frequency is shown on the y-axis. The oscillations appearing
in the spectrum at the Hartmann-Hahn condition (when the Rabi
frequency of electron spin matches the nuclear spin Larmor
frequency) indicate flip-flops between electron spins and nuclear
spins.
* * * * *
References