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Magnetic resonance spectroscopy of nitrogen-vacancy centers
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where Dgs ∼ 2.88 GHz is the fine structure splitting, and it significantly varies with temperature, dDgs/dT = -74.2(7} kHz/K [3].
Fig. 3. Fine and hyperfine structures of the 14NV− ground state. The fine structure levels are denoted by their spin–orbit symmetry and ms = 0, ±1 spin projections, and the hyperfine structure levels are denoted by their hyperfine symmetry and mI = 0, ±1 spin projections [2].
The NV− EPR signal was initially only detected under optical illumination, it took some time for the spin multiplicities of the NV− ground and optically excited states to be correctly identified. The first evidence of the spin triplet nature of the NV− ground state was obtained by the optical hole burning and magnetic circular dichroism study. Further evidence of a triplet ground state was obtained using ODMR, spin-locking and spin cross-relaxation studies.
Confirmation was ultimately provided by observations of the EPR signal in the dark.
One of the attractive features of the NV− center is the phenomenon of optically induced spin polarization of the triplet ground state. The polarization arises due to inter-system crossing from the excited triplet state to singlet levels and decay back to the ground state with an overall change of spin (see Fig. 4).
Fig. 4. Schematic representation of the NV− electronic structure including the 3A2 and 3E fine structure. The optical and infrared transitions are denoted by solid arrows and the weak and strong non-radiative transitions to, between and from the intermediate singlet states are denoted by dashed arrows [2].
In the magnetic field dependence of the photo-luminescence intensity of precisely oriented NV─ centers sharp lines are observed. The most prominent line is observed at 1024 G, which comes from a Level Anti-Crossing (LAC) of the triplet levels in the NV─ center (LAC line).
Other lines are called, perhaps, misleadingly, cross-relaxation lines [4]. In reality, all lines are
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due to the coherent spin dynamics and are caused by LACs of the entire spin system of the interacting defect centers. An example of an experimental Level-Crossing (LC) spectrum is given in Fig. 5.
Fig. 5. LC spectrum of the NV− centers in the diamond single crystal as measured with magnetic field modulation by lock-in amplifier. [5]
The detection of single negatively charged nitrogen-vacancy (NV−) color centers in 1997 [6] marks a critical point in the evolution of diamond based quantum technologies.
Although observations of ensembles of NV− centers were routinely performed prior to 1997, the detection of single centers soon enabled demonstrations of photostable single photon generation, which highlighted the NV− center for implementation in quantum optical networks, as well as demonstrations of optical preparation and readout of the center’s electronic spin, which identified the NV− center as a possible solid state spin qubit suitable for quantum information processing and quantum metrology devices. Following these demonstrations, the growth of research into the NV− center and the development of applications of the center have been incredibly rapid and a number of important milestones have been reached.
Fig. 6 (upper trace) demonstrates a typical ODMR signal of a single NV− center obtained by sweeping the microwave frequency without any applied magnetic field. The well-known ground state transition between ms = 0 and ms = ±1 sublevels is detected at 2.87 GHz, and an additional broad excited state line around 1.4 GHz is observed. By applying a magnetic field to the sample, the degeneracy of ms = ±1 is lifted by the Zeeman effect, leading to the appearance of two lines in the corresponding resonances of the ODMR spectrum (see Fig. 6 bottom trace).
Fig. 6. ODMR spectra of a single NV− center at zero magnetic field (upper trace) and with a magnetic field of amplitude B=43 G applied along the NV− symmetry axis, which corresponds to the [111] crystal axis (bottom trace). ESRs are evidenced both in the ground state and in the excited state [7].
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The applications of the NV− center each utilize one or a combination of the following five key properties of the center:
1. A bright photostable optical transition that is suitable for the detection of individual centers and single photon generation
2. An optical ZPL fine structure that is dependent on electric, magnetic and strain fields at low temperature, but is approximately electric and strain field independent at room temperature 3. A magnetically resonant and controllable ground state electronic spin that exhibits long
coherence times and coupling to proximal electronic and nuclear spins 4. Optical spin-polarization and readout of the ground state spin
5. Flexibility and robustness in fabrication.
Each of the room temperature implementations of the NV− center as a spin qubit employs the same prepare-manipulate/interact-readout mode of operation (see Fig. 7). An initial off-resonance optical pulse is used to prepare the ground state spin via optical spin-polarization.
This is followed by the application of static and microwave fields to manipulate the spin (and potentially radio frequency fields to manipulate coupled nuclear spins) and a period to allow the NV− center to interact with other spins and evolve. Finally, an off-resonance optical pulse is used to readout the ground state spin by measuring the integrated Stokes shifted fluorescence. It is clear that this mode of operation relies upon the performance of the optical spin-polarization and readout mechanisms, which are currently only crudely understood.
Fig. 7. Schematic representation of the prepare-manipulate/interact-readout mode of operation of the NV− spin qubit. An initial off-resonance (green) optical pulse is used to prepare the spin via optical spin-polarization. Control fields such as microwaves and static electric, magnetic and strain fields are applied to manipulate the spin and the other spins that it is interacting with.
Finally, an off-resonance (green) optical pulse is used to readout the spin via the integrated red shifted fluorescence. The pulse also prepares the spin for the next manipulate/interact step [8].
The spatial resolution of conventional NMR and MRI is limited to several micrometers even at large magnetic fields (>1 T), which is inadequate for many frontier scientific applications such as single-molecule NMR spectroscopy and in vivo MRI of individual biological cells.
A promising approach for nanoscale NMR and MRI exploits optical measurements of NV center in diamond, which provide a combination of magnetic field sensitivity and nanoscale spatial resolution unmatched by any existing technology, while operating under ambient conditions in a
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robust, solid-state system. Recently, single, shallow NV centers were used to demonstrate NMR of single nuclear spin [8-10]. Fig. 8 shows a schematic model of the experiment.
Fig. 8. Measuring the magnetic field of a nuclear spin oscillating at its resonance frequency [8].
a, The nuclear spins of interest (yellow arrow), perhaps in a biomolecule (colored ribbon structure), are brought within a few nanometers of a single NV− center or a collection of NV− centers embedded in diamond and located close to the surface. The sample may contain other unwanted spins (blue arrows). The luminescence of the NV− center is monitored while manipulating it with pulsed microwave radiation.
b, A schematic explaining the protocol for measuring the magnetic resonance of a nuclear spin.
The top panel shows the precession (black arrows), that is, a spinning-top-like motion of the nuclear spins (red arrows) at their resonance frequency due to an applied magnetic field.
This motion results in an oscillating magnetic field, represented by the red curve, that gets detected by the NV− spin. The rotation frequency of the NV− spins due to their precession in the applied field is slightly modified by the small additional fields from other spins, including the target nuclear spins. The middle panel shows how pulsed microwaves can be used to effectively switch that response by flipping the NV− spins. The blue line shows the sign of the NV− centre electron spin and its variation in time. Each time the spin is hit by a microwave pulse, denoted by the vertical lines, the spin changes its sign. Bottom panel:
In general, the oscillating nuclear spin field will speed up the NV− spins as much as it slows them down, so the NV− spins will not accumulate any phase, that is, they will end up in the same place they started. However, if the precession rate of the target nuclear spins is set to be precisely half the flipping rate of the NV− spins, the sign of the response of the NV− spins reverses exactly as often as the nuclear field varies. As a consequence the nuclear field always has the same effect, thus causing the NV− spins to accumulate a phase. This accumulation partially shifts the NV− spins from the ms = 0 to ms = ±1 state, thus altering the measured luminescence.
86 References
[1] L. Rondin et al., Phys. Rev. B 82 (2010) 115449.
[2] M.W. Doherty et al., Physics Reports 528 (2013) 1–45.
[3] V.M. Acosta et al., Phys. Rev. Lett. 104 (2010) 070801.
[4] E. van Oort, M. Glasbeek, Phys. Rev. B, 40 (1989) 6509-17.
[5] S.V. Anishchik et al., New J. Phys. 17 (2015) 023040.
[6] A. Gruber et al., Science 276 (1997) 2012.
[7] P. Neuman et al., New J. Phys. 11 (2009) 013017.
[8] D. Rugar et al., Nature Nanotech. 10 (2015) 120–124.
[9] T. Häberle et al., Nature Nanotech. 10 (2015) 125–128.
[10] S. J. DeVience et al., Nature Nanotech. 10 (2015) 129–134.
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