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Anisotropic interactions of a single spin and dark
Y. K. Kato1AbstractExperiments on single nitrogen (N centres in diamond, which include electron spin resonance1, Rabi oscillations2, single shot spin readout3 and two qubit operations with a nearby13C nuclear spin4, show the potential of this spin system for solid state quantum information processing. Moreover, N centre ensembles can have spin coherence times exceeding 50 s at room temperature5. We have developed an angle resolved magneto photoluminescence microscope apparatus to investigate the anisotropic electron spin interactions of single N centres at room temperature. We observe negative peaks in the photoluminescence as a function of both magnetic field magnitude and angle that are explained by coherent spin precession and anisotropic relaxation at spin level anti crossings. In addition, precise field alignment unmasks the resonant coupling to neighbouring 'dark' nitrogen spins, otherwise undetected by photoluminescence.
a, The atomic structure and relevant energy levels. The green 'bond' depicts the N symmetry axis. b, The spatial image of IPL on a linear colour scale, showing the emission from several N centres; NV1 (left to right) are marked. c, The intensity correlation function g(2)() versus for NV1, indicating single photon emission. d, Optically detected ESR for NV1. IPL versus microwave frequency MW (circles) with a lorentzian fit (solid line). The laser power is 1 mW for b and 370 W for c and d.
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The single crystal samples investigated here are commercially available (Sumitomo Electric Industries) high temperature high pressure diamond with two polished parallel (100) surfaces and nominal dimensions of 1.4 mm1.4 mm1.0 mm. They contain nitrogen impurities with densities of 1019 cm 3, measured by ultraviolet absorption18. N centres are naturally present with substantially lower densities ranging from 1010 to 1013 cm 3. For ensemble measurements, samples are irradiated with 1.7 MeV electrons with a dose of 51017 cm 3 and subsequently annealed at 900 for 2 h to increase the N centre concentration6.
The phonon broadened 3E3A transition of the N centre is detected by means of non resonant photoluminescence microscopy (see Methods). For example, Fig. 1b is a spatial image of the spectrally integrated photoluminescence from a diamond sample with the laser focused roughly 1 m below the surface. Multiple resolution limited features are observed in the 20 m20 m field. In order to determine that a given feature is due to a single emitter, a histogram is plotted of the time between consecutive photon detection events using a Hanbury Brown and Twiss detection geometry19, yielding the experimental intensity correlation function g(2)(). Figure 1c shows the data from a colour centre labelled NV1. The value of g(2)(0) is below 0.5, proving that NV1 is a single colour centre20. In addition, the rise of g(2)() above unity with increasing is indicative of intersystem crossing to the 1A metastable state20, 21.
These single photon emitters are further characterized by optically detected electron spin resonance (ESR; see Methods). Figure 1d contains data from NV1 with zero applied magnetic field. In this case, the 1 ground state levels are degenerate so that only one resonance (mS=01) is observed at 2.87 GHz,faux boucles d oreilles anciennes, the characteristic zero field splitting of N centres11. The data are fit with a lorentzian of 11 MHz full width at half maximum (solid line), which is comparable to reported values in similar diamond samples1.
Strain dependent optical measurements on ensembles of N centres have indicated that electric dipole transitions are allowed for dipoles in the plane perpendicular to the symmetry axis6. Figure 2a depicts an N centre with transition dipoles and in a (111) plane. The excitation is along [001] for all measurements, therefore IPL depends on the laser polarization angle owing to unequal excitation of the two dipoles. The dependence of IPL on is measured for 20 N centres and shows either vertical or horizontal lobes, as exemplified for three N centres in Fig. 2b. The measured anisotropies, defined as the ratio IPL(=0 (=90 are roughly 2:1 and 1:2 on average; a simple anisotropy calculation gives 3:1, 3:1, 1:3 and 1:3 for the N symmetry axis along [111], , and , respectively (see Methods). The measured data are modified by the presence of polarized background photoluminescence (subtracted from the data) and a small dip, most visible for NV2 at =0 which varies in depth from centre to centre. Nevertheless, comparison of the measured and calculated anisotropies enables the number of possible orientations of a given centre to be reduced from four to two.
(61 KB)In order to investigate these peaks further,r��plique boucles d oreilles van cleef prix, IPL is measured as a function of B with B at a series of angles in the plane; a selection of such data from NV1 is shown in Fig. 3a. As B approaches the [111] direction (0 the LAC peak narrows, as expected from ensemble measurements22, 23. At sufficiently small angles, however, the LAC peak amplitude decreases for NV1 (Fig. 3b) or even vanishes for some centres, such as NV4 (Fig. 3c). This is in contrast to the ensemble measurements22, 23 that showed a maximum in the LAC peak amplitude at =0 According to the hamiltonian above,replique boucle d oreille van cleef, however, spin mixing should vanish at =0 The presence of residual spin mixing at =0 has been attributed to strain and nuclear interactions24, which vary from centre to centre.
Figure 3: Controlled level mixing by means of magnetic field alignment.
a, IPL versus B for NV1 at specified magnetic field angles . b,r��plique boucle d oreille van cleef, Zoom of data in a (points) with fits (lines) to model described in the text. Data for =0 are taken with smaller field steps and fit with an angle of 0.2 to account for residual spin mixing (see the text). c, IPL versus B for NV4 (points) and fits (lines) at specified field angles. d, Normalized amplitudes A (points) of LAC and 500 G peaks versus with fits (lines). Laser power is 1 mW for NV1 and 2.9 mW for NV4.
Y. K. Kato1AbstractExperiments on single nitrogen (N centres in diamond, which include electron spin resonance1, Rabi oscillations2, single shot spin readout3 and two qubit operations with a nearby13C nuclear spin4, show the potential of this spin system for solid state quantum information processing. Moreover, N centre ensembles can have spin coherence times exceeding 50 s at room temperature5. We have developed an angle resolved magneto photoluminescence microscope apparatus to investigate the anisotropic electron spin interactions of single N centres at room temperature. We observe negative peaks in the photoluminescence as a function of both magnetic field magnitude and angle that are explained by coherent spin precession and anisotropic relaxation at spin level anti crossings. In addition, precise field alignment unmasks the resonant coupling to neighbouring 'dark' nitrogen spins, otherwise undetected by photoluminescence.
a, The atomic structure and relevant energy levels. The green 'bond' depicts the N symmetry axis. b, The spatial image of IPL on a linear colour scale, showing the emission from several N centres; NV1 (left to right) are marked. c, The intensity correlation function g(2)() versus for NV1, indicating single photon emission. d, Optically detected ESR for NV1. IPL versus microwave frequency MW (circles) with a lorentzian fit (solid line). The laser power is 1 mW for b and 370 W for c and d.
(40 KB)
The single crystal samples investigated here are commercially available (Sumitomo Electric Industries) high temperature high pressure diamond with two polished parallel (100) surfaces and nominal dimensions of 1.4 mm1.4 mm1.0 mm. They contain nitrogen impurities with densities of 1019 cm 3, measured by ultraviolet absorption18. N centres are naturally present with substantially lower densities ranging from 1010 to 1013 cm 3. For ensemble measurements, samples are irradiated with 1.7 MeV electrons with a dose of 51017 cm 3 and subsequently annealed at 900 for 2 h to increase the N centre concentration6.
The phonon broadened 3E3A transition of the N centre is detected by means of non resonant photoluminescence microscopy (see Methods). For example, Fig. 1b is a spatial image of the spectrally integrated photoluminescence from a diamond sample with the laser focused roughly 1 m below the surface. Multiple resolution limited features are observed in the 20 m20 m field. In order to determine that a given feature is due to a single emitter, a histogram is plotted of the time between consecutive photon detection events using a Hanbury Brown and Twiss detection geometry19, yielding the experimental intensity correlation function g(2)(). Figure 1c shows the data from a colour centre labelled NV1. The value of g(2)(0) is below 0.5, proving that NV1 is a single colour centre20. In addition, the rise of g(2)() above unity with increasing is indicative of intersystem crossing to the 1A metastable state20, 21.
These single photon emitters are further characterized by optically detected electron spin resonance (ESR; see Methods). Figure 1d contains data from NV1 with zero applied magnetic field. In this case, the 1 ground state levels are degenerate so that only one resonance (mS=01) is observed at 2.87 GHz,faux boucles d oreilles anciennes, the characteristic zero field splitting of N centres11. The data are fit with a lorentzian of 11 MHz full width at half maximum (solid line), which is comparable to reported values in similar diamond samples1.
Strain dependent optical measurements on ensembles of N centres have indicated that electric dipole transitions are allowed for dipoles in the plane perpendicular to the symmetry axis6. Figure 2a depicts an N centre with transition dipoles and in a (111) plane. The excitation is along [001] for all measurements, therefore IPL depends on the laser polarization angle owing to unequal excitation of the two dipoles. The dependence of IPL on is measured for 20 N centres and shows either vertical or horizontal lobes, as exemplified for three N centres in Fig. 2b. The measured anisotropies, defined as the ratio IPL(=0 (=90 are roughly 2:1 and 1:2 on average; a simple anisotropy calculation gives 3:1, 3:1, 1:3 and 1:3 for the N symmetry axis along [111], , and , respectively (see Methods). The measured data are modified by the presence of polarized background photoluminescence (subtracted from the data) and a small dip, most visible for NV2 at =0 which varies in depth from centre to centre. Nevertheless, comparison of the measured and calculated anisotropies enables the number of possible orientations of a given centre to be reduced from four to two.
(61 KB)In order to investigate these peaks further,r��plique boucles d oreilles van cleef prix, IPL is measured as a function of B with B at a series of angles in the plane; a selection of such data from NV1 is shown in Fig. 3a. As B approaches the [111] direction (0 the LAC peak narrows, as expected from ensemble measurements22, 23. At sufficiently small angles, however, the LAC peak amplitude decreases for NV1 (Fig. 3b) or even vanishes for some centres, such as NV4 (Fig. 3c). This is in contrast to the ensemble measurements22, 23 that showed a maximum in the LAC peak amplitude at =0 According to the hamiltonian above,replique boucle d oreille van cleef, however, spin mixing should vanish at =0 The presence of residual spin mixing at =0 has been attributed to strain and nuclear interactions24, which vary from centre to centre.
Figure 3: Controlled level mixing by means of magnetic field alignment.
a, IPL versus B for NV1 at specified magnetic field angles . b,r��plique boucle d oreille van cleef, Zoom of data in a (points) with fits (lines) to model described in the text. Data for =0 are taken with smaller field steps and fit with an angle of 0.2 to account for residual spin mixing (see the text). c, IPL versus B for NV4 (points) and fits (lines) at specified field angles. d, Normalized amplitudes A (points) of LAC and 500 G peaks versus with fits (lines). Laser power is 1 mW for NV1 and 2.9 mW for NV4.
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