Addressing a single NV − spin with a macroscopic dielectric microwave cavity
J.-M. Le Floch, C. Bradac, N. Nand, S. Castelletto, M.E. Tobar, T. Volz
AAddressing a single NV − spin with a macroscopic dielectric microwave cavity J.-M. Le Floch , C. Bradac , N. Nand , S. Castelletto , M.E. Tobar , and T. Volz School of Physics, The University of Western Australia, Crawley, WA 6009, Australia ARC Centre of Excellence for Engineered Quantum Systems Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne, Australia (Dated: September 22, 2018)We present a technique for addressing single NV − center spins in diamond over macroscopicdistances using a tunable dielectric microwave cavity. We demonstrate optically detected magneticresonance (ODMR) for a single NV − center in a nanodiamond (ND) located directly under themacroscopic microwave cavity. By moving the cavity relative to the ND, we record the ODMRsignal as a function of position, mapping out the distribution of the cavity magnetic field along oneaxis. In addition, we argue that our system could be used to determine the orientation of the NV − major axis in a straightforward manner. Over the past decade, nitrogen-vacancy (NV) colorcenters in diamond (Figure 1(a)) have attracted a greatdeal of interest due to their outstanding quantum prop-erties [1]. Experiments have demonstrated long ground-state spin coherence times of the negatively charged NVcenter (NV − ) even at room temperature [2]. This makesNV − centers in diamond ideal candidates for room-temperature qubits [3, 4] and for ultrasensitive quantumsensors for detecting magnetic [5–11] and electric fields[12] at the nanoscale even in biological settings [9, 13, 14].Both quantum information processing and quantumsensing with NV − spins require the (coherent) manipula-tion and addressing of individual spins typically throughthe application of microwave (MW) radiation at a fre-quency that is resonant with the ground-state spin tran-sition. The NV − exhibits a zero-field spin resonanceat 2.87 GHz, which occurs between the m s = 0 and m s = ± − spin to be in close proxim-ity (on the order of 10 µ m) to the wire or microstrip line.Besides the inhomogeneity of the field, these on-chip so-lutions can easily lead to significant sample heating andundesired sample drift. Loop antennas typically workin the far field but require orders of magnitude largeramount of radiated MW power.In order to address single NV − spins in diamond,we designed a so-called dielectric-loaded microwave res-onator (DLR) with high quality (Q) factor (see Fig-ure 1(c)). DLRs of this kind are typically used inlow-temperature electron paramagnetic resonance exper-iments for measuring the complex permittivity of ex-tremely low-loss dielectrics [15–17], but are also employedfor testing local Lorentz invariance in fundamental exper-iments [18]. In industrial settings, DLRs find applicationsin radar, proximity detection, information transmission,remote guiding, navigation and positioning [19, 20]. In FIG. 1: (a) Diamond lattice structure with an embedded NVcenter. (b) Level scheme for the NV − center including thehyperfine splitting of the triplet ground state ( A). Opticalpumping of the spin into the m S = 0 state occurs via anintersystem crossing to the singlet manifold. (c) Dielectriccavity with adjustable plunger. The outer diameter of thecavity is 32 mm, its height amounts to 20 mm. (d) Trans-mission spectrum of the cavity with a FWHM of 3.5 MHzcorresponding to a Q-factor of around 1000. The spectrumwas recorded using a Fieldfox N9918A (Agilent Technologies).(e) Numerically calculated cavity frequency as a function ofplunger position. The mode of interest TE , , tunes easilyacross the NV − ground-state spin transition. order to find an appropriate design for our DLR, we em-ployed the numerical method of lines [21] or finite ele-ment analysis. The design was guided by the desire tohave compact cavity dimensions and the requirement forthe field to couple evanescently to the NV − spins locatedin close vicinity under the cavity.We found the best configuration to be an open cylin-drically symmetric cavity with a pure transverse electric(TE) mode with two non-vanishing magnetic-field com-ponents, H r and H z . In contrast to whispering gallerymodes, the TE-field confinement into the dielectric isnot as high and exhibits less spurious modes, leading toa higher Q-factor [22]. We denote the different cavitymodes by TE m,n,p , where 2 m is the number of azimuthal a r X i v : . [ qu a n t - ph ] D ec nodes, n the number of radial nodes, and p the numberof nodes along the z-axis (symmetry axis) of the cylin-der. For pure TE-modes the azimuthal mode numbervanishes, i.e. m = 0. Due to the particular boundaryconditions, they only have three non-vanishing compo-nents of the electromagnetic field, E Θ , H r and H z . Byinserting a dielectric rod made of high-permittivity, low-loss microwave material, the field can be confined to anarea of roughly 10 ×
10 mm . From the few suitable ma-terials available [23], we chose TiO for which the funda-mental mode has a frequency of 2.2 GHz. For addressingthe NV − spin transition, we then use the higher-orderTE , , -mode resonating at 2.7 GHz. Frequency tuningis achieved by mechanical insertion of a metallic plungerwhich directly affects the electric field and shifts the res-onance frequency up to a value of 3.1 GHz (Figure 1(e)).The (loaded) Q-factor of this cavity mode is about 1,000(see Figure 1(d)). Note that for perfect input couplingwe would expect the circulating intra-cavity power to beenhanced by a factor Q compared to the incoming MWpower. However, in the current cavity the coupling coef-ficient is rather small (about 1%). FIG. 2: (a) Radial magnetic field strength H r in a two-dimensional cut along the vertical symmetry axis (y-axis ofthe graph) of the microwave cavity. (b) Analogous plot forthe strength of the vertical magnetic field H z . Shaded ar-eas indicate the dielectric material of the cavity. (c) and (d)Field intensities H r and H z along the radial direction in aplane 1 mm below the cavity. Both fields are normalized tothe local overall field strength √ H r + H z . In the center of thetrap, only H z is non-vanishing whereas directly under the di-electric (shaded region) H r is the dominant field component. The magnetic field of the DLR cavity has cylindricalsymmetry. Both the radial magnetic field strength, H r ,and the vertical magnetic field strength, H z , are dis-played in Figure 2. Figures 2 (a) and (b) show two-dimensional plots of the respective field strength in aplane that contains the symmetry axis of the cavity:The x-axis corresponds to the radial distance from the FIG. 3: (a) Experimental setup for measuring ODMR withthe dielectric MW cavity. The ND fluorescence is collectedfrom below using a confocal setup. The collected photons aresent to either a spectrometer or to avalanche photodetectors.(b) Single-spin ODMR signal for a ND in the dielectric MWcavity. (c) Saturation curve for the ODMR contrast as afunction of microwave power (after the signal generator). Theinset shows an autocorrelation signal with clear antibunchingdemonstrating that the ND contains a single NV − center. symmetry axis and the values on the y-axis indicate theheight above the bottom edge of the cavity. We note thatthe radial field component H r has a maximum right atthe bottom edge at r ≈ H z is well-containedwithin the cavity. Figure 2 (c) and (d) show the expectedvariation of the radial and vertical field in a plane 1 mmbelow the cavity. The plots are normalized to the lo-cal overall field strength (cid:112) H r + H z . The graphs clearlyshow that in the center of the cavity the H z componentdominates (due to symmetry) whereas right under thedielectric at r ≈ − spin located just below the cavity. The HPHT nan-odiamonds (MSY 0.1 µ m, Microdiamant) are placed ona glass coverslip approximately 1 mm below the cavitywhich is mounted on a x-y-z mechanical stage (see Fig-ure 3(a)). The ND fluorescence upon excitation witha 532 nm laser is collected using a home-built confocalmicroscope [24] and sent to either a spectrometer or toavalanche photodetectors. Once a suitable single NV − center is identified, we obtain an ODMR signal by ap-plying microwave radiation through our microwave cavityand recording the corresponding fluorescence as a func-tion of microwave frequency. The microwave signal isgenerated using a standard microwave generator (SMIQ06B, Rohde & Schwarz) and amplified (25S1G4A, Ampli-fier Research) before applying it to the cavity. A typicalODMR signal is displayed in Figure 3(b), clearly demon-strating the coupling of a single NV − spin to the macro-scopic microwave resonator. Note that the contrast ofthe ODMR signal was optimized by adjusting the cavityresonance frequency to the actual transition frequency ofthe selected NV − center. Depending on the ND, we founda maximum achievable contrast of up to 12%. Next, werecorded a saturation curve for the m s = 0 → m s = ± − spin. FIG. 4: ODMR contrast as a function of ND position relativeto the cavity axis. The maximum contrast is observed directlyunder the dielectric material in agreement with the expectedfield dependence from Figure 2. At the center of the cavity( r = 0), the contrast does not completely vanish due to thefinite value of H z . In order to demonstrate the spatial variation of themagnetic field, we recorded an ODMR signal as a func-tion of relative position between the ND and the centeraxis of the cavity by mechanically adjusting the cavityposition. In the low-power (or linear) regime, the con-trast of the ODMR signal measures the local microwavepower seen by the NV − spin. Figure 4 shows the resultof such a measurement taken along the x-axis in con-secutive 1-mm steps, while the z- and y-coordinates ofthe resonator were kept fixed with respect to the ND po-sition. In the figure, we plot the depth of the ODMRresonance as a function of position, normalized to 1. Theplot displays the expected variation in ODMR contrastand exhibits a maximum contrast of about 6% when theND is right below the dielectric of the cavity structureat r ≈ r = 0 indicates thatthe NV − spin has a non-vanishing in-plane component.Since we do not know the major axis of the NV − center,we cannot extract the full information about the cavitymagnetic field from Figure 4. Using a ND with a knownspin orientation, however, magnetic-field tomography ispossible. 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