Absorption-Based Diamond Spin Microscopy on a Plasmonic Quantum Metasurface
AAbsorption-Based Diamond Spin Microscopy on a Plasmonic Quantum Metasurface
Laura Kim, Hyeongrak Choi,
1, 2
Matthew E. Trusheim,
1, 3 and Dirk R. Englund
1, 2 Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA 02139, USA U.S. Army Research Laboratory, Sensors and Electron Devices Directorate, Adelphi, Maryland 20783, USA (Dated: November 24, 2020)Nitrogen vacancy (NV) centers in diamond have emerged as a leading quantum sensor platform,combining exceptional sensitivity with nanoscale spatial resolution by optically detected magneticresonance (ODMR). Because fluorescence-based ODMR techniques are limited by low photon collec-tion efficiency and modulation contrast, there has been growing interest in infrared (IR)-absorption-based readout of the NV singlet state transition. IR readout can improve contrast and collectionefficiency [1–3], but it has thus far been limited to long-pathlength geometries in bulk samples dueto the small absorption cross section of the NV singlet state. Here, we amplify the IR absorption byintroducing a resonant diamond metallodielectric metasurface that achieves a quality factor of Q ∼ − per µ m ofsensing area using numbers for present-day NV diamond samples and fabrication techniques. Theproposed PQSM enables a new form of microscopic ODMR sensing with infrared readout near thespin-projection-noise-limited sensitivity, making it appealing for the most demanding applicationssuch as imaging through scattering tissues and spatially-resolved chemical NMR detection. INTRODUCTION
The ability to optically measure quantities such as elec-tric field, magnetic field, temperature, and strain underambient conditions makes the NV system appealing fora range of wide-field sensing applications, from imagingbiological systems [4] and electrical activity in integratedcircuits [5] to studying quantum magnetism and super-conductivity in quantum materials [6–9]. NV-based mag-netometers have shown exceptional sensitivity at roomtemperature, but conventional fluorescence-based read-out methods result in sensitivity values far from the spinprojection noise limit primarily due to background fluo-rescence, poor photon collection efficiency, and low spin-state contrast [10]. These limitations can be overcomeby probing the infrared singlet transition near 1042 nmby absorption. However, this absorption-based readouthas only been demonstrated for bulk diamond sampleswith a large optical path length of millimeters [3, 11] tocentimeters [2, 12] due to the small absorption cross sec-tion of the singlet state transition. This long-pathlengthrequirement presents the central challenge in IR readoutto imaging microscopy, where the sensing depth shouldcommonly be below the micron-scale. The plasmonicquantum sensing metasurface (PQSM) solves this prob-lem by confining vertically incident IR probe light ina few-micron-thick diamond layer with a quality factornear 1,000. The PQSM consists of a metallodielectricgrating that couples surface plasmon polariton (SPP)excitations and Rayleigh-Wood anomaly (RWA) modes[13, 14]. The localized plasmonic resonance causes localfield concentration as well as a wavelength-scale field en- hancement when coupled with the RWA modes. Unlikefluorescence, the directional reflection (or transmission)can be captured with near-unity efficiency. In particu-lar, detection of the reflected coherent probe light witha standard camera enables shot-noise limited detection,eliminating the need of single photon detectors. Takentogether, our analysis predicts that the PQSM coupledto NV sensing layers can enable a sensitivity below 1 nTHz − per µ m of sensing area. RESULTSIR-absorption-based detection scheme
The principle of NV-based magnetometers lies in theZeeman energy shift of the NV defect spin sublevels thatcan be polarized and measured optically. As illustratedin Fig. 1c, the spin sublevels m s = 0 and m s = ± A ground triplet state, labelled as | i and | i , re-spectively, are separated by a zero-field splitting of D =2.87 GHz, whose transition can be accessed with a reso-nant microwave field. Upon spin-conserving off-resonantgreen laser excitation, a fraction of the population decaysnon-radiatively into the A metastable singlet state, | i ,predominantly from | i as k (cid:29) k , where k ij indicatesthe decay rate from level i to level j. After a sub-ns decayfrom | i to | i , the shelving time at | i exceeds 200 nsat room temperature [15]. Therefore, the population of | i can be measured by absorption of the singlet statetransition resonant at 1042 nm.Figure 1a shows the proposed PQSM for the IR-absorption-based detection scheme. The sensing surface a r X i v : . [ qu a n t - ph ] N ov FIG. 1. (a) Plasmonic quantum sensing metasurface (PQSM) consisting of a metallodielectric grating and proposed homodyne-detection-based sensing scheme. TM-polarized incoming light induces a SPP-RWA hybrid mode, creating a vertically extendedfield profile as shown in the the overlapping Re( E y ). With an applied microwave magnetic field, the PQSM generates spin-dependent reflection with an additional phase change, ∆ φ NV . The spin-dependent signal, | E sig | , is separated from the un-diffracted beam, | E ud | , in a dark-field excitation geometry and interferes with a local oscillator, | E LO | . The interfered outputbeam, I out ( I t , Ω R , R, ∆ φ LO ), is detected by a CCD camera. (c) Total electric field intensity of RWA-SPP resonances uponnormal incidence at λ = 1042 nm with p = 434 nm, w = 125 nm, and t = 125 nm. The arrow plot shows the magnetic fieldgenerated by a uniform driving current in an infinite array of plasmonic Ag wires. is pumped with a green laser at 532 nm for NV spininitialization and illuminated with transverse magnetic(TM) polarized probe light at λ = 1042 nm for IR read-out. The PQSM-NV layer causes a spin-dependent phaseand amplitude of the IR reflection. The spatially well-defined signal beam is separated from the incident probefield in a dark-field excitation geometry (i.e., k-vectorfiltering). By interfering with a local oscillator, phase-sensitive homodyne detection at the camera enables mea-surement at the photon shot noise limit. The PQSM dou-bles as a wire array for NV microwave control [16, 17]:with a subwavelength spacing, an array of the silver wiresproduces a homogeneous transverse magnetic field, ~B , asshown in Fig. 1b. Local excitation and probing of NVswithin a pixel are possible by running a current throughan individual wire. Metasurface design
Here we discuss photonic design criteria to maximizethe IR signal of spin ensemble sensors. The IR absorp-tion readout has only been successfully implemented withbulk diamond samples due to the intrinsic absorption cross sectional area that is about an order of magnitudesmaller than that of the triplet state transition [3, 12].This weak light-matter interaction can be enhanced bymodifying the electromagnetic environment of quantumemitters. The rate of absorption of a quantum emitterunder an oscillating electromagnetic field with frequency, ω , can be expressed following Fermi’s golden rule.Γ abs = 2 π ~ | h | ~µ · ~E | i | ρ ( ω ) (1)where ~µ = e · ~r is the transition dipole moment opera-tor, ~E is the electric fields, and ρ ( ω ) = π ~ γ ∗ ( ω − ω ) +( γ ∗ ) is the electronic density of states, which is modeled asa continuum of final states with a Lorentzian distri-bution centered at ω with linewidth γ ∗ . The equa-tion shows that the rate can be enhanced by increas-ing the electric field at the emitter position. Plas-monic structures can focus light intensity at subwave-length scales, and thus, they have been used to increasespontaneous emission rates of single emitters or ensem-bles of emitters confined in a nanometer-scale volume[18–26]. However, this field concentration comes withthe trade-off of reducing the number of NV centers, N NV , that are coupled to the optical field. Balancingthis trade-off depends on the use case: sensing appli-cations with a spatial resolution below the grating pe-riod benefit from highly localized SPP-like modes, whileapplications with larger lateral resolution benefit frommore RWA-like modes that average over a larger N NV .To guide the PQSM optimization, we adopt a figure ofmerit addressing the latter of h| E/E | i V pixel n NV , where h| E/E | i = R pixel | E/E | dV / R pixel dV is the spatiallyaveraged optical field enhancement over the single-passfield without plasmonic structure, E , d NV is the thick-ness of the diamond sensing layer with NV density of n NV , and V pixel = L d NV is the sensing volume.The SPP-RWA resonance delocalizes the plasmonicmodes, creating a large field enhancement within a few-micron-thick surface layer of diamond, as shown in thecorresponding spatially-resolved electric field intensityprofile (Fig. 1b). The structure dimensions can be cho-sen to find the desired balance between SPP modes andRWA modes: stronger SPP localization resulting in morelocalized sensing can be traded against better sensitiv-ity, and vice versa. SPPs do not couple with free-spacelight without satisfying the momentum matching condi-tions. An incoming far-field optical excitation can exciteSPPs modes via a grating structure with period p givenby G = 2 m/p where m is an integer. To form a met-allodielectric grating, the plasmonic nanostructures arearranged periodically with a period of λ /n , where λ is 1042 nm and n is the refractive index of diamond. Asevident in the dispersion relation of RWA (Eq. 2), this pe-riod satisfies the condition for first-diffraction-order RWAmode under normal incidence (i.e., k x = 0). ωc n = k x + m πp (2)where c is the speed of light in vacuum, k x = k sin( θ i ) isthe momentum component of free-space light in the di-rection of grating period, and m denotes the diffractionorder [13, 14]. When the RWA mode is excited, the inci-dent electromagnetic wave diffracts parallel to the grat-ing surface and creates a field profile that extends verti-cally away from the grating surface [27, 28]. Thus, theSPP-RWA hybrid mode shows the electric field intensityprofile extending a few microns from the grating surfacewhile maintaining a large field concentration near the Ag-diamond interface as shown in Fig. 1b. While the RWAmode alone does not depend on the properties of theplasmonic material (Eq. 2), the SPP-RWA hybrid modeis highly dependent on the dispersive permittivity of theplasmonic material. When silver is replaced with palla-dium (Pd), a weak plasmonic material, the electric fieldenhancement is heavily suppressed (refer to SI Section1). As the SPP-RWA mode delocalizes the field awayfrom the lossy material, this PQSM exhibits a qualityfactor of 935 at 1042 nm, an exceptionally high value fora plasmonic coupled mode.To determine the signal from a pixel of the PQSM containing an ensemble of emitters, the rate of absorptionis averaged over all four orientations of NV emitters. Fora given angle, θ , between the emitter’s transition dipoleorientation and the electric field created by the PQSMin the diamond layer, Eq. 1 can be expressed as Eq. 3in terms of the spontaneous emission rate of the singletstate transition, γ = ω |h | ~µ | i| π(cid:15) ~ c .Γ abs = 3 π ~ γγ ∗ ( λ n ) · (cid:15) (cid:15) | ~E | cos ( θ ) (3)where (cid:15) is the relative permittivity of diamond. For a[100] diamond plane, all four orientations of NVs are ex-pected to have equal contributions for the given SPP-RWA-induced field profile. The signal-to-noise ratio(SNR) of the pixelated plasmonic imaging surface is givenby Eq. 4 under the assumption of the shot noise limit.SNR = | N − N |√ N + N = s ∆ t mea L ~ ω I out ( I t , − I out ( I t , Ω R ) p I out ( I t ,
0) + I out ( I t , Ω R ) (4)where N and N are the average numbers of photons de-tected from the m s = 0 and m s = ± t mea is the total readout time, and I out ( I t , Ω R ) is the reflected intensity under green laserintensity, I t , and an applied microwave Rabi field, Ω R .In the limit of low contrast, the SNR can be re-writtenas follows:SNR = s I out (0 , t mea L ~ ω ( I NV ( I t , Ω R ) − I NV ( I t , ∝ h| E/E | i V pixel n NV (5)where I NV ( I t , Ω R ) = I out (0 , − I out ( I t , Ω R ) I out (0 , is the frac-tional change in IR intensity due to NV absorption, and I NV ( I t , Ω R ) − I NV ( I t , ∝ h| E/E | i V pixel n NV as de-scribed in detail in SI Section 3. Thus, the SNR scaleswith both spatially averaged electric field intensity en-hancement factor and sensing volume for a given NV den-sity. The PQSM combines a large field enhancement ofthe SPP mode and delocalization of the RWA mode, mak-ing the SPP-RWA hybrid mode well suited for ensemble-based sensing. Metasurface spin-dependent response
The spin-dependent IR absorption depends on the pop-ulation of the ground singlet state, and it can be ob-tained by calculating the local density of each sublevel, n | i i , based on the coupled rate equations described in SISection 2. As shown in Fig. 1c, we use an eight-level rate FIG. 2. (a) The population of the ground singlet state as a function of 532 nm laser intensity with (solid) and without (dotted)an applied microwave field at a given sensing depth of 5 µ m. (b) Input-intensity-normalized NV absorption, A pixel , per pixel(left y-axis) and corresponding phase changes of the spin-dependent reflected light, ∆ φ NV (right y-axis). (c) SNR/ √ ∆ t mea L under steady state operation as a function of I t with varying I s for homodyne (solid) and direct (dotted) detection. equation model that accounts for photoionization. Undercontinuous wave (CW)-ODMR, Fig. 2a shows the calcu-lated n | i , indicating that the population of the singletstates weakly depends on the IR probe intensity, I s , untilthe absorption rate becomes comparable to the excitedstate decay rate. The SPP-RWA-induced field enhance-ment modifies the absorption rate as well as the radiativedecay rate by γ rad → F p γ rad + γ quenching , where F p is thePurcell factor. However, due to the low intrinsic quan-tum efficiency of the singlet state transition ( γ rad Γ ≈ ∼ h| E/E | i . Similarly, the current PQSM structurecan induce a grating mode resonant at 532 nm with anoff-normal back illumination (refer to SI Section 1).Under an applied microwave field, an increase inthe population of the m s = ± I NV ( I t , Ω R ) >I NV ( I t , A pixel , (equiva- lently, I NV ( I t , Ω R ) × I out (0 , I s ) with varying sensing depthis shown in Fig. 2b. To account for stimulated emis-sion, a net population (i.e., n | i - n | i ) is used to calculatethe net spin-dependent NV absorption. Based on thecalculated A pixel , the NV-induced corresponding phasechange, ∆ φ NV , is obtained from the complex reflectioncoefficients simulated with FDTD method (Fig. 2b).The spin-dependent phase and amplitude changes ofthe signal allow for a phase-sensitive measurement. Here,we implement a phase-sensitive coherent homodyne de-tection, where a local oscillator interferes with the spin-dependent signal from the PQSM. A combination of R and ∆ φ LO is chosen to maximize the SNR (refer to SI Sec-tion 4) and the readout fidelity. The incident-intensity-normalized interfered intensity detected by the camera isgiven by Eq. 6. I out ( I t , Ω R , R, ∆ φ LO ) I s = (1 − R ) + R | r ( I t , Ω R ) | + 2 p (1 − R ) R | r ( I t , Ω R ) | cos(∆ φ LO + ∆ φ NV ( I t , Ω R ))(6)where R is the power splitting ratio of the beam split-ter, r ( I t , Ω R ) is the complex reflection coefficient of thePQSM, ∆ φ LO is the relative phase difference betweenthe LO and the reflected light of the PQSM when I t =0 and Ω R = 0, and ∆ φ NV ( I t , Ω R ) is an additional phasechange incurred by the NV absorption. Figure 2c showsSNR that is normalized by the measurement time andpixel area of L . Under the conditions considered in thiswork, the photon shot noise dominates, and a better SNRis achieved by biasing the interferometric readout with acontrolled phase difference. Homodyne detection is par-ticularly advantageous for fast imaging on focal planearrays. DISCUSSIONDC sensitivity
The shot-noise-limited sensitivity of a CW-ODMR-based magnetometer per root area based on IR absorp-tion measurement is given by Eq. 7. η A CW = ~ Γ MW gµ B √ ∆ t mea L SNR (7)where g ≈ .
003 is the electronic g-factor of the NVcenter, µ B is the Bohr magneton, and Γ MW is themagnetic-resonance linewidth which can be approxi-mated as Γ MW = 2 /T ∗ , assuming no power broadeningfrom pump or microwaves. For a given NV density of ∼
16 ppm, the dephasing time is limited by paramagneticimpurities with the conversion efficiency conservativelyapproximately as 16% [29]. An alternative magnetom-etry method to CW-ODMR, such as pulsed ODMR orRamsey sequences, can be exploited to achieve T ∗ -limitedperformance.It is useful to compare the photon-shot-noise-limitedsensitivity with the spin-projection-noise-limited sensi-tivity of an ensemble magnetometer consisting of non-interacting spins. η A, ensemblesp = ~ gµ B √ n NV d NV τ (8)where τ is the free precession time per measurement. Fig-ure 3a shows that the PQSM can achieve sub-nT Hz − sensitivity per µ m sensing surface area for a given anNV layer thickness of d NV = 5 µ m and remaining exper-imental parameters listed in Table . As expected, sensi-tivity improves with increasing green laser intensity untiltwo-photon-mediated photo-ionization processes start tobecome considerable. Furthermore, as shown in Fig. 3b,increasing the sensing depth from 500 nm to 10 µ m im-proves the sensitivity by a factor of up to ∼
9. Thereexists a trade-off between achievable sensitivity and spa-tial resolution.
AC sensitivity
Sources of the NV spin dephasing can be largely elimi-nated with coherent control techniques such as the Hahnecho sequence. With an added π -pulse halfway through FIG. 3. (a) Expected sensitivity per root sensing surface areawith homodyne (solid) and direct (dotted) detection as a func-tion of I t with varying I s for a given d NV = 5 µ m. The dottedblack line indicates 1 nT Hz − sensitivity for a 1 µ m sensingarea. The solid black line indicates the spin-projection-noise-limited sensitivity. (b) Sensing-depth-dependent sensitivitywith homodyne detection for a given I s = 1 mW/ µ m .TABLE I. Physical parameters used in this work.Parameter Value Reference k = k µ s − [30] k µ s − [30] k µ s − [30] k µ s − [30] k µ s − [30] k = k k = k − [15]Γ NV µ s − [30, 31] σ t × − m [32] σ s × − m [3, 12] σ NV × − m [30, 31] n NV × m − [33] T ∗
200 ns [10, 33] T µ s [10]Ω R π × FIG. 4. (a) Population of the singlet ground state with (solid) and without (dotted) an applied microwave field as a function ofreadout time at d NV = 5 µ m for a given I s = 1 mW/ µ m . (b) Readout fidelity and (c) AC sensitivity per root sensing surfacearea as a function of I t with varying I s at d NV = 5 µ m for homodyne (solid) and direct (dotted) detection. The solid blackline indicates the spin-projection-noise-limited sensitivity given by Eq. 8. the interrogation time, a net phase accumulated due toa static or slowly varying magnetic field cancels out, andthe interrogation time can be extended to a value of ∼ T .Thus, the AC sensitivity can improve by a factor of ap-proximately p T ∗ /T at the cost of a reduced bandwidthand insensitivity to magnetic field with an oscillating pe-riod longer than T . The sensitivity per root area for anensemble-based AC magnetometer is given by Eq. 9 [10]. η A a.c. = ~ σ R e τ/T gµ B √ n NV d NV τ r t I + t R τ (9)where T is the characteristic dephasing time, t I is theinitialization time, t R is the readout time, and σ R is thereadout fidelity. For a given NV density of ∼
16 ppm, T is about an order of magnitude longer than T ∗ [10].Rate equations are solved as a function of time to obtaintime-dependent population evolution as shown in Fig. 4a.The system loses spin polarization after a few microsec-onds of readout time. For given I t and I s , an optimalreadout time that maximizes the time-integrated signalis calculated and is shown to be near 500 ns (refer toSI Section 5). An additional shot noise introduced bythe optical readout is quantified with the parameter σ R (Eq. 10), which is equivalent to an inverse of readout fi-delity [10]. σ R = s a + b )( a − b ) (10) where a and b are the average numbers of photons de-tected from the m s = 0 and m s = ± − per 1- µ m sensingsurface area. CONCLUSION
In summary, we report a diamond quantum sensingsurface consisting of plasmonic nanostructures, whichshows a sub-nT Hz − sensitivity per a 1- µ m sensingsurface. This exceptional performance is achieved by theSPP-RWA resonance that optimizes an electric field en-hancement within a micron-scale NV layer. The plas-monic structures of the PQSM also provide an optimalmicrowave control by generating a homogeneous mag-netic field across a large sensing area. Combined witha homodyne detection, the PQSM makes a new typeof quantum microscope that enables high-speed imagingmeasurements at the photon shot noise limit.This PQSM has far-reaching implications in quantumscience. The metasurface-coupled quantum emitter ar-rays can enable manipulation of accumulated phase andpolarization at each position of a quantum emitter. Bysuperposing spin-dependent reflection or transmission, itmay even be possible to entangle different regions of themetasurface. The entangled quantum metasurface is use-ful in applications that demand measurements of corre-lated quantum fluctuation such as quantum spin liquidsin quantum materials [34, 35]. Such an approach can ex-ploit entanglement-enhanced quantum sensing protocolsto achieve performance beyond the standard quantumlimit [36, 37]. ACKNOWLEDGEMENTS
L.K. acknowledges support through an appointment tothe Intelligence Community Postdoctoral Research Fel-lowship Program at the Massachusetts Institute of Tech-nology, administered by Oak Ridge Institute for Scienceand Education through an interagency agreement be-tween the U.S. Department of Energy and the Office ofthe Director of National Intelligence. H. C. acknowledgessupport through Claude E. Shannon Fellowship and theDARPA DRINQS, D18AC00014 program. M.E.T. ac-knowledges support through the Army Research Lab-oratory ENIAC Distinguished Postdoctoral Fellowship.D.E. acknowledges support from the Bose Research Fel-lowship, the Army Research Office W911NF-17-1-0435,and the NSF CUA. We thank Dr. Jennifer Schloss andJordan Goldstein for helpful discussions. [1] V. M. Acosta, E. Bauch, A. Jarmola, L. J. Zipp, M. P.Ledbetter, and D. Budker, Appl. Phys. Lett. (2010).[2] L. Bougas, A. Wilzewski, Y. Dumeige, D. Antypas,T. Wu, A. Wickenbrock, E. Bourgeois, M. Nesladek,H. Clevenson, D. 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1, 2
Matthew E. Trusheim,
1, 3 and Dirk R. Englund
1, 2 Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA 02139, USA U.S. Army Research Laboratory, Sensors and Electron Devices Directorate, Adelphi, Maryland 20783, USA (Dated: November 24, 2020)
SECTION 1: METAL-DIAMOND METALLODIELECTRIC GRATING STRUCTURES
The SPP-RWA hybrid mode of the PQSM creates a vertically extended field down to about 5 µ m in depth (Fig. 1a),and exhibits a quality factor of 935 (Fig. 1b). FIG. 1. Silver-diamond metallodielectric grating (a) Total electric field intensity with an extended y-range (b) The spectrumobtained by Fourier transform of the time decay of the field at 287.8 THz shows Q = 935.618.
The dispersion for SPPs under the Bragg grating coupling condition (i.e., surface plasmon polariton-Bloch wave(SPP-BW) modes) is given by Eq. 1 [1]. Re h ωc r (cid:15) m (cid:15) d (cid:15) m + (cid:15) d i = (cid:12)(cid:12)(cid:12) k x + m πp (cid:12)(cid:12)(cid:12) (1)where (cid:15) m/d is the permittivity of metallic/dielectric material of the metallodielectric grating structure and m is theinteger denoting specific SPP modes [1, 2]. While RWA modes are independent of metal properties, the SPP-RWAhybrid becomes highly dependent on the properties of the plasmonic material. The SPPs play a role in creating a largefield enhancement in the metallodielectric grating structure, and a dramatic reduction in the electric field intensityis observed when silver is replaced with a weak plasmonic material, palladium (Fig. 2b). It is evident that the RWAis responsible for creating a vertically extended electric field as it is maintained even when silver is replaced with aperfect electric conductor (PEC), which cannot support SPPs (Fig. 2). FIG. 2. Field distribution, Re( E y ), of a grating structure made with diamond - (a) PEC (b) palladium and (c) silver with p =434 nm, w = 125 nm, and t = 125nm. a r X i v : . [ qu a n t - ph ] N ov Without changing geometric parameters of the PQSM, we can couple in the green laser excitation, which is necessaryto populate the singlet state, by inducing a grating resonance at 532 nm via a off-normal incidence (i.e., compensatingfor the momentum mismatch, k x ). For example, for the given structure geometry studied in this work, TM-polarizedillumination at 532 nm from the backside with θ i = 2.9 ◦ satisfies the condition for the RWA mode for m = 2. Figure 3shows the electric field intensity profile, and the corresponding spatially averaged electric field intensity, h| E/E | i , is1.98. FIG. 3. Total electric field intensity of a Ag-diamond grating structure with p = 434 nm, w = 125 nm, and t = 125 nm underTM-polarized illumination at 532 nm from the backside with an off-normal incidence ( θ i = 2.9 ◦ ). SECTION 2: RATE EQUATIONS FOR THE 8-LEVEL SCHEME
The local density of each sublevel, n | i i , is calculated based on the coupled rate equations (Eq. 2a - Eq. 2h) under theassumption of spin-conserving optical transition. We impose a number conservation constraint (i.e., P i n | i i = n NV ,where n NV is the total NV density). dn | i dt = − ( W pump + W MW ) n | i + W MW n | i + k n | i + k n | i + k n | i (2a) dn | i dt = W MW n | i − ( W pump + W MW ) n | i + k n | i + k n | i + k n | i (2b) dn | i dt = W pump n | i − ( k + k + k ) n | i (2c) dn | i dt = W pump n | i − ( k + k + k ) n | i (2d) dn | i dt = k n | i + k n | i − ( γ nr + F p γ r + γ quenching + W probe ) n | i + W probe n | i (2e) dn | i dt = ( γ nr + F p γ r + γ quenching + W probe ) n | i − ( W probe + k + k ) n | i (2f) dn | i dt = − (Γ NV + k + k ) n | i + W NV n | i (2g) dn | i dt = k n | i + k n | i + Γ NV n | i − W NV n | i (2h) k ij is the transition rate constant from state | i i to state | j i . Γ NV is the decay rate from | i to | i , and Γ = γ nr + F p γ r + γ quenching is the decay rate from | i to | i , where F p is the Purcell factor, γ quenching is the quenching rate,and γ nr and γ r are the non-radiative and radiative decay rates of state | i , respectively. W pump/probe is the opticalexcitation rate of the triplet/singlet transition given by σ t/s I t/s ~ ω t/s , where σ is the absorption cross sectional area, I is thelaser intensity, and ω is the angular frequency of the corresponding transition. The PQSM enhances the W pump/probe by a factor of ∼ h| E/E | i at λ = 532 nm/1042 nm. W MW is the microwave transition rate approximated as Ω R T ∗ / R is the Rabi angular frequency and T ∗ is the electron spin dephasing time [3]. All of the relevant parametersare listed in Table 1 of the main manuscript. SECTION 3: DERIVATION FOR SNR OF THE PQSM
The intrinsic rate of absorption can be written in terms of the intrinsic absorption cross section of the singlet statetransition, σ s (Eq. 3). Γ = σ s I s ~ ω (3)The plasmonic structures explored in this work enhance the rate of absorption of an emitter at the position ( x , y , z ) bya factor of | E ( x, y ) /E | , where E is the electric field in a homogeneous environment and E ( x, y ) is the electric fieldinduced by the SPP-RWA hybrid mode of the PQSM, invariant in z-direction. The fractional change in IR intensitydue to NV absorption, I NV ( I t , Ω R ), for a given pixel size of L illuminated with I s is defined as Eq. 4. I NV ( I t , Ω R ) = I out (0 , − I out ( I t , Ω R ) I out (0 , I s I out (0 , σ s N NV ( I t , Ω R ) L R d NV R p/ − p/ | E ( x,y ) E | dxdy R d NV R p/ − p/ dxdy (4)where N NV ( I t , Ω R ) is the total net NV population in the ground singlet state for a given V pixel , which is given by( n | i − n | i ) V pixel . The net population of the singlet ground state (i.e., n | i − n | i ) is used to account for stimulatedemission. The SNR is proportional to I NV ( I t , Ω R ) − I NV ( I t , I out ( I t , Ω R ) ≈ I out ( I t , ≈ I out (0 , I NV ( I t , Ω R ) − I NV ( I t ,
0) = σ s [( n | i − n | i ) Ω R − ( n | i − n | i ) ] V pixel L R R d NV R p/ − p/ | E ( x,y ) E | dxdy R d NV R p/ − p/ dxdy ∝ h| E/E | i V pixel n NV (5)where R is the reflection of the PQSM. Thus, the SNR of the pixelated plasmonic imaging surface under theassumption of the shot noise limit is given by Eq. 6.SNR = s I s ∆ t mea L R ~ ω σ s [( n | i − n | i ) Ω R − ( n | i − n | i ) ] p Z d NV Z p/ − p/ | E ( x, y ) E | dxdy (6) FIG. 4. Spatially averaged electric field intensity, h| E/E | i (left), and the figure of merit, h| E/E | i d NV (right), of the PQSM. The performance of an ensemble-based sensor scales with h| E/E | i V pixel . Although the electric field is highlyconcentrated near the metal surface as shown in the plotted h| E/E | i (Fig. S4), the figure of merit, h| E/E | i V pixel ,increases with d NV (or V pixel for a given pixel size of L ). SECTION 4: OPTIMIZING HOMODYNE DETECTION CONDITION
To find the optimal operating condition for homodyne detection, a combination of R and ∆ φ LO that maximizesSNR/ √ L (Eq. S14) is found numerically for given I s and I t , while I out ( I t , Ω R ) is replaced by I out ( I t , Ω R , R, ∆ φ LO )(Eq. 6 in the main manuscript). Figure 6 shows the contour plot of the area-normalized SNR as a function of ∆ φ LO and R for given I s , I t , and ∆ t mea . The optimal condition for homodyne detection is found at ∆ φ LO = 1.28 π and R = 0.87. FIG. 5. Homodyne detection. P is the incident power at 1042 nm given by I s L . The metasurface signal, | r / NV | P , and thelocal oscillator signal, P , are the input signals to a beam splitter (BS) with a power splitting ratio of R , and the interferedsignal is detected by a CCD camera.FIG. 6. Contour plot of SNR normalized by the pixel area of L as a function of R and ∆ φ LO for given I s = 1 mW/ µ m , I t =0.1 mW/ µ m , and ∆ t mea = 10 µ s. The maximum is found at ∆ φ LO = 1.28 π and R = 0.87, indicated by the crossover of thetwo dotted lines. SECTION 5: OPTIMAL READOUT CONDITION FOR PULSED MEASUREMENTS
As shown in Fig. 4a of the main manuscript, in pulsed measurements, the system achieves maximum spin contrastwithin the first 1 µ s of readout and finally loses polarization with increasing readout time, limited by the lifetime ofthe ground singlet state. Thus, there exists an optimal readout time that gives the maximum time-averaged signal.For given I t and I s , the optimal readout time, ∆ t mea , that maximizes the quantity of Eq. 7 is found, and the resultis plotted in Fig. 7. R t mea [( n | i ( t )) Ω R − ( n | i ( t )) ] dt R t mea dt (7) FIG. 7. Optimal readout time for pulsed measurements for a given d NV = 5 µ m.[1] W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. , 107401 (2004).[2] H. Gao, J. M. McMahon, M. H. Lee, J. Henzie, S. K. Gray, G. C. Schatz, and T. W. Odom, Opt. Express , 2334 (2009).[3] Y. Dumeige, M. Chipaux, V. Jacques, F. Treussart, J.-F. Roch, T. Debuisschert, V. M. Acosta, A. Jarmola, K. Jensen,P. Kehayias, and D. Budker, Phys. Rev. B Condens. Matter87