Diamond platforms for nanoscale photonics and metrology

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Diamond platforms for nanoscale photonics and metrology The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Accessed Citable Link Terms of Use Shields, Brendan John. 2014. Diamond platforms for nanoscale photonics and metrology. Doctoral dissertation, Harvard University. December 30, 2017 9:35:42 PM EST http://nrs.harvard.edu/urn-3:hul.instrepos:12274345 This article was downloaded from Harvard University's DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:hul.instrepos:dash.current.terms-ofuse#laa (Article begins on next page)

594

0 637 m s =0 m s = ±1 2.8 m s = ±1 m s =0 m s =1 m s = ±1 m s = ±1 150 m s = 0 m s = 1 m s =0

532 m s =0 V Q V (λ/n) 3 λ n

2π 15

2π 100 10 4 Q n = 2.4 Q

V m 1/ V m Q ΓX

air 0.3 light -lines PMMA e d waveguide bands bandgap X J 0.1 0 k a// x 0 0 1 E Air 2 z(+m) ï 1 1 b 1 5+m f 4 Target NV N h(nm) g.. onto substrate. 30+m 1+m 0.2..to polymer.. GaP wafer.. intensity (a.u.) normalized frequency a/h a V PC tip 0 film 1 PMMA c glass y(+m) ï 0 excitation & collection ï ï 0 x(+m) 6B;m`2 kxr, U V.BbT2`bBQM 7Q` i?2 T?QiQMB+ +`vbi H bh # BM B`- HQM; i?2 r p2;mb/2 /B`2+iBQM kx c i?2 BMb2i b?qrb i?2 +`vbi H UQ` M;2V M/ BMp2`b2 +`vbi H U#Hm2V /B`2+iBQMbX h?2 H iib+2? b T2`B@ Q/B+Biv Q7 a = 176MK-?QH2 ` /Bmb Q7 53 MK- M/ bh #?2B;?i Q7 110 MKX U#V 1M2`;v /2MbBiv 7Q` 7mM/ K2Mi H KQ/2 BM +`Qbb@b2+iBQM M/ U+V BM TH M2X U/V a1jx U2V h?2 T?QiQMB+ +`vbi Hb `2 i` Mb72``2/ 7`QK i?2 : S +?BT QMiQ bm#bi` i2 pb TQHvK2` bi KTX U7V "`Q /@# M/ `2~2+iBpBiv K2 bm`2k2mi Q7 + pbiv `2bQM M+2 rbi? Q 6 103 X U;V h?2 S* bh # Bb TQbBiBQM2/ `2H ibp2 iq i `;2i M MQ+`vbi H BM i?2 TQHvK2` }HKX Rk

n s 1.5 Q 13 10 3 V m =0.74(λ/n ) 3 n =3.4 λ = 670 0.85 0.15 Q 6 10 3 Q 30

a y(µm) 5 15 25 b 5 15 25 PL reflection 5 15 25 x(µm) NV c 100 cts/s/nm 100 cts/s/nm cavity and NV 4 2 0 d 4 2 I 0 I cb fits I c 2 2 (2) g (t ) 1 (2) g (t ) 0 620 640 660 680 700 720 1 1 0.5 0 1 0.5 0 λ(nm) 0 100 200 300 0 100 200 300 t (ns) t (ns) intensity (a.u.) e 1.4 1.2 1 0 f 1.4 1.2 1 uncoupled, τ =16.4 ±1.1 ns 0 coupled, τ =12.7 ± 1.2 ns c 0 20 40 60 t(ns) 500 0.2 I 0 I cb I c f c (λ 2 ) = 5.3,f c (λ 1 ) = 0.7 6 1064 20 100 0.5

λ 1 = 667.3 λ 2 = 643.0 Q 1 = 550 Q 2 = 610 1 2 I 0 800 I c I cb

τ 0,c = 16.4 ± 1.1, 12.7 ± 1.5 F (λ) F (λ) =I c (λ)τ 0 /I 0 (λ)τ c F (λ 1 )=2.2 F (λ 2 ) 7.0 F (λ) a 180 S d (ω, r) =C NV + C cav f c ( r ) L(ω) 2 +2C int R[e i φ f c ( r )L(ω)], C NV C cav C int L(ω) =1/(1 + i(ω ω c )/κ) ω c κ = ω c /2Q φ

a target NV b c e target NV 4 µm scanning tip x d 1 µm PL reflection 680 λ 1 665 650 λ 2 f PL λ(nm) fits 635 200 0 200 x(nm) 1 0.8 0.6 0.4 0.2 0 g experiment c f (λ, x x+ y ^ y) ^ 1 slip 200 0 200 theory 0.3 y(µm) 0 y(nm) 0.3 c ^ h f (λ, x x+ y ^ y-98 ^ o 1 nm z, 20 ) 300 0 300 x(nm) x = 3.4 f c (λ 1, r) 80 f c (λ 1, r) z = 98 ± 5 y = 70 ± 5 µ x

f c (ω, r) C NV C cav C int C NV C cav C int C int =0 f c (λ = 643, r)=5.3,f c (667, r)=0.7 S d (ω, r) f c (ω 1, r) ω 1 =2πc/λ 1 f c (ω 1, r) µ z = 98 ± 5 20 x x 190

1 10 6 80

Q 7 23

25 250 n =2.4

Q 400 65 165 175 500 400 Q

T Q 2 Tot /Q2 wg Q Q scat 8 10 6 Q Q wg 5.3 10 5 Q Q Tot 5 10 5 1.8 (λ/n) 3 Q Q scat =1 10 4 <Q wg 3.7(λ/n) 3 Q

Q Q 532 800 Q

532 g 2 (0) = 0.2 685 695 705 682

23 7 Q 0.2 5.3 23

23

Q 573 613 622 631 637 1 7 0.5 Q

F P 7

F P = 3 4π 2 ( ) λ 3 Q n V E NV µ NV 2 E max 2 µ NV 2, E NV,max µ NV λ n = 2.4 V = [ ɛ( r ) E( r ) d r] 2 /max [ɛ( r ) E( r ] ) 2 573 I res ZPL =(η cav F P + η NV ) 1 τ 0, η cav,nv τ 0

F P =0 I off res ZPL = η NV F NV τ 0. η cav = η NV Q ZPL I off res ZPL χ = η cavf P η N V = Ires 1. χ Q 3.7 (λ/n) 3 Q Q 23 7

Q 10 3

0 0

0 m s =0 0 0 300 300 20

532 594 637 310 532

500 532 594 637 0 62.5 n diamond n glass 532 m s = ±1 25 m s =0 m s =1

0 594 0 0 655 0 0 594 0 0 g 1 g 0 0 γ 0 γ 1 F C g 0,1 γ 0,1 594 0.875

594 0 γ 1 γ 0 g 1 g 0 594 0 594 µ γ 0,γ 1,g 0,g 1 594

15 t tg 1 1 P t R F C (P ) F C 0.9 µ 0 532 150 300 594 t probe = 900 11 g 1 t probe 1 t R = 240 820 0.723 ± 0.006

0.975 ± 0.007 p s =0.216 ± 0.001 m s =1 m s =0 594 m s = 1 m s =0 637 0 m s =0 m s =1 60 145 594 20 22.5 637 40 300 500 500

100 532 300 900 594 11 240 594 820 0.723 ± 0.006 900 p s =0.216 ± 0.001 ±

m s =0 m s =1 594 637 m s =0 0 m s =1 500 500 594 40 300 500 500 m s =0 0.162 ± 0.007 m s =1 0.504 ± 0.009 0 40 60 0 80 20

500 500 m s = 0 m s =1 β 0 β 1 β 0 β 1 β 0,1 β 0,1 20 β 0,1 m s =1 β 1 60 δb = π τ + ti + t R σ R 2gµ B T τ 2, g µ B τ t I t R T N τ + t I + t R σ R

σ R t R 100 532 300 900 594 11 m s =0 m s =1 60 594 135 30 637 7.1 t R σ R (t R ) = a 1+b/t 1/4 R a b t R σ R (t R ) σ R (t R ) (τ + t I + t R )/τ 2 t I 6.5 t I =1.5/p s p s =0.200 ± 0.006

σ R =1 τ 200 532 α 0,1 m s =0, 1 σ trad R = 1+ 2(α 0 + α 1 ) (α 0 α 1 ) 2 σ trad R α 0 20 = 0.238 ± 0.001 α 1 =0.154 ± 0.002 σ trad R = 10.6 ± 0.3 σ SCC R = (β 0 + β 1 )(2 β 0 β 1 ) (β 0 β 1 ) 2.

β 0,1 σ SCC R,best =2.76 ± 0.09 σr SCC (t R ) 6.5 t R σr SCC (t R ) β 0,1 t R σr SCC (t R ) t R 5 σr SCC (t R ) σr SCC (t R ) σr SCC (t R ) σ SCC R,best (t R) δb T = π τ + 2gµ ti + t R σscc R (t R ) τ 2

t R σr SCC (t R ) 6.5 5 2 2 t R = 575 900 1/2 0

Q 10 5 Q

N j λ j γ j γ NR r i p i j I ij = cp i η ij γ ij k γ ik + γ NR = cp i η ij γ ij Γ i

η ij Γ i = k γ ik + γ NR c β ij = γ ij /Γ i j Γ i =1/τ i i 0 I ij I 0j = p iη ij γ ij Γ 0 p 0 η 0j γ 0j Γ i I ij I 0j = γ ijγ 0 γ 0j Γ i = F ij Γ 0 Γ i, F ij = γ ij /γ 0j = I ij Γ i /I 0j Γ 0 i =1 F 1j = F (λ j )

a 80 40 0 b 80 cts/s/nm cts/s/nm 2 uncoupled NV uncoupled cav. 1 coupled NV/cav. fits x(nm) 200 160 120 80 c Scan over NV centre 40 2 1 40 0 620 660 700 740 λ(nm) 640 660 680 700 fit λ(nm) C int =0.6 x 1 x 2 x 2 667 643 x 1 λ 1 λ 2 λ 2

F(λ) 7.0 6 4 2 2.2 0 640 660 680 700 720 740 λ(nm) F (λ)

a.1 λ 2 pump a.2 λ 2 a.3 λ 1, y-polarized, x-polarized, y-polarized y 0 100-100 0 100 200-600 0 x(nm) 600-600 0 x(nm) 600-600 0 600 x1 x2 b c degrees λ 2 λ 1 collection from x2 collection from x1 620 640 660 680 700 720 740 λ(nm) 100 80 60 40 20 d intensity (cts/s/nm) 0 620 640 660 680 700 720 740 λ(nm) 0 90 667 643 643 667 λ 1

C int = 0.6 = 2.87 m s = 0 m s = ±1 m s = ±1 m s = ±1 m s =0 m s = ±1

(2) g (τ) 1.5 1 0.5 τ(ns) 0 40 20 0 20 40 60

Luminescence intensity (a.u.) 7 (a) 6.5 6 5.5 Luminescence intensity (a.u.) 0.135 (b) 0.13 0.125 5 0.12 4.5 4 2.7 2.8 2.9 3 ν(ghz) microwave frequency 0.115 0 200 400 600 800 t(ns) microwave pulse duration ν ν =2.77 ν m s =0 t ν =2.77 σ = g e a H = 2 a a 2 (σ z)+ig(σa aσ ),

dρ dt = i[h, ρ]+κ 2 (2aρa a aρ ρa a)+ γ 2 (2σρσ σ σρ ρσ σ)+ γ d 2 (σ zρσ z ρ) γ κ γ d σ z =[σ,σ] g, e 0, 1. da =( i dt 2 κ ) a + g σ 2 dσ =(i dt 2 γ 2 γ d) σ + g σ z a a(0) = 0,σ(0) = 1 σ z a = a c 1 = ( i 2 κ 2 ) c2 = ( i 2 γ 2 γ d) λ = c 1 +c 2 (c 1 c 2 ) 2 4g 2 λ + = c 1 +c 2 + (c 1 c 2 ) 2 4g 2 a(t) = (eλ +t e λ t )g (c1 c 2 ) 2 4g 2 σ(t) = (c 1 c 2 )(e λ t e λ +t )+ (c 1 c 2 ) 2 4g 2 (e λ t + e λ +t ) 2 (c 1 c 2 ) 2 4g 2

E (+) = γσê NV + κaê c + c.c., ê NV ê c ˆf( k, ω) E + = U F ( γσê NV + κaê c ), U F = k,ω ( ˆf( k, ω))( ˆf( k, ω) ) S(ω) 0 E + (t)e (t ) dtdt ω = ω c,κ γ d,g γ d,κ S (ω) ê NV U F ê NV +2R[ê NV U F ê c e i φ f c 1 ( r ) 1+i(ω ω c )/κ ]+ ê c U F ê c f c 1 ( r ) 1+i(ω ω c )/κ 2, F =(g( r, µ )) 2 /κγ r µ / µ ê NV U F ê c S d (ω) =C 1 +2C 2 R[e i φ f c 1 ( r ) 1+i(ω ω c )/κ ]+C 3f c 1 ( r ) 1+i(ω ω c )/κ 2,

C i C 2 /C 1 0.6 C 2 /C 1 0 PL(ω, r) e( r ) PL(ω, r) = e( r r )S d (ω, r )dl dl r PL(ω, r) = S d (ω, r) e ( r ) PL ( r ) S d (ω, r ) e ( r )

300 600 294 2 3 2 3 3 2 3 2 2 15

3 400 400 4 3 400 800 800 8 12 800 1200 1200 2 465 300 13

9 F (τ) =A + Be (τ/t 2) n e ((τ jtrev)/t dec) 2, j=0 A =0.844 ± 0.001 B =0.143 ± 0.005 n =1.72 ± 0.14 T rev = 36.48 ± 0.04µ T dec =7.47 ± 0.22µ T 2 = 201 ± 7µ 0 g 1 g 0 0 γ 1 γ 0 γ 1,0 0 τ 1 t 1 γ 1 (t R t 1 )+γ 0 t 1 t R p(n NV, odd) = tr 0 i 1 j=1 dτe (g 0 g 1 )τ g 0 t R (tr τ) (j 1) k=1 t k 0 i=1 g i 1g i 1 0 i 1 j=1 τ (j 1) k=1 τ k 0 ds j dt j PoissPDF(γ 1 τ + γ 0 (t R τ),n)

p(n NV, even) = tr 0 i 1 j=1 dτe (g 0 g 1 )τ g 0 t R (tr τ) (j 1) k=1 t k 0 i=1 (g 1 g 0 ) i i j=1 τ (j 1) k=1 τ k 0 dτ j dt j PoissPDF(γ 1 τ + γ 0 (t R τ),n) +e g 1t R PoissPDF(γ 1 t R,n) τ [0,t R ] PoissPDF(x, n) n x p(n NV, even) 0 1 0 i p(n NV, odd) = p(n NV, even) = tr 0 tr 0 dτg 1 e (g 0 g 1 )τ g 0 t R BesselI(0, 2 g 1 g 0 τ(t R τ)) g1 g 0 τ dτ t R τ e(g 0 g 1 )τ g 0 t R BesselI(1, 2 g 1 g 0 τ(t R τ)) +e g 1t R PoissPDF(γ 1 t R,n), BesselI(n, x)

875 594 8 F C T 1/g 1 (P ) 594 P T T g 1 g 0,1 g 0 /g 1 = p(nv )/p(nv 0 ) 875 8 594 875 14.5 a P/(1 + P/P sat )+dc P sat dc ap 2 /(1 + P/P sat ) P sat

594 g 0 ap 2 /(1 + P/P sat ) P sat = 134 a = 39 µ 2 g 1 ap 2 /(1 + P/P sat ) P sat = 53.2 a = 310 µ 2 γ 0 a P/(1 + P/P sat )+dc dc =0.268 a =1.65 µ P sat = 134 γ 1 a P/(1 + P/P sat )+dc a = 46.2 µ P sat = 53 γ 0,1 g 0,1

F C n thresh =[1, 2, 3] F C F C (P, t R ) n n thresh NV n<n thresh NV 0 t R n thresh =[1, 2, 3] m s =0 t I τ t R

N T = N(τ + t I + t R ) ( gµb Bτ ψ(τ) = cos π ) m s =0 i sin ( gµb Bτ π ) m s =1, g g B m s =0, m s =1 ( ) p 0 = cos 2 gµb Bτ π p 1 = 1 p 0 =sin 2 ( gµb Bτ π ). D 0 (n) D 1 (n) ψ(τ) P (n) =p 0 D 0 (n)+p 1 D 1 (n). δb S = n σ S δb = σ S S/ B = π gµ B τ σ S D 0 D 1,

p 0 = p 1 =1/2 N 1/ N σ R δb = π τ + ti + t R σ R 2gµ B T τ 2. = 2gµ Bτ π σ S S/ B σ R =1 σ R t I t R σ R σ R m s =0 m s =1 β 0 m s =0 β 1 m s =1 D 0 (n) D (n) 0 π 2gµ B =8.9 1

D D 0 σd 2 σ 2 D 0 P (n) =p 0 (β 0 D (n)+(1 β 0 )D 0 (n)) + (1 p 0 )(β 1 D (n)+(1 β 1 )D 0 (n)) σ R p 0 = p 1 =1/2 σr SCC = 2gµ Bτ σ S π S/ B S = p 0 (β 0 D +(1 β 0 ) D 0 )+(1 p 0 )(β 1 D +(1 β 1 ) D 0 ) = β ( 0 + β 1 D + 1 β ) 0 + β 1 D 0 2 2 S B = gµ Bτ π (β 0 β 1 )( D D 0 ) [ ] σs 2 = n 2 P (n) S 2 σ SCC R = n=0 = 1 4 (β 0 + β 1 )(2 β 0 β 1 )( D D 0 ) 2 + β ( 0 + β 1 σd 2 + 1 β ) 0 + β 1 σ 2 D 2 2 0 (β 0 + β 1 )(2 β 0 β 1 ) (β 0 β 1 ) 2 1+2 σ2 D /(2 β 0 β 1 )+σ 2 D 0 /(β 0 + β 1 ) ( D D 0 ) 2

σ R D (n) D 0 (n) σ SCC R (β 0 + β 1 )(2 β 0 β 1 ) (β 0 β 1 ) 2. β 0 β 1 m s =0 m s =1 σ R β 0,1 m s =0 m s =1 β 0,1 σr SCC (t R ) σ SCC R t R t R σr SCC

σr SCC σr SCC (t R ) D D 0 D (n) σ D D γ 1 t R σ SCC R (β 0 + β 1 )(2 β 0 β 1 ) 2 (β 0 β 1 ) 2 1+. (2 β 0 β 1 )γ 1 t R γ 1 t 3/4 σ SCC R σ SCC R = a 1+b/t 1/4 a =1.328 b = 39.3 a σr,best SCC

ɛ