Diamond platforms for nanoscale photonics and metrology
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- Σώστρατος Αλαφούζος
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1 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 Diamond platforms for nanoscale photonics and metrology. Doctoral dissertation, Harvard University. December 30, :35:42 PM EST 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 (Article begins on next page)
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18 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
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20 532 m s =0 V Q V (λ/n) 3 λ n
21 2π 15
22 2π Q n = 2.4 Q
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26 V m 1/ V m Q ΓX
27 air 0.3 light -lines PMMA e d waveguide bands bandgap X J k a// x 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 X U;V h?2 S* bh # Bb TQbBiBQM2/ `2H ibp2 iq i `;2i M MQ+`vbi H BM i?2 TQHvK2` }HKX Rk
28 n s 1.5 Q V m =0.74(λ/n ) 3 n =3.4 λ = Q Q 30
29 a y(µm) b PL reflection x(µm) NV c 100 cts/s/nm 100 cts/s/nm cavity and NV d 4 2 I 0 I cb fits I c 2 2 (2) g (t ) 1 (2) g (t ) λ(nm) t (ns) t (ns) intensity (a.u.) e f uncoupled, τ =16.4 ±1.1 ns 0 coupled, τ =12.7 ± 1.2 ns c t(ns) I 0 I cb I c f c (λ 2 ) = 5.3,f c (λ 1 ) =
30 λ 1 = λ 2 = Q 1 = 550 Q 2 = I I c I cb
31 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
32 a target NV b c e target NV 4 µm scanning tip x d 1 µm PL reflection 680 λ λ 2 f PL λ(nm) fits x(nm) g experiment c f (λ, x x+ y ^ y) ^ 1 slip theory 0.3 y(µm) 0 y(nm) 0.3 c ^ h f (λ, x x+ y ^ y-98 ^ o 1 nm z, 20 ) x(nm) x = 3.4 f c (λ 1, r) 80 f c (λ 1, r) z = 98 ± 5 y = 70 ± 5 µ x
33 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
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38 Q 7 23
39 n =2.4
40 Q Q
41 T Q 2 Tot /Q2 wg Q Q scat Q Q wg Q Q Tot (λ/n) 3 Q Q scat = <Q wg 3.7(λ/n) 3 Q
42 Q Q Q
43 532 g 2 (0) =
44 23 7 Q
45 23
46 Q Q
47 F P 7
48 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 ] ) I res ZPL =(η cav F P + η NV ) 1 τ 0, η cav,nv τ 0
49 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
50 Q 10 3
51 0 0
52 0 m s =
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54 n diamond n glass 532 m s = ±1 25 m s =0 m s =1
55 g 1 g 0 0 γ 0 γ 1 F C g 0,1 γ 0,
56 594 0 γ 1 γ 0 g 1 g µ γ 0,γ 1,g 0,g 1 594
57 15 t tg 1 1 P t R F C (P ) F C 0.9 µ t probe = g 1 t probe 1 t R = ± 0.006
58 0.975 ± p s =0.216 ± m s =1 m s =0 594 m s = 1 m s = m s =0 m s =
59 ± p s =0.216 ± ±
60 m s =0 m s = m s =0 0 m s = m s = ± m s = ±
61 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
62 σ R t R m s =0 m s = 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
63 σ R =1 τ 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 = ± α 1 =0.154 ± σ trad R = 10.6 ± 0.3 σ SCC R = (β 0 + β 1 )(2 β 0 β 1 ) (β 0 β 1 ) 2.
64 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
65 t R σr SCC (t R ) t R = /2 0
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67 Q 10 5 Q
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70 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
71 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 )
72 a b 80 cts/s/nm cts/s/nm 2 uncoupled NV uncoupled cav. 1 coupled NV/cav. fits x(nm) c Scan over NV centre λ(nm) fit λ(nm) C int =0.6 x 1 x 2 x x 1 λ 1 λ 2 λ 2
73 F(λ) λ(nm) F (λ)
74 a.1 λ 2 pump a.2 λ 2 a.3 λ 1, y-polarized, x-polarized, y-polarized y x(nm) x(nm) x1 x2 b c degrees λ 2 λ 1 collection from x2 collection from x λ(nm) d intensity (cts/s/nm) λ(nm) λ 1
75 C int = 0.6 = 2.87 m s = 0 m s = ±1 m s = ±1 m s = ±1 m s =0 m s = ±1
76 (2) g (τ) τ(ns)
77 Luminescence intensity (a.u.) 7 (a) Luminescence intensity (a.u.) (b) ν(ghz) microwave frequency 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 ),
78 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
79 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,
80 C i C 2 /C 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 )
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83 9 F (τ) =A + Be (τ/t 2) n e ((τ jtrev)/t dec) 2, j=0 A =0.844 ± B =0.143 ± n =1.72 ± 0.14 T rev = ± 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)
84 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) 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)
85 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 ) a P/(1 + P/P sat )+dc P sat dc ap 2 /(1 + P/P sat ) P sat
86 594 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
87 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
88 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,
89 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
90 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 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 β ) 0 + β 1 σ 2 D (β 0 + β 1 )(2 β 0 β 1 ) (β 0 β 1 ) σ2 D /(2 β 0 β 1 )+σ 2 D 0 /(β 0 + β 1 ) ( D D 0 ) 2
91 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
92 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 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
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