3 Rb 1
1 4 1.1 4 1. 4 5.1 5. 5 3 8 3.1 8 4 1 4.1 External Cavity Laser Diode: ECLD 1 4. 1 4.3 Polarization Beam Splitter: PBS 13 4.4 Photo Diode: PD 13 4.5 13 4.6 13 5 Rb 14 6 15 6.1 ECLD 15 6. 15 6.3 16 6.4 16
7 17 A 18 B C LS 1 D Hyperfine Structure E 4 3
1 1.1 197 1. Rb 4
.1 J =, ± 1 F =, ± 1 J J = F F = g = e g = e. 1 Torr 5Torr 3 E t E t h (..1) (..1) E E = h (..) (..1) (..) 1 (..3) π t 5
τ γ τ 1 = L( ) 1 γ π L ( ) = (..4) γ 4π ( ) + = Full Width of Half Maximum: FWHM γ = (..5) π θ 1 + cosθ (..6) c (3..6) c = cosθ (..7) 1 = cosθ f ) m z + d z z z ( z 6
f ( = z ) π m k B T 1/ m z exp kbt (..8) k B T z (..8) m G( ) = exp c (..9) k BT = FWHM 1/ kbt ln = (..1) c m 7
3 3.1 MHz ~ GHz MHz ~ GHz Rb Fig3.1 Fig3.1 1 8
Fig3. Fig3.. Fig3. 1 N1 N N N Fig3.3 Fig3.3 9
4 4.1 External Cavity Laser Diode: ECLD Laser Diode: LD GaAs Fig4.1 h W g < h < W W (4.1.1) fc fv Wg W fc W fv W < W W (4.1.1) h g fc fv h ' Fig4.1 1
ECLD ECLD LD Littrow LD Littman-Metcalf Fig4. Fig4.3 Littrow Littman-Metcalf θ θ m d λ 1 ( θ θ ) mλ d sin 1 + sin = (4.1.) Fig4. Fig4.3 Littrow Fig4. Littrow LD 78nm d=1/18mm Fig4.4 78nm (4.1.) Littrow 1 45 1 LD PZT LD LD 11
LD PZT LD 8% mw khz Fig4.4 4. / /4 / /4 Fig4.5 Fig4.5 x y E E lin_ red lin_ blue = E xˆ sin( ωt + kz+ φ = E yˆ sin( ωt + kz+ φ lin_ red ) lin_ blue ) (4..1) Fig4.5 k xˆ yˆ 1
Fig4.5 E E lin_ red lin_ blue = E xˆ sin( ωt kz+ φ) + E = E xˆ sin( ωt + kz+ φ) + E yˆ sin( ωt kz+ φ + π / ) yˆ sin( ωt + kz+ φ π / ) (4..) x y 4.3 Polarization Beam Splitter: PBS PBS Fig4.6 4.4 Photo Diode: PD Fig4.6 LD PD 4.5 85Rb 87 Rb Rb Rb 4.6 1 LD 6~7 13
5 Rb Fig5.1 S+1 L =,1,,3, L = S, P, D,... n L Fig5.1 Rb 795nm D1 78nm D J Fig5. 14
6 6.1 ECLD ECLD LD PZT 1 1mA LD PZT 1V PZT 6. Fig6.1 PZT 87Rb 78.47nm 78.34nm 85 Rb 78.44nm 78.38nm Fig6.1 15
6.3 FWHM ECLD 6.4 78.47nm 6.4 5V 5 6.3 16
7 ECLD 3 17
A + t x( t) γ x( t) + ω x( ) = (A.1) ω k m γ t ( t x t) = x e cos( ω ) (A.) ω I(ω) (A.) 1 i ω e ω t x( t) = A dω π ( ) (A.3) 1 + iωt 1 A( ω) = x( t) e dt = π π = x 8π i 1 + ( ω ω ) + γ i( ω ω ) 1 + + γ x e γ t cos( ω t) e iωt dt (A.4) ( ) I(ω) A( ω) A * ( ω ) ω ω << ω ω + ω C I ( ω ω ) = (A.5) ( ω ω ) + ( γ ) C 18
L( ω ω I L ( ω ω ) dω 1 ) = I( ω ω) = 1 γ L ( ω ω) = (A.6) π ( ω ω ) + ( γ ) γ = (A.7) π (3..5) τ τ γ ~ h (A.3) 19
B L = r p ( i ) L = r h (B.1) L 1 1 L = h sin θ (B.) sin θ θ θ sin θ ϕ Y L Y ( L +1) h Y = L (B.3) ( ) L L L +1 L L = L( L +1)h (B.4)
C LS LS J L S J = L + S (C.1) L S L S J J J = L + S, L + S 1,, L S (C.) + 1 S ( S L) 1 + L ( S > L) H ˆ = ξ( L S) (C.3) FS ξ L S J = L + S ˆ J S L H FS = ξ (C.4) J J Ĥ (.1.3) J, L, S > fs ˆ ξ h < J, L, S H FS J, L, S >= L [ J ( J + 1) S( S + 1) L( + 1) ] (C.5) 1
D Hyperfine Structure F J I F = J + I (D.1) J I J I F F F = J + I, J + I 1,, J I (D.) + 1 I ( I J ) +1 J ( I > J ) k Hˆ ( ) HFS = k Hˆ HFS (D.3) k k F, J, I > k < F J I Hˆ HFS F J I >= < F J I Hˆ ( ),,,,,, F, J, I > HFS k (D.4) k = 1 I 1 J 1 ˆ ) (1 H HFS = A( I J) (D.5)
A k = I 1 1 J ˆ () H HFS 6 = B ( I J ) + 3I J I( I + 1) J( J + 1) I(I 1)J (J 1) (D.6) B,... k = 3,4,5 k 3 ˆ 6K + 3K I ( I + 1) J( J + 1) < F, J, I HHFS F, J, I >= AK + B I (I 1) J(J 1) (D.7) 1 K = [ F ( F + 1) I( I + 1) J ( J + 1) ] (D.8) (D.7) 1 I 1 J 1 I J =1 1 3
E M J M J = J, J 1,, J (E.1) J +1 W ze FS ξ h = W FS µ J H ex [( J( J + 1) L( L + 1) S( S + 1) )] + µ B M J g J H ex (E.) µ M g g B g J ( J + 1) + S( S + 1) L( L + 1) J( J + 1) J J g J = 1+ (E.3) J H ex µ J µ J = µ B g J J (E.4) 4