lecture16

lecture16 - LIGHT-MATTER INTERACTION Two-level atom in an...

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Two-level atom in an optical resonator hv o = E 2 -E 1 Three forms of interaction: Spontaneous emission Absorption Stimulated emission LIGHT-MATTER INTERACTION Book: 13.3 E 2 E 1  f N 2 N 1 Density of photon states
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Rate equations of isolated two-level system pumped by a light source Isolated two-level system: N 1 +N 2 =N t Interaction with light Define (population inversion) Then 2 22 1 .. . () dN Spon E Stim E Absor dt AN t BN t f BN t f   ) t ( N ) t ( N ) t ( N 1 2 )) t ( N N ( ) t ( N )) t ( N N ( ) t ( N t 2 1 2 t 2 1 1 E 2 , N 2 E 1 , N 1  f Book: 14.2
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Differential equation in N(t) Solution No pumping: Spontaneous lifetime of states in E 2 : = 1/A t AN ) t ( N ) f B 2 A ( dt ) t ( N d f B 2 A AN e ] f B 2 A AN ) 0 ( N [ ) t ( N t t ) f B 2 A ( t ) t ( N N ) t ( N , e ) 0 ( N ) t ( N 2 t 1 At 2 2
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Light on Light off Light on and then off Conclusion: No two-level system can be pumped into population inversion
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Ruby laser Excited level Metastable level Ground level Pumping is from E 1 to E 3 (determined by external light source) Lasing is from E 2 to E 1 (determined by optical cavity) hf pumping E 3 , N 3 E 2 , N 2 E 1 , N 1 THREE-LEVEL SYSTEM Book: 14.2
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31 3 32 3 1 3 P 3 21 2 32 3 1 2 L 2 21 2 31 3 2 1 L 1 3 P 1 N N ) N N ( A dt dN N N ) N N ( A dt dN N N ) N N ( A ) N N ( A dt dN ) f ( B A P 13 P ) f ( B A 12 L Pumping transition probability Lasing transition probability Isolated three-level system: N 1 +N 2 +N 3 =N t = constant
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Systems in steady state, d/dt=0 1. Necessary condition for population inversion (P.I.) ( N 2 > N 1 ): 3 1 3 31 32 13 3 2 2 2 21 0 (1 / ) ) / 0 ) P P L L dN AN N dt A N dN N dt A   21 32 32 21 3 21 21 3 11 1 1 () ) P tP A NN NA   32 21 For P.I. is not possible
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2. Pumping required for P. I. Minimum pumping needed for P. I. 31 32 3 21 32 21 3 P 1 1 1 , 1 1 1 1 A ) 1 ( 1 ~ 1 1 1 1 A 31 32 21 21 32 21 3 Pm small Ruby laser t 21 ~3 ms t 31 ~3.3 ms t 32 ~50 ns
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THREE-LEVEL SYSTEM
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% of useful transitions, E 3 E 2 % of wasteful transitions, E 3 E 1 Efficient system: 32 31 31 31 32 32 ) / 1 ( ) / 1 ( / 1 32 31 32 31 32
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lecture16 - LIGHT-MATTER INTERACTION Two-level atom in an...

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