ECE615_Lecture_23

ECE615_Lecture_23 - It can be shown that the motion...

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Unformatted text preview: It can be shown that the motion equations for and are equivalent to: (1) Lecture 23 Optical Bloch Equations ( 29 ( ) ( ) exp ba ba t t i t ρ σ ϖ = ⋅- ba σ σ ≡ ( 29 1 2 u iv σ =- ρ ϖ 1 2 u v u T- = ∆ - ɺ 1 2 v u v T Ew κ- = -∆- + ɺ ( 29 1 1 eq w T Ev w w κ- = --- ɺ Bloch equations consider (in the absence of relaxation processes) using (1) all damping terms are negative, therefore 1 ba w w = 1 2 ba κ μ- = ℏ ( 29 2 2 2 2 2 2 2 2 2 2 d uu vv ww u v v u v Ew w Ev u v w dt κ κ = + + = ∆ - ∆ +- = + + ɺ ɺ ɺ 2 2 2 u v w const ∴ + + = 2 2 2 1 u v w + + ≤ when 0, 1, E w u v = = - = = 2 2 2 1 u v w ⇒ + + = expectation value of the dipole moment as shown in book (2) the equation of a damped, driven harmonic oscillator, the driven term product Harmonic Oscillator Form of the Density Matrix Equations ˆ . . ba ab d c c ρ μ μ ≡ = + ɶ ɶ 2 2 2 2 2 ba ba ba d d d Ew T ϖ ϖ μ- + + = ɺɺ ɺ ɶ ɶ ɶ ɶ ℏ 1 2 eq ba w w w E d T ϖ- = -- ɺ ɶ ɶ ɺ ℏ In the equation of a damped, driven harmonic oscillator, the driven term...
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This note was uploaded on 01/10/2011 for the course ECE 615 taught by Professor Shalaev during the Fall '10 term at Purdue.

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ECE615_Lecture_23 - It can be shown that the motion...

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