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【導(dǎo)讀】..)ρρρργγ(1221???
【正文】 mine N2 x’s in terms of the N(N1) relaxation coefficients g and the N(N1)/2 pure dephasing parameters Γ~There are (N23N)/2 conditions on the relaxation parameters。 they are not independent! BohmAharanov–type Effects “ Changes in a system A, which is apparently physically isolated from a system B, nevertheless produce phase changes in the system B.” We shall show how changes in A – a subset of energy levels of an Nlevel atomic system, produce phase changes in energy levels belonging to a different subset B , and quantify these effects. Dissipative Terms Orthonormal basis: Population Relaxation Equations (g??? Phase Relaxation Equations knknHi rrr ? G??? ],[?kknknknnnkknnnnn Hi rgrgrr ???????? ],[?},...2,1:{| Nnn ??Quantum Liouville Equation (Phenomological) Incorporating these terms into a dissipation superoperator LD Writing r(t? as a N2 column vector V? Nonzero elements of LD are (m,n)=m+(n1)N rr VLLV DH )( ???)(],[ rrr DLHi ????Liouville Operator for a ThreeLevel System Threestate Atoms 1 3 2 1 g23 g12 g13 3 2 g12 g32 Vsystem Ladder system 3 2 g21 g23 Lsystem 1 Decay in a ThreeLevel System ?????????G?G???????11212212211222121121ρ)tγ1(ρtγρtρtρ)tγ1(ρtγ)(eeeeeetrTwolevel case In above choose g21=0 and G=1/2 g12 which satisfies 2level constraint )21γ12γ(2/1 ??G???????????????????3332312322212/13122/22)1(11)(rrrrrgrgrrgrgrrtetetetetAnd add another level all new g=0 . “Eigenvalues” of a Threelevel System Phase Decoherence in ThreeLevel System ????????????G?G??3332312322212/13122/11)(rrrrrrrrrrtetet“Eigenvalues” of a Threelevel System Pure Dephasing Time (units of 1/G) Three Level Systems FourLevel Systems Constraints on FourLevel System
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