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Download Quantum optics : including noise reduction, trapped ions, by Miguel Orszag PDF

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By Miguel Orszag

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Additional resources for Quantum optics : including noise reduction, trapped ions, quantum trajectories, and decoherence ; with 92 problems with hints for solutions

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1). 24) = μβ − νβ ∗ = α. 26) a cosh r − a† exp(iθ) sinh r | 0 + | α |2 = sinh2 r+ | α |2 . Finally, using a similar procedure, one can verify that a2 sq = α2 − cosh r sinh r exp(iθ) . 28) 2 + exp(iφ)(a† + α∗ − a† ) S(ξ) | 0 1 2 = 0 | S † (ξ) exp(−iφ)a + exp(iφ)a† S(ξ) | 0 4 = 1 exp(−2iφ) ξ, 0 | a2 | ξ, 0 + exp(2iφ) ξ, 0 | a†2 | ξ, 0 4 +1 + 2 ξ, 0 | a† a | ξ, 0 . We take θ = 2φ, thus getting ΔX12 sq 1 1 + 2 sinh2 r − 2 cosh r sinh r 4 e−2r = . 29) Similarly e2r . 4 If we now go back to the original quadratures, we readily find ΔY12 (ΔX)2 sq (ΔY )2 sq sq = θ 1 exp(−2r) cos2 + exp(2r) sin2 4 2 θ 1 = exp(−2r) sin2 + exp(2r) cos2 4 2 = θ 2 θ 2 , .

18 2. 5 Decay Between Levels If we consider the spontaneous emission between the two levels (Fig. 1), then the upper state will decay as d ρaa = −γρaa . 39) dt On the other hand, this event will increase the population in level b, so d ρbb = γρbb . 40) dt The calculation of γ comes from a quantum electrodynamical theory called the Wigner–Weisskopf Theory, that will be covered in a later chapter. It involves the interaction of an atom with an infinite number of harmonic oscillators, at zero temperature, that is in the vacuum state.

43) γ2 . 43) is illustrated in the Fig. 3. We notice that the oscillations occur when the Rabi frequency ν is much bigger than the damping γ. References Fig. 3. 1. 35). References 1. : Lasers, Theory and Applications. Plenum Press, NY (1981) 2. : The Quantum Theory of Light. Clarendon Press, Oxford (1983) 3. : Elements of Quantum Optics. Springer Verlag, Berlin (1990) 4. : Lasers in Applied and Fundamental Research. : Foundations of Laser spectroscopy. : Introduction to Quantum Optics. Gordon and Breach, London (1973) 3.

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