By A.S.; Talmy, V. (trans.) Kompaneyets

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112) For a given light source, if g (2) (0) < 1 then the photon-number distribution P(n) has a smaller variance than the equivalent Poisson distribution, and the source is said to be sub-Poissonian and nonclassical. This effect is referred to as photon antibunching, in the sense that it is unlikely or impossible for many photons to arrive simultaneously at the detector. For incoherent (chaotic) light the opposite is true, and the twofold detection probability is instead enhanced with respect to that of statistically independent particles, giving g (2) > 1.

N m m = |n 1 , n 2 , . . n m = ⎣ j=1 ⎤ 1 aˆ † n j! 102) where |0 ≡ |0 0 ⊗ |0 1 . . |0 n = |00 . . 0 is the m-mode vacuum. These states p form an orthonormal basis for the Hilbert space Hm of p photons in m modes, and an arbitrary pure superposition state can therefore be written as d |ψ = ⎡ bi |n 1,i , n 2,i . . n m,i = ⎣ i m d bi i j=1 ⎤ 1 aˆ † ni j ! 103) where d is the Hilbert space dimension and i |bi |2 = 1. Many experiments in quantum optics deal with a large number of modes and a fixed number of photons.

68 is only satisfied only for a discrete subset of spatial distributions E0 , referred to as waveguide modes. ), but for a simple one-dimensional model we can find an analytic solution. Consider for example the refractive index profile shown in Fig. 78) n = n2 |x| ≥ a. 80) in the core and cladding respectively, where γ 2 and κ2 are real parameters which depend on both on the structure and material of the waveguides, and on the wavelength of incident light. 83) where G i are constants which depend on the waveguide parameters and the optical wavelength.

### A course of theoretical physics, vol.1: fundamental laws by A.S.; Talmy, V. (trans.) Kompaneyets

by Paul

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