Binomial States of Light Revisited
Antonio Vidiella-Barranco1996, Coherence and Quantum Optics VII
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Abstract
The single mode binomial states of the quantized electromagnetic field are defined, in terms of the number state basis In) as1: (1) where The probability of ocurrence of m photons, is a binomial distribution, Each photon has a probability p of being emitted, having M independent ways of doing it. It is interesting to note that if p → ∞ and M → such that pM = α constant, ∣p, M 〉 → ∣α〉 where ∣α〉 is a coherent state. If p → 1, then ∣p, M〉(number state having M photons). Therefore, the binomial states could allow a continuous interpolation betweeen fundamentally different quantum-mechanical states. Their generation could be in principle accomplished in a. system containing N 2 molecules mixed with CO 2 1 , as well as in a free electron laser2.
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