Creating quanta with an annihilation operator
S. S. Mizrahi, V. V. Dodonov · Journal of Physics A Mathematical and General · 2002
The asymmetric nature of the boson 'destruction' operator â and its 'creation' partner ↠is made apparent by applying them to a quantum state |ψ⟩ different from the Fock state | n ⟩. We show that it is possible to increase (by many times or by any quantity) the mean number of quanta in the new 'photon-subtracted' state â|ψ⟩. Moreover, for certain 'hyper-Poissonian' states |ψ⟩ the mean number of quanta in the (normalized) state â|ψ⟩ can be much greater than in the 'photon-added' state â†|ψ⟩. The explanation of this 'paradox' is given and some examples elucidating the meaning of Mandel's q -parameter and the exponential phase operators are considered.