Abstract
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.
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