Creating quanta with "annihilation" operator

Abstract

An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner ${\hat{a}}^{†}$ is made apparent by applying them to a quantum state $|\psi >$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|\psi >$. Moreover, for certain `hyper-Poissonian' states $|\psi >$ the mean number of quanta in the (normalized) state $\hat{a}|\psi >$ can be much greater than in the `photon-added' state ${\hat{a}}^{†}|\psi >$. 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.

10 pages, LaTex, an extended version with several references added and the text divided into sections; to appear in J. Phys. A

References in corpus (2)

• Quantum-optical catalysis: generating "Schroedinger kittens" by means of linear optics
• Completeness of photon-added squeezed vacuum and one-photon-states and of photon-added coherent states on a circle

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