We introduce states a^(†m) ξ〉and a^(m)ξ〉, where ξ〉is a two-mode squeezed vacuum state. We examine the properties of these states by analytic derivation. Because of the entanglement between the modes of the field, photon adding (or subtracting) for one of the modes results in interesting outcomes. For a two-mode squeezed vacuum state, the effect of annihilation of m a-photons is just the same as creation of m b-photons. Annihilation of photons of mode a (or mode b) actually increases the mean number of photons of mode a and mode b. We also calculate Mandel Q parameter, cross-correlation function and squeezing of the field.
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