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arXiv:quant-ph/0108125 · Physics Letters A

Completeness of photon-added squeezed vacuum and one-photon states and of photon-added coherent states on a circle

C. Quesne

Published Oct 1, 2001• 17 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(01)00554-0

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We show that the photon-added squeezed vacuum a m S ( z )|0 and the photon-added squeezed one-photon state a m S ( z )|1 , where m is a non-negative integer, may be regarded as even and odd nonlinear coherent states, respectively. To achieve this, we derive an operator-valued function f ( N , m ) of the number operator N = a a such that a m S ( z )| i ( i = 0,1) are eigenstates of f ( N , m ) a 2 . Based on this, and using the unified method developed by Shanta et al , we find that a m S ( z )| i can be equivalently expressed in exponential forms. The eigenstates of f ( N ,- m ) a 2 are also constructed and their nonclassical features are studied in detail.
We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, displaced photon-number states, and coherent phase states. Combining a mode prepared in such a state and a mode prepared in a photon-number state, the state of the mode in one of the output channels of the beam splitter ``collapses'' to a photon-added state, provided that no photons are detected in the other output channel. We present analytical and numerical results, with special emphasis on photon-added coherent and squeezed vacuum states. In particular, we show that adding photons to a squeezed vacuum yields superpositions of quantum states which show all the typical features of Schrödinger-cat-like states.