We propose a scheme to generate a new kind of non-Gaussian state—the Laguerre polynomial excited coherent state (LPECS)—by using multiphoton catalysis with coherent state input. The nonclassical properties of the LPECS are studied in terms of nonclassical depth, Mandel’s parameter, second-order correlation, quadrature squeezing, and the negativity of the Wigner function (WF). It is found that the LPECS is highly nonclassical and its nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and the parameters of the unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced by increasing the catalysis photon number. In addition, we examine the effect of decoherence using the WF, which shows that the negative region, the characteristic time of decoherence, and the structure of the WF are affected by catalysis photon number and the parameters of the unbalanced BS. Our work provides general analysis on how to prepare polynomial quantum states, which may be useful in the fields of quantum information and quantum computation.

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We theoretically introduce a new kind of non-Gaussian state--Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that the normalized factor is related to the two-variable Hermite polynomials. We then investigate the nonclassical properties in terms of Mandel's Q parameter, quadrature squeezing, second correlation, and the negativity of Wigner function (WF). It is shown that all these properties are related to the amplitude of coherent state, catalysis number and unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced as catalysis number and keeps a constant for single-photon catalysis. In addition, we examine the effect of decoherence by Wigner function, which show that the negative region, characteristic time of decoherence and structure of WF are affected by catalysis number and unbalanced BS. Our work provides a general analysis about how to prepare theoretically polynomials quantum states.