A new optical field generated as an output of the displaced Fock state in an amplitude dissipative channel**Project supported by the National Natural Science Foundation of China (Grant Nos. 11174114 and 11175113)and the Natural Science Foundation of Wuxi Institute of Technology of China (Grant No. 4013012931).

Abstract

We propose a new optical field and show that such an optical field can be generated as an output of a displaced Fock state in an amplitude dissipative channel. We derive new generating function formulas and binomial formula involving two-variable Hermite polynomials to reach this result. The photon number average in this new optical field is which indicates that controlling the photon number can be realized by adjusting the value of m or |α|2 or κ. The time evolution law of displaced Fock state in a thermo reservoir is thus revealed.