Statistical properties of photon-added coherent state in a dissipative channel
Liyun Hu, Hong-Yi Fan · Physica Scripta · 2009
We adopt a new approach (using the entangled state representation) to study time evolution of the mixed state in a dissipative channel (DC) with decay rate κ. We then investigate the statistical properties of the m -photon-added coherent state (PACS) in the DC, by deriving the analytical expressions of the Wigner function (WF), which turns out to be the Laguerre–Gaussian function. The criterion time for the definite positivity of WF: , valid for arbitrary m , is revealed. Time evolution of the photocount distribution is also derived analytically, which is related to two-variable Hermite polynomials. The tomogram of PACS is also calculated through the intermediate coordinate–momentum representation.