摘要： In continuation of previous papers where the addition of photons into the two-mode entangled quantum states was studied, we proposed a scheme to establish and generate photon-added ‘entangled Barut–Girardello coherent states’ (PAEBGCSs), by applying photon creation operators on the two-mode EBGCSs, where the latter is introduced by Hach et al. (JOSA B 35:2433, 2018), as a new class of quantum states connected to the simple harmonic oscillator and generated through a Mach–Zehnder interferometer, and the dynamics of their entanglement is analyzed in details. In addition, the EBGCSs include strong non-classical properties; then, to gain insight into the effectiveness of photon addition to them and comparing with the case already discussed as the photon-added entangled Klauder–Perelomov coherent states, we present a general analysis of non-classical properties such as photon statistics and squeezing and photon number distribution. We also derive the concurrence measure to quantify the entanglement of these states and look for conditions that provide information on whether these become maximally entangled. We show that the photon addition plays an important role in non-classical effects, and this operation can be applied to enhance the entanglement of the PAEBGCSs. For instance, entanglement preserving against quantum polarization is occurred by adding photons to the EBGCSs. Finally, an experimental procedure for generating the PAEBGCSs in the framework of cavity quantum electrodynamics is established.