Decoherence effects in quantum nondemolition measurement induced entanglement between Bose-Einstein condensates

We study the robustness of quantum nondemolition (QND) measurement-induced entanglement between Bose-Einstein Condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach-Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement, and correlation criteria. Our analysis does not use the Holstein-Primakoff approximation and is capable of modeling long light-atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than $ 1/\sqrt{N}$, where $ N $ is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show remarkable robustness that makes the scheme promising for various quantum information applications.