Entanglement transfer in a noisy cavity network with parity-deformed fields

We investigate the effects of parity-deformed fields on the dynamics of entanglement transfer to distant noninteracting atomic qubits. These qubits are embedded in two distant lossy cavities connected by a leaky short-length fiber (or additional cavity). The process is studied within a single-excitation subspace, the parity-deformed cavity photons allowing the introduction of static local classical fields, which function as a control. The mechanism of state transfer is analyzed in comparison to the uncontrolled case. We find that the transfer evolution exhibits an asymmetry with respect to atom-field detuning, being sensitive to the sign of the detuning. Under a linear interaction controlled by the local classical fields, we show that the entanglement distribution can be both amplified and preserved against the noise. These results motivate developments towards the implementation or simulation of the purely theoretical model employing parity-deformed fields.