  We investigate the effects of parity-deformed radiation fields on the
dynamics of entanglement transfer to distant noninteracting atom qubits. These
qubits are embedded in two separated lossy cavities connected by a leaky fiber,
which acts as a cavity buffer with delocalized modes. 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.
