  The main challenge in deterministic quantum state transfer between remote
mechanical resonators is the local decoherence and the transmission losses in
the communication channel. In the path of overcoming this limitation, here we
employ a shortcut to adiabatic passage protocol to devise a fast and reliable
evolution path between two remote mechanical modes in separate optomechanical
systems. A quantum state transfer between the two nodes is conceived by
engineering their coupling to an intermediate fiber optical channel. The
coupling pulses are operated such that the dark eigenmode of the system is
decoupled from the fiber modes and transitions to the bright modes are
compensated for by counterdiabatic drives. We show that one obtains a quantum
state transfer with high fidelity for various Gaussian states. The efficiency
is compared to that of adiabatic passage protocol in the presence of losses and
noises. Our results show that while the adiabatic passage protocol is very
sensitive to the decoherence, the shortcut to adiabaticity provides a robust
and fast quantum state transfer even for small values of the coupling strength.
The performance of both protocols are also investigated for the case of
multimode fiber through numerical and an effective single-model model which is
found by the elimination of off-resonant fiber modes. Our findings may pave the
way for using optomechanical systems in the realization of continuous-variable
Gaussian quantum state transfer.
