Amplification of bosonic interactions through squeezing in the presence of decoherence

We consider the amplification of bosonic interactions through parametric control that implements squeezing along orthogonal quadratures. We show that bosonic interactions described by certain classes of quadratic and quartic Hamiltonians can be enhanced in this way while simultaneously overcoming noise and decoherence. In general, the amplification method enhances both desired and undesired interactions present in the system. Depending on the case, however, detrimental processes can be less amplified than the desired couplings. We leverage this observation to improve the fidelity for preparing Bell-type entangled states between two bosonic modes in the presence of noise and losses. We also investigate noise models for which the protocol either fails or partially achieves a loss-tolerant state preparation speedup. Our work facilitates faster preparation of complex quantum states and implementation of entangling gates in the presence of decoherence mechanisms.