Can reactive coupling beat motional quantum limit of nano waveguides coupled to microdisk resonator

Dissipation is generally thought to affect the quantum nature of the system in an adverse manner, however we show that dissipatively coupled nano systems can be prepared in states which beat the standard quantum limit of the mechanical motion. We show that the reactive coupling between the waveguide and the microdisk resonator can generate the squeezing of the waveguide by injecting a quantum field and laser into the resonator through the waveguide. The waveguide can show about 70--75% of maximal squeezing for temperature about 1--10 mK. The maximum squeezing can be achieved with incident pump power of only 12 $\mu$W for a temperature of about 1 mK. Even for temperatures of 20 mK, achievable by dilution refrigerators, the maximum squeezing is about 60%.