Measurement-based preparation of non-Markovian and multimode mechanical states

Nanomechanical resonators are a key tool for future quantum technologies such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature non-classical states is a major outstanding challenge. Here, we explore the use of measurement-based state conditioning to achieve this. We demonstrate conditional cooling of a nanomechanical resonator that has non-Markovian decoherence, and show theoretically that the non-Markovianity makes quantum squeezing significantly easier to achieve. We further show that collective measurement of multiple resonator modes improves the quality of state preparation. This allows us to achieve collective thermomechanical squeezing, in experiments that go beyond the validity of the rotating-wave approximation. Our modelling shows that non-Markovianity and multimode conditioning can both enable room temperature quantum squeezing with existing technology. Together, our results pave the way towards realising room temperature quantum nanomechanical devices and towards their application in quantum technology and fundamental science.