Control of motional quantum states for levitated particles

Over the past decade, great progress in the engineering of optomechanical platforms has pushed nano- and micro-meter-sized objects into the realm where quantum effects start to manifest themselves. Recently, platforms based on the optical levitation of particles have emerged that offer superior isolation from their environment while benefitting from the flexibility and tunability of all-optical manipulation. These experiments combine established methods from optomechanics with strategies from atomic physics, matterwave interferometry, and control theory to explore quantum physics at a macroscopic scale. Along with their unrivaled sensitivity, levitated nanoparticles hold promises ranging from commercial sensing applications to the search for new physics. In this research project, we aim to utilize methods from control theory to develop real-time- capable control algorithms to generate motional quantum states of an optically levitated nanoparticle in a vacuum. We estimate the center-of-mass motion of a charged particle using the information carried by scattered photons of the trapping laser. By combining our Heisenberg-limited measurements with stochastic control concepts, we introduce feedback cooling methods that can ultimately cool the particle into its quantum ground state, i.e., the lowest energy state that is allowed by quantum mechanics. Once the energy of the particle is sufficiently low, fast and reliable electro-optical control over the laser power allows us to engineer even more complex quantum states such as mechanical squeezed states. To do so, however, we will need to extend the control and estimation algorithms beyond linear feedback cooling, using optimal control tools. To implement such algorithms in real time, we will develop new signal processing hardware that uses data from the experiment and provides the optimal feedback signal to generate mechanically squeezed states. The resulting squeezed states provide plenty of opportunities with respect to quantum- enhanced sensing applications where the limitations on the achievable accuracy due to quantum mechanics are circumvented. Furthermore, squeezed states are a tool for coherent state expansion, which is essential to create superposition states, i.e., states where the particle is at different locations simultaneously. Demonstrating such states experimentally for massive particles is a big challenge and the methods and hardware developed in this project will provide a significant step towards this longstanding goal.