We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a field programmable gate array, is sufficient to perform closed-loop parametric feedback cooling of the center-of-mass motion to sub-Kelvin temperatures. The translational center-of-mass motion along the optical axis of the trapped nanoparticle has been cooled by 3 orders of magnitude, from a temperature of 300 K to a temperature of $162\pm 15$ mK.

In this paper we consider the problem of tracking the state of a quantum system via a continuous weak measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency.

In this paper we show how weak measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace. Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of the differences between purification and generating entanglement.

This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the integration of stochastic master equations for the quantum system, and efficient parameter estimation methods from classical signal processing. The classical techniques use sequential Monte Carlo (SMC) methods, which aim to optimize the selection of points within the parameter space, conditioned by the measurement data obtained. We illustrate these methods using a specific example, an SMC sampler applied to a nonlinear system, the Duffing oscillator, where the evolution of the quantum state of the oscillator and three Hamiltonian parameters are estimated simultaneously.

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in postselection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using an experiment in levitated optomechanical systems as an example.

Quantum sensors based on atom interferometers can provide measurements of inertial quantities with unprecedented accuracy and precision. It has been suggested that this sea change in sensing could provide an inertial navigation capability that is comparable with current satellite based navigation systems. However, the accuracy of sensor measurements is not the only factor that limits the accuracy of inertial navigation systems. In this paper, we explore the fundamental limits to inertial navigation, and explain how quantum inertial sensors could be used to alleviate some of the problems encountered in current classical inertial navigation systems, but not to solve the fundamental instability inherent in inertial navigation methods.