Continuous measurements of small systems: Feedback control, thermodynamics, entanglement

Technological and scientific advancements over the past 30-40 years make it possible to fabricate nanometer-sized systems where fluctuations and quantum effects are important features. These systems can be controlled and measured with high accuracy, making them suitable for exploring fundamental aspects of the microscopic world. This thesis makes contributions in this direction, focusing on the theory of continuous, Markovian feedback control and stochastic as well as quantum thermodynamics.In Paper I and III, we study an implementation of Maxwell’s demon in a double quantum dot. A feedback protocol, based on charge detection, transfers electrons against an external voltage bias, without performing any net work. The protocol is studied for both classical and quantum dynamics. We characterize the electronic transport properties, explore information-to-work conversion with realistic detector models, as well as the quantum-to-classical transition.Paper II introduces a novel master equation for continuous, Markovian feedback control. This equation describes the dynamics of a quantum system and a detector with finite bandwidth. For a fast detector, the equation reduces to a Markovian master equation for the system alone. This equation can describe protocols that depend linearly as well as nonlinearly on the measured signal. For linear protocols, this equation coincides with theWiseman-Milburn equation, illustrating a compelling connection to previous work in the field.Paper IV investigates a specific feedback protocol for increasing the entanglement generation in an autonomous thermal machine. Under optimal conditions, we find that the protocol significantly increases the entanglement. The entanglement violates the CHSH inequality and can uphold quantum teleportation.Paper V presents a setup for generating maximally entangled states in autonomous thermal machines. First, we show that maximal bipartite entanglement can be generated in a system of three qubits. This is lat