Chapter 5 considers the case of diffusive continuous measurements, where the measurement outcomes and quantum state dynamics are analogous to a Brownian noise process. We motivate this type of measurement by considering the example of a double quantum dot system being measured by a quantum point contact. The intrinsic shot noise of the measurement naturally brings about an effective time-continuous measurement. A second example of a superconducting circuit made from Josephson junctions readout with a microwave frequency electromagnetic wave is also discussed in detail. The mathematics of quantum trajectory theory is then pedagogically built up, resulting in the stochastic Schrodinger equation, the stochastic master equation, and the stochastic path integral. We also discuss experimental data and its comparison with this theoretical formalism. These experiments allow us to peer into the inner workings of wavefunction collapse, giving an empirical handle on the many philosophical issues that arise in quantum measurement.

This first chapter gives an introduction to the book and guides the reader through much of the history of the field of quantum mechanics, focusing on what we view as the most important episodes in the field. We discuss the essential properties of quantum mechanics and how they have been reimagined in the decades that followed the era of the founders.

Experimental chapter that presents experimental devices that allow us to detect individual quantum systems and observe quantum jumps occurring at random times. Described: superconducting single photon detectors, detection of arrays of ions and atoms, the shelving technique that allows us to measure the quantum state of the single atom, state selective field ionization of single Rydberg atoms, detection of single molecules on a surface by confocal microscopy, articial atoms in circuit quantum electrodynamics (cQED)