Appendix A: Semiclassical approximation

Covering some of the most exciting trends in quantum optics - quantum entanglement, teleportation, and levitation - this textbook is ideal for advanced undergraduate and graduate students. The book journeys through the vast field of quantum optics following a single theme: light in media. A wide range of subjects are covered, from the force of the quantum vacuum to astrophysics, from quantum measurements to black holes. Ideas are explained in detail and formulated so that students with little prior knowledge of the subject can follow them. Each chapter ends with several short questions followed by a more detailed homework problem, designed to test the reader and show how the ideas discussed can be applied. Solutions to homework problems are available at www.cambridge.org/9780521869782.

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems.State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function.It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

This book explains what quantum states of light look like. Of special interest, a single photon state is explained by using a wave picture, showing that it corresponds to the complementarity of a quantum. Also explained is how light waves are created by photons, again corresponding to the complementarity of a quantum. The author shows how an optical wave is created by superposition of a "vacuum" and a single photon as a typical example. Moreover, squeezed states of light are explained as "longitudinal" waves of light and Schrödinger's cat states as macroscopic superposition states.

As part of the Physics 2010 decadal survey project, the Department of Energy and the National Science Foundation requested that the National Research Council assess the opportunities, over roughly the next decade, in atomic, molecular, and optical (AMO) science and technology. In particular, the National Research Council was asked to cover the state of AMO science, emphasizing recent accomplishments and identifying new and compelling scientific questions. Controlling the Quantum World, discusses both the roles and challenges for AMO science in instrumentation; scientific research near absolute zero; development of extremely intense x-ray and laser sources; exploration and control of molecular processes; photonics at the nanoscale level; and development of quantum information technology. This book also offers an assessment of and recommendations about critical issues concerning maintaining U.S. leadership in AMO science and technology.

Quantum information describes the new field which bridges quantum physics and information science. The quantum world allows for completely new architectures and protocols. While originally formulated in continuous quantum variables, the field worked almost exclusively with discrete variables, such as single photons and photon pairs. The renaissance of continuous variables came with European research consortia such as ACQUIRE (Advanced Coherent Quantum Information Research) in the late 1990s, and QUICOV (Quantum Information with Continuous Variables) from 2000OCo2003. The encouraging research results of QUICOV and the new conference series CVQIP (Continuous Variable Quantum Information Processing) triggered the idea for this book. This book presents the state of the art of quantum information with continuous quantum variables. The individual chapters discuss results achieved in QUICOV and presented at the first five CVQIP conferences from 2002OCo2006. Many world-leading scientists working on continuous variables outside Europe also contribute to the book.

This book is an up-to-date introduction to the quantum theory of measurement. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neuman, and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as "squeezed light," single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book begins with a brief introduction to the relevant theory and goes on to discuss all aspects of the design of practical quantum measurement systems.