This book provides a firm grounding in those techniques needed to derive analytic solutions to relevant model problems. The book begins with a brief review of the mathematical foundations of quantum theory, especially those relevant to the description of atoms and optical fields and their coherent interactions. The following chapters treat the operators and states required, the rules for manipulating these, and the techniques commonly employed for calculating their statistical properties. A chapter is devoted to the important topic of dissipative processes and to the effects that these have on quantum optical systems. The final chapter discusses dressed states, that is, the eigenstates of interacting systems, including those that are dissipative. Fourteen short appendices summarize the more important topics in mathematics required in the book or present the lengthier calculations not included in the chapters. A selective bibliography is given at the end of the book.

We demonstrate the transfer of information encoded as orbital angular momentum (OAM) states of a light beam. The transmitter and receiver units are based on spatial light modulators, which prepare or measure a laser beam in one of eight pure OAM states. We show that the information encoded in this way is resistant to eavesdropping in the sense that any attempt to sample the beam away from its axis will be subject to an angular restriction and a lateral offset, both of which result in inherent uncertainty in the measurement. This gives an experimental insight into the effects of aperturing and misalignment of the beam on the OAM measurement and demonstrates the uncertainty relationship for OAM.

We propose an interferometric method for measuring the orbital angular momentum of single photons. We demonstrate its viability by sorting four different orbital angular momentum states, and are thus able to encode two bits of information on a single photon. This new approach has implications for entanglement experiments, quantum cryptography and high density information transfer.

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We examine the optical helicity, the optical spin and the ij-infrazilches in electromagnetic theory and show that these conserved quantities can be combined to form a new description of the angular momentum associated with optical polarization: one that is analogous to the familiar description of optical energy and linear momentum. The symmetries of Maxwell's equations that underlie the conservation of our quantities are presented and discussed. We explain that a similar but distinct set of quantities, Lipkin's zilches, describe the 'angular momentum' of the curl of the electromagnetic field, rather than the angular momentum of the electromagnetic field itself. References 15

The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.