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 OAMmeasurement 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.

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 present a fully canonical quantization scheme for the electromagnetic field in dispersive and lossy linear dielectrics. This scheme is based on a microscopic model, in which the medium is represented by a collection of interacting matter fields. We calculate the exact eigenoperators for the coupled system and express the electromagnetic field operators in terms of them. The dielectric constant of the medium is explicitly derived and is shown to satisfy the Kramers-Kronig relations. We apply these results to treat the propagation of light in dielectrics and obtain simple expressions for the electromagnetic field in the medium in terms of space-dependent creation and annihilation operators. These operators satisfy a set of equal-space commutation relations and obey spatial Langevin equations of evolution. This justifies the use of such operators in phenomenological models in quantum optics. We also obtain two interesting relationships between the group and the phase velocity in dielectrics.

Entanglement in a Twist: The strong correlations observed in quantum mechanically entangled particles, such as photons, offer potential for secure communication and quantum information processing. Leach et al. (p. 662 ) now show such strong quantum correlations between the complementary variables—angular position and orbital angular momentum—of two photons created during the parametric down-conversion process in a nonlinear crystal. This demonstration of entanglement in an angular basis establishes that angles are genuine quantum observables and can therefore be considered a resource for quantum information processing, capable of secure, high-dimension, key distribution.