This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schrödinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.

We present conditions every measure of entanglement has to satisfy, and construct a whole class of "good" entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.[ S0031-9007(97) We have witnessed great advances in quantum information theory in recent years. There are two distinct directions in which progress is currently being made: quantum computation and error correction on the one hand (for a short survey see [1,2]), and nonlocality, Bell's inequalities, and purification, on the other hand [3,4]. There has also been a number of papers relating the two methods (e.g., [5,6]). Our present work belongs to this second group. Recently it was realized that the CHSH (ClauserHorne-Shimony-Holt) form of Bell's inequalities are not a sufficiently good measure of quantum correlations in the sense that there are states which do not violate the CHSH inequality, but, on the other hand, can be purified by local interactions and classical communications to yield a state that does violate the CHSH inequality [3]. Subsequently, it was shown that the only states of two two-level systems which cannot be purified are those that can be written as the sum over density operators which are direct product states of the two subsystems [7]. Therefore, although it is possible to say whether a quantum state is entangled or not, the amount of entanglement cannot easily be determined for general mixed states. Bennett et al. [5] have recently proposed a measure of entanglement for a general mixed state of two quantum subsystems. However, this measure has the disadvantage that it is hard to compute for a general state, even numerically. In this Letter we specify conditions which any measure of entanglement has to satisfy and construct a whole class of "good" entanglement measures. Our measures are geometrically intuitive.Unless stated otherwise, the following considerations apply to a system composed of two quantum subsystem of arbitrary dimensions. First, we define the term purification procedure more precisely. There are three distinct ingredients in any protocol that aims at increasing correlations between two quantum subsystems locally.Local general measurements (LGM).-These are performed by the two parties (A and B) separately and are described by two sets of operators satisfying the completeness relations P i A y i A i I and P j B y j B j I. The joint action of the two is described by P ij A i ≠ B j , which again describes a local general measurement.Classical communication (CC).-This means that the actions of A and B can be classically correlated. This can be described by a complete measurement on the whole space A 1 B which, as opposed to local general measurements, is not necessarily decomposable into a direct product of two operators as above, each acting on only one subsystem. If r AB is the joint state of subsyst...

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We describe how a quantum system composed of a cavity field interacting with a movable mirror can be utilized to generate a large variety of nonclassical states of both the cavity field and the mirror. First we consider state preparation of the cavity field. The system dynamics will prepare a single mode of the cavity field in a multicomponent Schrödinger-cat state, in a similar manner to that in a Kerr medium. In addition, when two or more cavity modes interact with the mirror, they can be prepared in an entangled state, which may be regarded as a multimode generalization of the even and odd coherent states. We show also that near-number states of a single mode may be prepared by performing a measurement of the position of the mirror. Second we consider state preparation of the mirror and show that this macroscopic object may be placed in a Schrödinger-cat-like state by a quadrature measurement of the light field. In addition, we examine the effect of the damping of the motion of the mirror on the field states inside the cavity and compare this with the effect of cavity field damping.