Methods in Theoretical Quantum Optics

Abstract

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.

Polarization squeezing and continuous-variable polarization entanglement

“…The relations (2.1) to (2.4) are equivalent to the well-known Schwinger representation of angular momentum operators in terms of a pair of quantum harmonic oscillators [12][13][14][15]. The quantum numbers l and m of the angular momentum state are related to the quantum numbers n x and n y of the harmonic oscillators by …”

Entanglement Reciprocation between Qubits and Continuous Variables

“…Observing the identity j ih j D j0ih0jD y withD the displacement operator [9], we suggest to project the field to the vacuum after displacing it by the amplitude ÿ . After the interaction with the qubit pair, a coherent field of amplitude can be injected into the cavities, thus implementing an effective displacement operation [12].…”

“…The normalization constant is denoted by N , and the coherent state is expanded [9] such as j i P m C m jmi, where C m m e ÿ 2 =2 = m! p gives a Poissonian weight with the average photon number n 2 .…”

“…In the limit of 2 1, the Poissonian distribution is replaced by a Gaussian distribution over the variable n with mean value and variance equal to 2 [9] so that C 2 n e ÿ 2 2n n! 1 2 2 p e ÿ nÿ 2 2 =2 2 .…”

Vacuum as a less hostile environment to entanglement

“…Various types of nonclassical properties, which have their origin in quantum coherence, have been discussed for a unipartite system, particularly, in the context of quantum optics [1]. Quantum coherence in a multipartite system can give a strong correlation between particles, which cannot be explained by classical theory [2,3].…”