**10. References**


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Jeong Ryeol Choi

*Republic of Korea*

**Nonclassical Properties of Superpositions of**

**Electromagnetic Fields in Time-Varying Media**

In spite of remarkable advance of quantum optics, there would be many things that are yet to be developed regarding the properties of light. One of them is the behavior of light propagating or confined in time-varying media. If the characteristic parameters of medium such as electric permittivity, magnetic permeability, and electric conductivity are dependent on time, the medium is classified as time-varying media. After the publication of a seminal paper by Choi and Yeon (Choi & Yeon, 2005), there has been a surge of renewed research for electromagnetic field quantization in time-varying media and for the properties of corresponding quantized fields (Budko, 2009; Choi, 2010a; Choi, 2010b). Some important examples that the theory of optical wave propagation in time-varying media is applicable are magnetoelastic delay lines (Rezende & Morgenthaler, 1969), wave propagation in ionized plasmas (Kozaki, 1978), the modulation of microwave power (Morgenthaler, 1958), and novel imaging algorithms for dynamical processes in time-varying physical systems (Budko, 2009). To study the time behavior of light rigorously, it may be crucial to quantize it. The purpose of this chapter is to analyze nonclassical properties of superpositions of quantum states for electromagnetic fields in time-varying linear media. The methods for quantization of a light propagating in free space or in transparent material is well known, since each mode of the field in that case acts like a simple harmonic oscillator. However, the quantization procedure for a light in a time-varying background medium is somewhat complicate and requires elaborate technic in accompanying mathematical treatments. One of the methods that enable us to quantize fields in such situation is to introduce an invariant operator theory (Lewis & Riesenfeld, 1969) in quantum optics. The invariant operator theory which employs Lewis-Riesenfeld invariants is very useful in deriving quantum solutions for time-dependent Hamiltonian systems in cases like this. The light in homogeneous conducting linear media which have time-dependent parameters will be quantized and their quantum properties will be investigated on the basis of invariant operator theory. The exact wave functions for the system with time-varying parameters will be derived in Fock, coherent, and squeezed states

For several decades, much attention has been devoted to the problem of superposed quantum states (the Schrödinger cat states) of an optical field (Choi & Yeon, 2008; Ourjoumtsev et

**1. Introduction**

in turn.

**Coherent and Squeezed States for**

*Department of Radiologic Technology, Daegu Health College,*

*Yeongsong-ro 15, Buk-gu, Daegu 702-722*

