Squeezed Operator And Squeezed State In Quantum Optics

Quantum optics is a subject in studying the coherence and the quantum statistical properties of radiation field, as well as the quantum characters of light interacting with matter. Squeezing effects, due to the quantum fluctuation of one quadrature phase smaller than that in coherent state, can be used in optical communication and other fields. Therefore, squeezed operators and squeezed states have been important topic since 1970s due to their wide applications in optical communication and precise measurement in quantum optics. Many attempts have been made to find new squeezed states and new form of squeezing operators so that new experimental implementation could be proposed. The thesis is divided roughly into two parts. In the first part, we introduce a linear, canonical transformation of the fundamental field operators a and a ?that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding a nonlinear function of any of fundamental quadrature operators X and P to the linear transformation, thus making the original Bogoliubov transformation quadrature dependent. These nonlinear quadrature-dependent Bogoliubov transformations can in fact be constructed by the combination of two unitary transformations, a quadrature-dependent displacement followed by the standard squeezed transformation. Such decomposition turns a nonlinear problem into an essentially linear one so that we are able to express explicitly the mean values and deviations of the quadrature operators and the photon variables under the multiphoton states in terms of those quantities averaged over the standard squeezed states involving only the quadrature-independent Bogoliubov transformation. The results greatly facilitate calculations of the properties and the quantities related to the canonical nonlinear quadrature-dependent Bogoliubov transformations because of the following two reasons. One is nonlinear problems have been reduced to linear ones, another is the calculations have been transformed into those involving only the standard squeezed state. In the next part, we find a new N-mode squeezing operator for the N-mode quadratures exhibiting the standard squeezing;,the corresponding squeezed state vacuum in N-mode Fock space is derived by virtue of the technique of integration within ordered product of operators. The entanglement involved in such a state is explained. The optical network for producing the N-mode squeezed state is proposed. Our results will be helpful for understanding the squeezed operator and squeezed state in quantum optics.