Abstract
Abstract This chapter focuses on linear canonical unitary transformations of mode annihilation and creation operators, both for bosons and for fermions. The generators of such transformations (which form a Lie algebra) are introduced for the specific case of two-mode systems, and the effects of these transformations on two-mode Fock states are evaluated. Applications of linear canonical transformations to two-mode interference associated with beam splitters and the distinction between boson and fermion cases are presented, followed by a treatment of pair creation processes such as squeezing in one- and two-mode bosonic systems. Treatments of thermofields – used to map mixed thermal states of single-mode systems onto pure states of two-mode systems, which are related to the two-mode vacuum state by a linear transformation – and the Bogoliubov transformations – used in describing excitations in Bose–Einstein condensates – round off the chapter.
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