Algebraic analysis of non-Hermitian quadratic Hamiltonians

We study a general one-mode non-Hermitian quadratic Hamil-tonian that does not exhibit PT-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the exceptional points. We also put forward an algebraic alternative to the generalized Bogoliubov transformation that enables one to con-vert the quadratic operator into a simpler form in terms of the original creation and annihilation operators. We carry out a similar analysis of a two-mode oscillator that consists of two identical one-mode oscillators coupled by a quadratic term.& COPY; 2023 Elsevier Inc. All rights reserved.