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Abstract
We present a general qubit-boson interaction Hamiltonian that describes the Jaynes–Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes–Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.
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1 CONACYT-Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, Mexico (GRID:grid.450293.9) (ISNI:0000 0004 1784 0081)
2 CSIC-Universidad de Zaragoza, Zaragoza, Instituto de Nanociencia y Materiales de Aragón (INMA) and Departamento de Física de la Materia Condensada, Zaragoza, Spain (GRID:grid.11205.37) (ISNI:0000 0001 2152 8769)
3 Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, Mexico (GRID:grid.450293.9) (ISNI:0000 0004 1784 0081)
4 Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Monterrey, Mexico (GRID:grid.419886.a) (ISNI:0000 0001 2203 4701)