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.
Highlights
The standard model of particle physics classifies all elemental physical objects into fermions and bosons[1,2]
We started from the well-known analogy between supersymmetric quantum mechanics and the Jaynes–Cummings model to propose an extension that includes nonlinear boson processes, nonlinear dispersive interaction, and nonlinear multiboson exchange between the qubit and the boson
Our model helps realizing that the original Jaynes–Cummings model and most of its proposed extensions belong to a single Hamiltonian class
Summary
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. Quantum technologies provide multiple experimental platforms where a single pseudo-fermion and boson degrees of freedom interact; for example, two-internal levels of a neutral atom interacting with a single mode of the quantum electromagnetic field[10], those of a trapped ion interacting with a quantum center of mass vibration mode[11], a superconducting Josephson junction interacting with the quantum mode of a strip-line r esonator[12], or a quantum dot interacting with a two-dimensional photonic r esonator[13] In these realizations, we may write the SUSY exchange operators and Hamiltonian,. Some of us studied a, slightly complicated in hindsight, g eneralization[30,31,32,33,34,35] that reduces to our general scheme
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