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arXiv:2010.13867 · Scientific Reports

Underlying SUSY in a generalized Jaynes–Cummings model

F. H. Maldonado-Villamizar, Carlos A. González-Gutiérrez, L. Villanueva-Vergara, B. M. Rodríguez-Lara

Published Aug 13, 2021• 15 citations

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.

DOI: 10.1038/s41598-021-95259-1

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The aim of this work is to define and investigate the generalized Jaynes-Cummings (JC) Hamiltonian by means of supersymmetric (SUSY) quantum mechanics methods. We have considered trigonometric and hyperbolic Pöschl-Teller (PT) potentials as two natural ingredients to modify the standard JC model. We show that these generalized JC Hamiltonians have a list of characteristics in common with the JC Hamiltonian, for example: matrix intertwining, excitation number symmetry, Rabi frequency, formulas for atomic inversion and classical and revival times. Therefore, we conclude that JC Hamiltonians can be considered as one example of a wider a class of generalized Hamiltonians which can be useful in broader interaction problems.

We present a generalized Jaynes-Cummings model (JCM) with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state. The field operators of the JCM Hamiltonian are identified as the elements of the

{\mathrm{su}}_{\mathit{q}}

(1,1) quantum algebra in their Holstein-Primakoff realizations. We lay emphasis on the time evolution of field quadruatures and atomic population inversion of the generalized JCM. The revivals of radiation squeezing are obtained for any values of initial squeezing.

Abstract In the photon-atom interaction, one of the most interesting phenomena can be collapse-revival effect in population inversion of atomic levels. Since a single-photon-transition Jaynes–Cummings model can be generalized to a multiphoton-transition Jaynes–Cummings model, of which the Hamiltonian can exhibit a supersymmetric Lie algebra structure, in this paper, quantum collapse and revival in atomic population inversion, which is a collaborative effect of a variety of quantum Rabi oscillations with various quantum Rabi frequencies, is studied for the supersymmetric multiphoton-transition Jaynes–Cummings model. In the literature, it has been pointed out that quantum collapse and revival might find an application in qubit design. We expect that a supersymmetric two-level system might serve as such a kind of qubits. Compared with ordinary two-level qubits, more information could be stored in the basis vectors of supersymmetric qubits, and this could increase the degrees of freedom of tensor product (multi-component extension) of basis vectors of this multiphoton-atom interacting system. For this reason, some characteristics of the collapse-revival effect driven by ordinary coherent states and Yurke–Stoler coherent states will be addressed in this paper. The influence of various characteristic parameters of this supersymmetric Jaynes–Cummings model and the quantized optical fields on the quantum collapse and revival in the population inversion will be indicated in some numerical illustrative examples.