In this paper the p-level Rabi model with Z p -graded symmetry is discussed. The p-level Rabi Hamiltonian is constructed by introducing the generalized Pauli matrices. The energy and wave function for the p-level Rabi equation are obtained by using the standard perturbation method.
ZN symmetric chiral Rabi model: a new N-level system
We present a new tractable quantum Rabi model for N-level atoms by extending the Z2 symmetry of the two-state Rabi model. The Hamiltonian is ZN symmetric and allows the parameters in the level separation terms to be complex while remaining hermitian. This latter property means that the new model is {\em chiral}, which makes it differ from any existing N-state Rabi models in the literature. The ZN symmetry provides partial diagonalization of the general Hamiltonian. The exact isolated (i.e. exceptional) energies of the model have the Rabi-like form but are N-fold degenerate. For the three-state case (N=3), we obtain three transcendental functions whose zeros give the regular (i.e. non-exceptional) energies of the model.
The spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of the standard (one-photon) Rabi Hamiltonian, published by D. Braak [Phys. Rev. Lett. 107, 100401 (2011)]. The Hamiltonian is rewritten as a set of two differential equations. Symmetries that get hidden after further treatment are found. One can plainly see how the Hilbert space splits into four disjunct subspaces, categorized by four values of the symmetry parameter $c=\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}i$. There were only two values, $\ifmmode\pm\else\textpm\fi{}1$, for the standard Rabi model. The values of c are in fact the eigenvalues of the respective parity operators. Four analytic functions are introduced by a recurrence scheme for the coefficients of their series expansion. All their roots yield the complete spectrum of the Hamiltonian. Eigenstates in Bargmann space can also be found.
Abstract: The general quantum-mechanical properties of two-level systems are very relevant for the study of different physical subjects of great interest, as, for instance, magnetic resonance, nuclear physics, molecular dynamics, masers, neutrino oscillations, quantum computation, etc. In this work we present a nonperturbative approach to the study of the oscillations among two quantum states when an interaction term is considered. First, we show that using a simple parametrization for the superposition of the two states, it is possible to derive easily the Rabi equation. Next, we show that the Pauli matrices can be conveniently used to write the Hamiltonian operator and to derive the Rabi equation, directly applying the time evolution operator to the initial state of the system.
Zn symmetric chiral Rabi model: a new N-level system
We present a new tractable quantum Rabi model for N-level atoms by extending the Z2 symmetry of the two-state Rabi model. The Hamiltonian is ZN symmetric and allows the parameters in the level separation terms to be complex while remaining hermitian. This latter property means that the new model is a chiral model. The ZN symmetry provides partial diagonalization of the general Hamiltonian. The exact isolated (i.e. exceptional) energies of the model have the Rabi-like form but are N-fold degenerate. For the three-state case (N=3), we obtain three transcendental functions whose zeros give the regular (i.e. non-exceptional) energies of the model.
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.
Abstract We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [ J. Phys. A 46 (2013) 265302 ], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.