Using extended coherent states, an analytically exact study has been carried out for the quantum Rabi model with two equivalent qubits. Compact transcendental functions of one variable have been derived leading to exact solutions. The energy spectrum is clearly identified and analyzed. Also obtained analytically are the necessary and sufficient conditions for the occurrence of isolated exceptional solutions, which are not doubly degenerate as in the one-qubit quantum Rabi model.

arXiv:1401.6531Europhysics Letters (EPL)May 29, 201428 citations

arXiv:1403.4737

$Z_N$ symmetric chiral Rabi model: a new $N$ -level system$Z_N$ symmetric chiral Rabi model: a new $N$-level system

Yao-Zhong Zhang

Published Mar 19, 2014• 6 citations

arXiv HTML PDF

Abstract

We present a new tractable quantum Rabi model for

N

-level atoms by extending the

\mathbb Z_2

symmetry of the two-state Rabi model. The Hamiltonian is

\mathbb Z_N

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

\mathbb Z_N

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.

DOI: 10.48550/arxiv.1403.4737

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Z_N

symmetric chiral Rabi model: a new

N

-level system

We present a new tractable quantum Rabi model for

N

-level atoms by extending the

\mathbb Z_2

symmetry of the two-state Rabi model. The Hamiltonian is

\mathbb Z_N

N

-state Rabi models in the literature. The

\mathbb Z_N

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.

\mathbb Z_n

symmetric chiral Rabi model: a new

N

-level system

We present a new tractable quantum Rabi model for

N

-level atoms by extending the

\mathbb Z_2

symmetry of the two-state Rabi model. The Hamiltonian is

\mathbb Z_N

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

\mathbb Z_N

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.

\mathcal {PT}

‐Symmetric Quantum Rabi Model: Solutions and Exceptional Points

The analytically exact solutions to the mixed quantum Rabi model including both one- and two-photon terms are found by using Bogoliubov operators. Transcendental functions in terms of

4 \times 4

determinants responsible for the exact solutions are derived. These so-called

G

-functions with pole structure can be reduced to the previous ones in the unmixed models. The zeros of

G

-functions reproduce completely the regular spectra. The exceptional eigenvalues can be also obtained by another transcendental function. From the pole structure, we can derive two energy limits when the two-photon coupling strength tends to the collapse point

1/2

. Surprisingly, all energy levels only collapse to the lower one, which diverges negatively. All the level crossings in the unmixed models are relaxed to avoided crossings in the present mixed model due to absence of parity symmetry. Very interestingly, the effective one-photon coupling is enhanced in the presence of the two-photon coupling, which paves a highly efficient and economic way to access the deep-strong coupling regime even though the original one-photon coupling is weak.