Hidden symmetry operators for asymmetric generalized quantum Rabi models

The true level crossing in the asymmetric quantum Rabi model without any obvious symmetry can be exhibited in the energy spectrum if the qubit bias is a multiple of the cavity frequency, which should imply the existence of the hidden symmetry. In this work, within a Bogoliubov operator approach, we can readily derive the symmetry operators associated with the hidden symmetry hierarchically for arbitrary multiples. The symmetry operators for small multiples in the literature can be extremely easily reproduced in our general scheme. In addition, a general parity operator is deﬁned through the symmetry operator, which naturally includes the well-known party operator of the symmetric model. We believe that the present approach can be straightforwardly extended to other asymmetric Rabi models to ﬁnd the relevant symmetry operators.

Section: Discussionmentioning

confidence: 99%

General symmetry operators of the asymmetric quantum Rabi model

Xie¹,

Chen²

2022

“…The GAA approach can be readily applied to other light-matter interaction models, such as the anisotropic Rabi model and the Rabi-Stark model, where the hidden symmetry is also present [49,51] and the Juddian points are exactly solvable. An interesting property of these two models is that a parameter-dependent CI occurs in the ground state, and their topological transitions could be explored analytically within the framework of the GAA.…”

Section: Discussionmentioning

confidence: 99%

“…Operators responsible for the hidden Z 2 symmetry in the AQRM have recently been found [47,48]. More generally, this hidden symmetry is seen to be universal in asymmetric light-matter interaction models [49], with corresponding hidden symmetry operators found for a number of asymmetric generalizations of the QRM [50,51].…”

Section: Conical Intersections In the Aqrmmentioning

confidence: 91%

Generalized adiabatic approximation to the asymmetric quantum Rabi model: conical intersections and geometric phases

Li¹,

Ferri²,

Tilbrook³

et al. 2021

Self Cite

The asymmetric quantum Rabi model (AQRM), which describes the interaction between a quantum harmonic oscillator and a biased qubit, arises naturally in circuit quantum electrodynamic circuits and devices. The existence of hidden symmetry in the AQRM leads to a rich energy landscape of conical intersections (CIs) and thus to interesting topological properties. However, current approximations to the AQRM fail to reproduce these CIs correctly. To overcome these limitations we propose a generalized adiabatic approximation (GAA) to describe the energy spectrum of the AQRM. This is achieved by combining the perturbative adiabatic approximation and the exact exceptional solutions to the AQRM. The GAA provides substantial improvement to the existing approaches and pushes the limit of the perturbative treatment into non-perturbative regimes. As a preliminary example of the application of the GAA we calculate the geometric phases around CIs associated with the AQRM.

“…Most recently, the present authors also reproduced the symmetry operators for arbitrary integer biases within BOA in a more simple and general scheme [29]. In addition, the symmetry operators of other related asymmetric one-photon models have been investigated in the references [30,31].…”

Section: Introductionmentioning

confidence: 95%

“…Interestingly, the highest degree of the polynomial (32) is 2N in the asymmetric tpQRM rather than N in the one-photon AQRM at the same order level crossings. This is because the nolinear two-photon interaction, similar to the asymmetric Rabi-Stark model case where the Stark term Δa † aσ z /2 also induce the 2N-degree in the J-square [31], which need further research.…”

Section: Symmetry Operatorsmentioning

confidence: 99%

Symmetry operators of the asymmetric two-photon quantum Rabi model

Xie¹,

Chen²

2022

The true level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) have been observed when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Generally, such level crossings imply the existence of the hidden symmetry because the bias term breaks the obvious symmetry exactly. In this work, we propose a Bogoliubov operator approach (BOA) for the asymmetric tpQRM to derive the symmetry operators associated with the hidden symmetry hierarchically. The explicit symmetry operators consisting of Lie algebra at low biases can be easily obtained in our general scheme. We believe the present approach can be extended for other asymmetric Rabi models to ﬁnd the relevant hidden symmetry.