General symmetry operators of the asymmetric quantum Rabi model

Abstract

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.

Symmetry operators of the asymmetric two-photon quantum Rabi model

“…It was quickly verified analytically in the literature [26][27][28] that the symmetry operators can be constructed one by one within Fock space. 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].…”

“…/(2β) = N, N is an integer. To discuss the hidden symmetry responsible for this double degeneracy, we will follow the same BOA scheme in [29].…”

“…Given the diagonalized Hamiltonian, we move to the symmetry operator J associated with the hidden symmetry. It should satisfy the commutation condition [J, H] = 0, as same as the one-photon AQRM in [26][27][28][29]. For the asymmetric tpQRM, we define J as…”

The heat kernel of the asymmetric quantum Rabi model

“…One of the motivations is the potential application of the QRM to the development quantum computation and quantum information sciences. In parallel, there is a growing interest in the mathematical study of the properties of the QRM, including the study of solutions and dynamics [5,6], large spectral asymptotics [7], symmetry and degeneracy for asymmetric QRMs [8,9], entanglement properties [10], Floquet analysis [11], spectral zeta functions [12,13] and algebro-geometric analysis [14,15].…”