Analytical solution and hidden symmetry operators of asymmetric two-mode quantum Rabi model

Zhang, Yan; Xia, Yang; Li, Jurihui; Ma, Jimying; Liu, Yan

doi:10.1088/1751-8121/ac5a22

Cited by 3 publications

(4 citation statements)

References 48 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The preliminary symmetry operators of the asymmetric tpQRM for low biases = 2β and 4β was given in our unpublished work [47]. Interestingly, the same idea was used to derive the lowest symmetry operator in the asymmetric two-mode QRM most recently [48].…”

Section: Discussionmentioning

confidence: 99%

Symmetry operators of the asymmetric two-photon quantum Rabi model

Xie¹,

Chen²

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Symmetry operators of the asymmetric two-photon quantum Rabi model

Xie¹,

Chen²

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…While the wave function corresponding to the first-order QPT of tpARSM is much more complicated than that of isotropic two-photon Rabi models, we can refer to the discussion in the two-mode QRM [18], in which the coefficient e m is simply determined by f m , as shown in equation (15) in [18]. At the pole energy = E E m pole , to avoid the divergence of function e m , we can set f m = 0, then, z m = 0/0 is arbitrary.…”

Section: First-order Quantum Phase Transitionsmentioning

confidence: 99%

“…A more physical insight was presented by Chen uses the Bogoliubov operator approach (BOA) in [16], providing an algebraic solution that offers a concise paradigm for the QRM. Since the QRM was analytically solved, several generalized QRMs corresponding to different interaction processes have been studied, and various properties of these models have been studied, such as symmetry of the system [17][18][19][20][21][22], energy level crossing [23][24][25][26][27][28], energy spectrum collapse [26,27,[29][30][31], and quantum phase transitions (QPTs) [27,[32][33][34][35]. The two-photon quantum Rabi model (tpQRM) is another widely concerned generalized Rabi model, which describes nonlinear interaction and can be regarded as the second-order expansion of the light-matter interaction.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution and spectral structure of the two-photon anisotropic Rabi-Stark model

Yan,

Cheng,

Qiu

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

Since the realization of the strong coupling between light and matter in experimental setups, the quantum Rabi model and its generalized models describing the interaction between the boson field and the two-level system have attracted extensive interest again. The study of anisotropic generalized Rabi models enables us to better understand the novel physical properties of the interaction between light and matter in the ultra-strong and deep-strong coupling regions. In this work, the two-photon anisotropic Rabi-Stark model (tpARSM) is analytically solved by using the Bogoliubov operator approach and the $su(1,1)$ Lie algebra. We derive the G-function, whose zeros give the regular spectrum of the system. By studying the pole structure of the G-function and the coefficients in the function, exceptional solutions, including the first-order quantum phase transition points, doubly degenerate exceptional solutions and nondegenerate exceptional solutions, are obtained. By discussing the spectral structure, we give the conditions for the first-order quantum phase transition of tpARSM. Furthermore, we find that the property that all of the lowest doubly degenerate crossing points in the two-photon Rabi-Stark model have the same energy only holds for the special case of the tpARSM in which the anisotropy parameter is equal to 1. Finally, from the perspective of first-order quantum phase transitions, concise conditions for the ground state energy level to collapse to or escape from the collapse point for the tpARSM are presented. A good understanding of the tpARSM will lay a good foundation for studying the extended two-photon systems involving multiple levels and multiple bosonic modes, and even the relevant open quantum systems.

show abstract

“…Soon after, Chen analytically solved QRM using Bogoliubov operator approach (BOA) [30], which is a more concise and physical method. With the breakthrough of experimental and theoretical research on QRM, some generalized QRMs were further studied, such as asymmetric QRM [29][30][31][32], anisotropic QRM [33][34][35][36], two-photon QRM (tpQRM) [30,[37][38][39][40], two-mode QRM [39,41,42], quantum Rabi-Stark model (RSM) [43] et al…”

Section: Introductionmentioning

confidence: 99%

Spectral structure of two-mode Rabi–Stark model

Liu

Qiu

Liu

et al. 2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

The analytical solutions of the two-mode Rabi-Stark model are obtained by using the Bogoliubov operators approach in su(1, 1) Lie algebra space, which ﬁt the exact numerical results well. The structure of the energy spectra is related to many fundamental physics characters such as symmetry, quantum phase transition, spectral collapse et al. In this paper, the spectral structure of two-mode Rabi-Stark model is discussed analytically. The regular energy spectrum is given by the zeros of the G-function, and the poles appearing in the G-function are responsible for the exceptional solutions. The double degenerate exceptional solutions could be predicted by discussing the divergence of the coeﬃcients in the G-function. If the numerator and denominator of Ωn vanish, the lowest double degenerate exceptional solutions for the n-th energy levels would be located, including the ﬁrst-order quantum phase transition point, the corresponding energy (−∆⁄U) is independent of the coupling strength and the energy level, even independent of the Bargmann index q. While, the nondegenerate exceptional solutions can be reproduced by the nondegenerate exceptional G-functions, the results show that more nondegenerate exceptional solutions would be found in the subspace with larger q. Then, the regular solution and two kinds of exceptional Juddian solutions of two-mode Rabi-Stark model are accurately located. The spectra collapse energy are dependent on the strength of Stark coupling and the frequency of two-level system, and Stark coupling could results in the limit of E0 pole line is higher than that of En pole lines, which may cause more energy levels separate from the collapse energy.

show abstract

Analytical solution and hidden symmetry operators of asymmetric two-mode quantum Rabi model

Cited by 3 publications

References 48 publications

Symmetry operators of the asymmetric two-photon quantum Rabi model

Symmetry operators of the asymmetric two-photon quantum Rabi model

Analytical solution and spectral structure of the two-photon anisotropic Rabi-Stark model

Spectral structure of two-mode Rabi–Stark model

Contact Info

Product

Resources

About