Integrability and solvability of the simplified two-qubit Rabi model

Peng, Jie; Ren, Zhongzhou; Guo, Guangjie; Ju, Guo-Xing

doi:10.1088/1751-8113/45/36/365302

Cited by 23 publications

(33 citation statements)

References 31 publications

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“…While extensions for the QRM where the number of qubits [28][29][30][31][32][33] or fields [34][35][36] are increased have been studied in the literature, here, we want to focus in one configuration that might prove interesting. Let us imagine a two-level atom interacting with the fields of two cavities in an orthogonal configuration, under minimal coupling and the long wavelength approximation, we can arrive to what we will call a cross-cavity quantum Rabi model,…”

Section: Introductionmentioning

confidence: 99%

Cross-cavity quantum Rabi model

Alderete¹,

Rodríguez-Lara²

2016

J. Phys. A: Math. Theor.

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We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single trapped ion. We provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep strong coupling regimes. We also show that the particular case of degenerate field frequencies and balanced couplings allows us to cast the model as two parity deformed oscillators in any given coupling regime.

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Section: Introductionmentioning

confidence: 99%

Cross-cavity quantum Rabi model

Alderete¹,

Rodríguez-Lara²

2016

J. Phys. A: Math. Theor.

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“…The two‐qubit system is fundamental to the construction of the universal quantum gate in quantum computation, [ 109–111 ] and the two‐qubit QRM can describe a two‐qubit system mediated by a resonant cavity. [ 112–118 ] The Hamiltonian of two‐qubit QRM reads as

{\overset{H}{true}}_{T Q R} = ω {\overset{a}{true}}^{†} \hat{a} + \sum_{i = 1, 2} [\frac{{normalΩ}_{i}}{2} {\hat{σ}}_{x}^{i} + g_{i} {\hat{σ}}_{z}^{i} (() \hat{a} + {\overset{a}{true}}^{†})]

where the numbers 1,2 represent the two qubits. The variational method in polaron picture also works well for the two‐qubit QRM as compared to the ED in Figure a,b.…”

Section: Quantum States In Polaron Picturementioning

confidence: 99%

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

Liu

Ying

et al. 2021

Adv Quantum Tech

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The light–matter interaction not only is ubiquitous in nature but also can be simulated in various artificial systems. Besides the tunability of artificial quantum systems, the experimental access to the ultra‐strong and even deep‐strong couplings has brought a regime with novel phenomenology. Theoretically the finding of the integrability for the quantum Rabi model (QRM) has attracted tremendous attention to the study of the QRM and its extensions which are fundamental models of the light–matter interaction. With the continuing enhancements of coupling strengths, a most fascinating phenomenon of these light–matter models is that they can exhibit few‐body quantum phase transitions (QPTs), while a full understanding of these QPTs is a challenge. The polaron picture is a method capable of analyzing these fundamental models in the entire coupling regime and extracting the essential physics behind the QPTs. A review of its extensive applications on the fundamental light–matter models is presented, with discussions on the phase diagrams and QPT‐related features. The universality of critical exponent of the anisotropic QRM as well as the possibility of QPTs in A2 terms are also addressed.

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“…The two-qubit Rabi Hamiltonian [29,[32][33][34][35][36][37][38][39][40] in the presence of a parametric oscillator [41][42][43][44] can be written as ( = 1 herein)…”

Section: Diagonalization Of the Hamiltonian Via Adiabatic Approximationmentioning

confidence: 99%

Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator

Yogesh,

Maity

2021

Preprint

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Quantum coherence and quantum correlations are studied in the strongly interacting system composed of two qubits and an oscillator with the presence of a parametric medium. To analytically solve the system, we employ the adiabatic approximation approach. It assumes each qubit's characteristic frequency is substantially lower than the oscillator frequency. To validate our approximation, a good agreement between the calculated energy spectrum of the Hamiltonian with its numerical result is presented. The time evolution of the reduced density matrices of the two-qubit and the oscillator subsystems are computed from the tripartite initial state. Starting with a factorized two-qubit initial state, the quasi-periodicity in the revival and collapse phenomenon that occurs in the two-qubit population inversion is studied. Based on the measure of relative entropy of coherence, we investigate the quantum coherence and its explicit dependence on the parametric term both for the two-qubit and the individual qubit subsystems by adopting different choices of the initial states. Similarly, the existence of quantum correlations is demonstrated by studying the geometric discord and concurrence. Besides, by numerically minimizing the Hilbert-Schmidt distance, the dynamically produced near maximally entangled states are reconstructed. The reconstructed states are observed to be nearly pure generalized Bell states. Furthermore, utilizing the oscillator density matrix, the quadrature variance and phase-space distribution of the associated Husimi Q-function are computed in the minimum entropy regime and conclude that the obtained nearly pure evolved state is a squeezed coherent state.

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Integrability and solvability of the simplified two-qubit Rabi model

Cited by 23 publications

References 31 publications

Cross-cavity quantum Rabi model

Cross-cavity quantum Rabi model

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator

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