The mixed quantum Rabi model

Duan, Liwei; Xie, You-Fei; Chen, Qing-Hu

doi:10.1038/s41598-019-54756-0

Cited by 20 publications

(13 citation statements)

References 64 publications

(105 reference statements)

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“…A few typical models are listed in Table 1 . Besides introducing the asymmetry from the bias, [ 3 ] as inspired by experimental setups nonlinear terms can be also added to interplay with the linear coupling, such as the two‐photon process, [ 10–12,60–63 ] the Stark‐like coupling, [ 11,12,64,65 ] and the A 2 term. [ 33 ] As one knows, the reduced symmetry from the JCM to the QRM leads to avoided crossings, [ 8 ] while the nonlinearity and the bias results in various patterns of symmetry breaking, different orders of transitions and a rich physics of tricriticalities and quadruple points.…”

Section: Paradigmatic Modelsmentioning

confidence: 99%

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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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Section: Paradigmatic Modelsmentioning

confidence: 99%

“…[ 107,108 ] It has been found that there exists a scaling behavior for the Stark‐like term. [ 11,12 ] The case of

χ = 0

was also considered for integrability, [ 61,62 ] studied by mean‐field [ 60 ] and even used in mapping to the Dirac equations in (1+1)‐dimensional curved spacetime. [ 28 ]…”

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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“…A similar route has recently been used to investigate the dynamics of a pair [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ] or a chain [ 32 , 33 ] of coupled spins (also greater than

) subjected to time-independent and time-dependent [ 34 , 35 , 36 ] external magnetic fields. Symmetry arguments have also been exploited to elegantly bring to light intriguing dynamic features of physical systems living in Hilbert spaces of infinite dimensions [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 ]. In Section 4 it is demonstrated that the time evolution of the two dipolarly coupled spins nests a qutrit subdynamics governed by a Hamiltonian model that is explicitly derived.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

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We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

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“…Beyond atomic physics, it can also be extended to any other systems that have an analogy with the cavity-QED, such as quantum-dots in microcavities and various types of qubits that are transversely coupled to superconducting cavities. Moreover, the extended versions of the QRM have been widely investigated [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Two-photon sideband transition in a driven quantum Rabi model : Quantitative discussions with derived longitudinal drives and beyond the rotating wave approximation

Ann,

Kessels,

Steele

2021

Preprint

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In this work, we analytically and numerically study the sideband transition dynamics of the driven quantum Rabi model (QRM). We focus in particular on the conditions when the external transverse drive fields induce first-order sideband transitions. Inducing sideband transitions between two different systems is an essential technique for various physical models, including the QRM. However, despite its importance, a precise analytical study has not been reported yet that successfully explains the sideband transition rates in a driven QRM applicable for all system parameter configurations. In our study, we analytically derive the sideband transition rates b ased on second-order perturbation theory, not relying on the rotating wave approximation (RWA) [1]. Our formula are valid for all ranges of drive frequencies and system's parameters. Our analytical derived formula agrees well with the numerical results in a regime of moderate drive amplitudes. Interestingly, we have found a non-trivial longitudinal drive effect derived from the transverse drive Hamiltonian. This accounts for significant corrections to the sideband transition rates that are expected without considering the derived longitudinal effect. Using this approach, one can precisely estimate the sideband transition rates in the QRM not confining themselves within specific parameter regimes. This provides important contributions for understanding experiments described by the driven QRM.

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The mixed quantum Rabi model

Cited by 20 publications

References 64 publications

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

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

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Two-photon sideband transition in a driven quantum Rabi model : Quantitative discussions with derived longitudinal drives and beyond the rotating wave approximation

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