Spectral determinant of the two-photon quantum Rabi model

Braak, Daniel

doi:10.48550/arxiv.2206.02509

Cited by 4 publications

(13 citation statements)

References 38 publications

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“…It should be noted that when g → ω/2, β tends to zero, which leads to spectral collapse [15,24,26,28,31]. Beyond the spectral collapse point (g > ω/2), the nonlinear Rabi model becomes no longer self-adjoint [28]. Therefore, we only focus on 0 < g < ω/2 in this paper.…”

Section: Methodsmentioning

confidence: 99%

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Unified approach to the nonlinear Rabi models

Duan

2022

New J. Phys.

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An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry. There exist exact isolated solutions, which are located at the level crossings between different parities and correspond to eigenstates with finite dimension. Beyond the exact isolated solutions, the regular spectrum can be achieved by finding the roots of the G-function. The corresponding eigenstates are of infinite dimension. It is noteworthy that the expansion coefficients of the eigenstates present an exponential decay behavior. The decay rate decreases with increasing coupling strength. When the coupling strength tends to the spectral collapse point $g \rightarrow \omega / 2$, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of novel physics in nonlinear quantum optics.

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Section: Methodsmentioning

confidence: 99%

“…Table 1 gives the exact isolated solutions for k = 1 4 and 1 2 , where we have fixed = ω = 1. The coupling strength g corresponding to E = β(k + M) is determined by (28). When k = 1 4 , it corresponds to the two-photon Rabi model.…”

Section: Exact Isolated Solutionsmentioning

confidence: 99%

Unified approach to the nonlinear Rabi models

Duan

2022

New J. Phys.

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“…To discuss the difference between the linear (

) and nonlinear (

) cases for quantum metrology, let us start with zero bias

. The model has a phase transition in the low-frequency limit

at the critical point

[ 65 , 68 ] with

[ 17 , 19 ], and

is the critical value of

beyond which the Hamiltonian ( 1 ) is no longer self-adjoined and becomes unphysical [ 59 , 69 , 70 , 71 , 72 , 73 ]. The transition in this limit is second-order-like at

[ 17 , 18 , 19 , 20 , 26 , 27 , 28 ] and first-order-like at finite

[ 65 , 68 ].…”

Section: Relation Between Transition Order and Accuracymentioning

confidence: 99%

“…In Figure 1 c, we only plot up to

as the maximal QFI for a larger

would be out of scale. For these values, the system is close to the point of spectral collapse [ 59 , 71 , 72 , 73 ] where part of the discrete spectrum becomes continuous. Although this regime may not be easily realizable, we see that it has by far the greatest potential with regard to quantum metrology.…”

Section: Relation Between Transition Order and Accuracymentioning

confidence: 99%

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

Ying

Felicetti

Liu

et al. 2022

Entropy

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The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

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“…Furthermore, Chen et al achieved the exact analytical solutions to the two-photon and two-mode Rabi models with the Bogoliubov operator approach [11,22,23]. There are also some attempts to solve the two-photon and two-mode Rabi models in the Bargmann space [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A unified approach to the nonlinear Rabi models

Duan

2022

Preprint

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An analytical approach is proposed and applied to study the two-photon, two-mode and intensitydependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with Z2 symmetry. There exist some exact isolated solutions which correspond to eigenstates with finite dimensions. Beyond the isolated solutions, the regular spectrum can be achieved by finding the roots of the G-function. The corresponding eigenstates are of infinite dimension. It is noteworthy that the coefficients of the eigenstates present an exponential decay behavior. The decay rates decrease with the increase of the coupling strength. When the coupling strength tends to the spectral collapse point g → ω/2, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of the novel physics in nonlinear quantum optics.

show abstract

Spectral determinant of the two-photon quantum Rabi model

Cited by 4 publications

References 38 publications

Unified approach to the nonlinear Rabi models

Unified approach to the nonlinear Rabi models

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

A unified approach to the nonlinear Rabi models

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