Generalized rotating-wave approximation for the two-qubit quantum Rabi model

Zhang, Yuyu; Chen, Qing-Hu

doi:10.1103/physreva.91.013814

Cited by 33 publications

(20 citation statements)

References 39 publications

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“…The GRWA approach has been successfully applied to other light-matter interaction models related to the QRM, namely to the two-qubit Rabi model [71] and to a biased version of the QRM [72]. A so-called symmetric implementation the GRWA, that exploit more efficiently the symmetries of the model has also been proposed for the single-and two-photon models [73].…”

Section: B Generalized Rwamentioning

confidence: 99%

Theoretical Methods for Ultrastrong Light–Matter Interactions

Boité

2020

Adv Quantum Tech

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This article reviews theoretical methods developed in the last decade to understand cavity quantum electrodynamics in the ultrastrong-coupling regime, where the strength of the light-matter interaction becomes comparable to the photon frequency. Along with profound modifications of fundamental quantum optical effects giving rise to a rich phenomenology, this regime introduces significant theoretical challenges. One of the most important is the break-down of the rotating-wave approximation which neglects all non-resonant terms in lightmatter interaction Hamiltonians. Consequently, a large part of the quantum optical theoretical framework has to be revisited in order to accurately account for all interaction terms in this regime. We give in this article a broad overview of the recent progress, ranging from analytical estimates of ground-state properties to proper derivations of master equations and computation of photodetection signals. For each aspect of the theory, the basic principles of the methods are illustrated on paradigmatic models such as quantum Rabi and spin-boson models. In this spirit, most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached, such as semiconductor microcavities and superconducting circuits. The validity of these models is discussed in the last part of the article, where we address recent debates on fundamental issues related to gauge invariance in the ultrastrong-coupling regime.

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Section: B Generalized Rwamentioning

confidence: 99%

Theoretical Methods for Ultrastrong Light–Matter Interactions

Boité

2020

Adv Quantum Tech

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“…In the two-qubit model, recall that the mean photon number of the ground state obtained by GRWA [46] is…”

Section: The Advantage Of the Variational Methodsmentioning

confidence: 99%

Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model

Mao

Li²,

Wang

et al. 2019

Phys. Rev. A

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We present an analytical method for the two-qubit quantum Rabi model. While still operating in the frame of the generalized rotating-wave approximation (GRWA), our method further embraces the idea of introducing variational parameters. The optimal value of the variational parameter is determined by minimizing the energy function of the ground state. Comparing with numerical exact results, we show that our method evidently improves the accuracy of the conventional GRWA in calculating fundamental physical quantities, such as energy spectra, mean photon number, and dynamics. Interestingly, the accuracy of our method allows us to reproduce the asymptotic behavior of mean photon number in large frequency ratio for the ground state and investigate the quasiperiodical structure of the time evolution, which are incapable of being predicted by the GRWA. The applicable parameter ranges cover the ultrastrong coupling regime, which will be helpful to recent experiments. * An adiabatic approximation has been proposed for the two-qubit quantum Rabi model [29]. It plays well when arXiv:1904.09567v1 [quant-ph]

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“…Yet, such systems are of current fundamental interest, as short associated electromagnetic pulses can manipulate qubits on a large bandwidth. Recently, several methods have thus been designed to overcome the limitations of the theoretical treatment [28,[35][36][37]. These are based on various unitary transformations leading to approximate analytical expressions over an extended driving range.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR

Giscard

Bonhomme

2020

Phys. Rev. Research

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Comprehending the dynamical behavior of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalization of the Hamiltonian do not work in this setting. In fact, since the inception of Magnus' expansion [Commun. Pure Appl. Math. 7, 649 (1954)], no fundamentally novel mathematical approach capable of solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here on an entirely different nonperturbative approach, termed path sum, which is always guaranteed to converge, yields the exact analytical solution in a finite number of steps for finite systems, and is invariant under scale transformations of the quantum state space. Path sum can be combined with any state-space reduction technique and can exactly reconstruct the dynamics of a many-body quantum system from the separate, isolated, evolutions of any chosen collection of its subsystems. As examples of application, we solve analytically for the dynamics of all two-level systems as well as of a many-body Hamiltonian with a particular emphasis on nuclear magnetic resonance applications: Bloch-Siegert effect, coherent destruction of tunneling, and N-spin systems involving the dipolar Hamiltonian and spin diffusion.

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Generalized rotating-wave approximation for the two-qubit quantum Rabi model

Cited by 33 publications

References 39 publications

Theoretical Methods for Ultrastrong Light–Matter Interactions

Theoretical Methods for Ultrastrong Light–Matter Interactions

Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model

Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR

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