scholarly journals Entanglement generation in the ultra-strongly coupled Rabi model

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560016 ◽  
Author(s):  
Matteo Bina ◽  
Stefano Maffezzoli Felis ◽  
Stefano Olivares
Keyword(s):  
Bosonic Field ◽  
Entanglement Generation ◽  
Strongly Coupled ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Rabi Model ◽  
Resonator Mode ◽  
Rotating Wave ◽  
Maximally Entangled States ◽  
Degenerate Regime

We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.

Solution of two-qubit Rabi model with extended generalized rotating-wave approximation

2021 ◽  
pp. 2150213
Author(s):  
Zhanyuan Yan ◽  
Peihua Qu ◽  
BingBing Xu ◽  
Shihui Zhang ◽  
Jinying Ma
Keyword(s):  
Order Approximation ◽  
Photon Number ◽  
Energy Spectra ◽  
Hamiltonian Matrix ◽  
Diagonal Form ◽  
Coupling Region ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Rabi Model ◽  
Rotating Wave

The generalized rotating-wave approximation (GRWA) method is extended to the two-qubit quantum Rabi model. In the first-order approximation (one photon exchange), the Hamiltonian matrix in photon number space is simplified by introducing two variational parameters. However, the Hamiltonian matrix is not a diagonalizable matrix yet. Furthermore, by presenting a constraint condition on coupling strength and atomic transition frequency, the Hamiltonian matrix is simplified and an effective solvable Hamiltonian with block diagonal form is obtained. In the even and odd parity space, the energy spectra and eigenstates of the two-qubit quantum Rabi model are achieved analytically. Most of the energy spectra, especially the lower energy levels, agree well with the numerical exact results in ultra-strong coupling region, and the ground state wave function can gives a fairly accurate result of mean photon number.

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

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
Bin-Bin Mao ◽  
Liangsheng Li ◽  
Yimin Wang ◽  
Wen-Long You ◽  
Wei Wu ◽  
...  
Keyword(s):  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Rabi Model ◽  
Rotating Wave

scholarly journals Perturbation series for Jacobi matrices and the quantum Rabi model

2021 ◽  
Vol 41 (3) ◽  
pp. 301-333
Author(s):  
Mirna Charif ◽  
Lech Zielinski
Keyword(s):  
Perturbation Series ◽  
Convergence Radius ◽  
Rotating Wave Approximation ◽  
Tridiagonal Matrices ◽  
Wave Approximation ◽  
Near Resonance ◽  
Rabi Model ◽  
Rotating Wave ◽  
Adjoint Operators

We investigate eigenvalue perturbations for a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. In particular we obtain explicit estimates for the convergence radius of the perturbation series and error estimates for the Quantum Rabi Model including the resonance case. We also give expressions for coefficients near resonance in order to evaluate the quality of the rotating wave approximation due to Jaynes and Cummings.

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