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

Abstract

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]

Theoretical Methods for Ultrastrong Light–Matter Interactions

“…Such an ansatz was later improved by considering squeezed coherent states [77], and deformed, frequency renormalized polarons [78,79]. This approach was also applied to the two-qubit [80] and two-photon [81] Rabi models. Unlike the GRWA or the effective Hamiltonians presented above, these polaron-based methods have been used mostly to extract ground-state properties, although possible extensions to excited states have been proposed [78].…”

Radiation induced interaction potential of two qubits strongly coupled with a quantized electromagnetic field

“…Quantum Rabi model (QRM) describes the interaction of a two-level atom with a resonant single-mode quantum field in a cavity [1,2]. This model plays fundamental role in the radiation-matter interaction in cavity quantum electrodynamics [3][4][5], quantum optics [6], quantum information [7] and physics of condensed matter [8]. Recently, the model attracted attention due to the fact that in many systems it is possible [9,10] to control the interaction strength in a wide range, including the so called ultra strong coupling (USC) regime, which corresponds to the variation interval from 0.3 to 1.0 of a dimensionless coupling constant f between an atom (qubit) and a field.…”

Exact solution for the quantum Rabi model with the $\boldsymbol{\mathsf{A}}^{2}$ term

“…Quantum Rabi model describes the interaction of a two level atom with a single-mode quantum field in a cavity [3,4]. This model plays fundamental role in the radiation-matter interaction in cavity quantum electrodynamics [5][6][7], quantum optics [8], quantum information [9] and physics of condensed matter [10]. In addition, it was recently demonstrated [11] that the QRM is an exactly integrable system and the problem of determining its spectrum of stationary states is reduced to the numerical solution of many-term recurrent relations.…”

“…Presently there exist systems (ion bound to the cavity [13,14], super-conducting qubit [15][16][17], polaritons [18]) that provide the strong interaction [19][20][21][22][23] between an atom and the field, which corresponds to the situation when the dimensionless coupling constant f of the atom-field interaction in QRM reaches values of the order of unity [24][25][26]. This motivates both experimental and theoretical investigations of physical effects appearing in this fully quantum regime [6,24,[27][28][29][30][31].…”

“…[11]. In addition, there exists a numerous number of works [24] which construct an approximate solution for the strong coupling regime or provide the uniform approximation [6,[37][38][39] for a large range of variation of the coupling constant. In order to investigate how the QRMA behavior is modified with respect to the conventional QRM we will compare the exact numerical solution [27,37] of the system of Eqs.…”