The quantum Rabi model for two qubits

Abstract

We study a system composed of two nonidentical qubits coupled to a singlemode quantum field. We calculate the spectra of the system in the deep-strongcoupling regime via perturbation theory up to second-order corrections and show that it converges to two forced oscillator chains for cases well into that regime. Our predictions are confirmed by the numerical calculation of the spectra using a parity decomposition of the corresponding Hilbert space. The numerical results point to two interesting types of behavior in the ultra-strongcoupling regime: the rotating wave approximation is valid for some particular cases and there exist crossings in the spectra within each parity subspace. We also present the normal modes of the system and give an example of the time evolution of the mean photon number, population inversion, von Neumann entropy and Wootters concurrence in the ultra-strong-and deep-strong-coupling regimes.

Searching for structure beyond parity in the two-qubit Dicke model

“…All the analytic recurrence relations were confirmed by our numerical eigenstates. These results reduce and simplify those provided in [6] and are equivalent to those presented more recently in [7]; e.g., the spectra of the system reduce to two degenerate forced oscillator chains for cases well into the deep strong coupling regime, g ω 0 , where it is possible to fully describe the dynamics of the system [6]. We performed a statistical analysis of the boson field distributions, e.g.…”

“…. following [6]. The subspace size, S, was increased until a convergence error, δλ n (S) = |λ n (S) − λ n (S + 1)|, where λ n (S) is the nth eigenvalue for a matrix of size S and ∆V n (S) = 1 − | V n (S)|V n (S + 1) |, where |V n (S) is the nth eigenstate for a matrix of size S, of less than 10 −10 was obtained; in the case shown, the size was S = 4000 and the convergence errors were δλ n ∈ [10 −15 , 10 −11 ] and ∆V n ∈ [10 −17 , 10 −15 ].…”

“…This two-qubit full Dicke model has a well known parity symmetry [6,7] but no other fully conserved constant of motion has been found for it. It can be realized experimentally with solid state devices [8,9] and trapped ions [10,11].…”

Two-photon Rabi model: analytic solutions and spectral collapse

“…G R (E) was then recovered within the extended coherent states approach, which avoids the mapping into the Bargmann space of analytic functions [7]. These results have stimulated extensive research in the QRM and related models [8,9,10,11,12,13,14,15,16,17,18,19,20].…”

Dark-like states for the multi-qubit and multi-photon Rabi models

“…The qubitphoton ultrastrong coupling regime has been reached in recent circuit QED experiment [11]. However, in this regime, the Jaynes-Cummings model fails, so many researches then focus on the Rabi model, which include the analytical solution of the Rabi model retrieved by Chen et al using Bogoliubov operators [12], two-photon [13][14][15], two-qubit [16][17][18][19][20] and multiqubit [21][22][23] generalizations, exact real time dynamics [24,25], deep strong coupling [26], anisotropic Rabi model [27] and so on [28][29][30].…”