Ground state configurations in two-mode quantum Rabi models

S. A. Chilingaryan

S. A. Chilingaryan, B. M. Rodríguez-Lara

Abstract We study two models describing the interaction of a two-level system with two quantum field modes in a parallel or orthogonal setup. We show that both models present a partial two-mode SU (2) symmetry and that they can be solved in the exceptional case of fields with the same frequency. We study their ground state configurations; that is, we find the quantum precursors of the corresponding semi-classical phase transitions, as well as their whole spectra to infer their integrability. We show that the first model is isomorphic with the quantum Rabi model and shows the standard crossover from a vacuum to a non-vacuum ground state configuration. The second model shows a crossover involving four ground state configurations: one vacuum, two non-vacuum single modes and one non-vacuum dual mode. We give analytic and numerical pointers that may suggest its integrability in certain regimes. We also show that, in the single excitation subspace, an excited two-level system may entangle two initial vacuum fields even in the ultra-strong coupling regime.

Hongbo Liang, Wen-Nian Liu, Wen-Bo Li

Anne Boutet de Monvel, Lech Zieliński

Kelvin M. C. Lee, C. K. Law

We examine a generalized Rabi model formed by two identical qubits interacting with a common oscillator mode. In the near-resonance configuration where the oscillator frequency is close to the transition frequency of the qubit, we determine the ground state of the model approximately by using a variational method and a transformation method. Both methods are shown to approximate the ground state accurately for a range of coupling strengths in the ultrastrong-coupling regime. In addition, the accuracy of the approximation can be further improved by using perturbation theory. We also characterize the ground-state entanglement between the two qubits by calculating the negativity.

Yue 越 Chen 陈, Maoxin 卯鑫 Liu 刘, Xiaosong 晓松 Chen 陈

We investigate the two-mode quantum Rabi model (QRM) describing the interaction between a two-level atom and a two-mode cavity field. The quantum phase transitions are found when the ratio η of transition frequency of atom to frequency of cavity field approaches infinity. We apply the Schrieffer–Wolff (SW) transformation to derive the low-energy effective Hamiltonian of the two-mode QRM, thus yielding the critical point and rich phase diagram of quantum phase transitions. The phase diagram consists of four regions: a normal phase, an electric superradiant phase, a magnetic superradiant phase and an electromagnetic superradiant phase. The quantum phase transition between the normal phase and the electric (magnetic) superradiant phase is of second order and associates with the breaking of the discrete Z 2 symmetry. On the other hand, the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1) symmetry. Several important physical quantities, for example the excitation energy and average photon number in the four phases, are derived. We find that the excitation spectra exhibit the Nambu–Goldstone mode. We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities. To confirm the validity of the low-energy effective Hamiltonians analytically derived by us, the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.