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arXiv:1504.02748 · Journal of Physics B Atomic Molecular and Optical Physics

Exceptional solutions in two-mode quantum Rabi models

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

Published Oct 23, 2015• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/48/24/245501

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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.
Abstract We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single trapped ion. We provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep-strong coupling regimes. We also show that the particular case of identical field frequencies and couplings allows us to cast the model as two parity deformed oscillators in any given coupling regime.
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.
Interaction of the vacuum field of an optical mode with an electronic two-level system can drive non-perturbative light-matter dynamics, resulting in an exotic quantum ground state containing a sizeable population of virtual excitations. In the deep-strong coupling (DSC) regime, where the Rabi frequency,ΩR\Omega_{\mathrm{R}}ΩR​, exceeds the eigen-frequencies of the coupled systems, this extreme ground state can result in spectacular effects of cavity-QED, such as the expected release of the virtual photon ground state population as vacuum radiation by non-adiabatic modulation of the coupling mechanism [1], [2]. However, for resonant coupling of two single modes [3], the finite oscillator strength of resonant electronic excitation sets a natural limit to the achievable coupling strength, hindering further exploration of this exciting field.
Abstract Since the realization of the strong coupling between light and matter in experimental setups, the quantum Rabi model and its generalized models describing the interaction between the boson field and the two-level system have attracted extensive interest again. The study of anisotropic generalized Rabi models enables us to better understand the novel physical properties of the interaction between light and matter in the ultra-strong and deep-strong coupling regions. In this work, the two-photon anisotropic Rabi-Stark model (tpARSM) is analytically solved by using the Bogoliubov operator approach and the su(1, 1) Lie algebra. We derive the G-function, whose zeros give the regular spectrum of the system. By studying the pole structure of the G-function and the coefficients in the function, exceptional solutions, including the first-order quantum phase transition points, doubly degenerate exceptional solutions and nondegenerate exceptional solutions, are obtained. By discussing the spectral structure, we give the conditions for the first-order quantum phase transition of tpARSM. Furthermore, we find that the property that all of the lowest doubly degenerate crossing points in the two-photon Rabi-Stark model have the same energy only holds for the special case of the tpARSM in which the anisotropy parameter is equal to 1. Finally, from the perspective of first-order quantum phase transitions, concise conditions for the ground state energy level to collapse to or escape from the collapse point for the tpARSM are presented. A good understanding of the tpARSM will lay a good foundation for studying the extended two-photon systems involving multiple levels and multiple bosonic modes, and even the relevant open quantum systems.
Abstract The quantum Rabi model, which describes the interaction between a simplified atom and a mode of the electromagnetic field, is a cornerstone of modern quantum optics. One of the key assumptions of the model is that the ‘atom’ is a perfect two-level system. We explore what happens when one generalises the atom to a multilevel system, with m ground and n excited states coupled to the same field. We focus on the case where the excited and ground states form distinct, well-separated, manifolds of near-degenerate levels (so that the spacing between the excited states on a given manifold is much less than the average spacing between the manifolds) and consider either uniform or random couplings between the individual ground and excited levels. We find that the system reduces approximately to a direct sum of Rabi models with a range of different couplings. Importantly, the strongest coupling is enhanced in a way that depends on the number of levels, for the simple case where n = m, the coupling scales with n for uniform couplings and 2 n for random couplings (in the limit of large n). Our work thus suggests that multilevel Rabi systems could provide an attractive alternative route to accessing regimes of very strong coupling in light-matter systems.
We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson elds and propose its quantum simulation by two-dimensional, bichromatic, rst-sideband driving of a single trapped ion. We provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep strong coupling regimes. We also show that the particular case of degenerate eld frequencies and balanced couplings allows us to cast the model as two parity deformed oscillators in any given coupling regime.