Ground-state phase diagram of the quantum Rabi model

Abstract

The Rabi model plays a fundamental role in understanding light-matter interaction. It reduces to the Jaynes-Cummings model via the rotating-wave approximation, which is applicable only to the cases of near resonance and weak coupling. However, recent experimental breakthroughs in upgrading light-matter coupling order require understanding the physics of the full quantum Rabi model (QRM). Despite the fact that its integrability and energy spectra have been exactly obtained, the challenge to formulate an exact wavefunction in a general case still hinders physical exploration of the QRM. Here we unveil a ground-state phase diagram of the QRM, consisting of a quadpolaron and a bipolaron as well as their changeover in the weak-, strong- and intermediate-coupling regimes, respectively. An unexpected overweighted antipolaron is revealed in the quadpolaron state, and a hidden scaling behavior relevant to symmetry breaking is found in the bipolaron state. An experimentally accessible parameter is proposed to test these states, which might provide novel insights into the nature of the light-matter interaction for all regimes of the coupling strengths.Comment: 14 pages, 13 figures, Physical Review A, in pres

Theoretical Methods for Ultrastrong Light–Matter Interactions

“…A coherent state in this representation of the Hamiltonian correspond to a polaron state in the original basis. 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.…”

“…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]. Other applications of polaron transformations in the context of QED are presented in Sec.…”

Frequency-renormalized multipolaron expansion for the quantum Rabi model

“…This is our motivation of the present work. Very recently, we have introduced a trial wavefunction based on the concept of polaron and anti-polaron picture in order to explore the phase diagram of the QRM [32]. An important feature of this trial wavefunction is that it provides a unified framework to accurately describe the physics of the QRM both in the weak-and strong coupling regimes.…”

Nonlinear quantum Rabi model in trapped ions

“…The QRM is a fruitful physical model with applications in condensed matter, quantum optics, and quantum information processing. In fact, the QRM has been investigated in many contexts, such as quantum phase transitions [15][16][17], dissipative QRM [18], generalized QRM [19][20][21][22], multiparticle QRM [23][24][25][26], and quantum thermodynamics [27], among others. Furthermore, proposals and experimental realizations of the QRM in different quantum simulators as optical lattices [28], circuit QED [29], as well as trapped ions [30][31][32][33] have been put forward.…”