Hidden symmetry and tunneling dynamics in asymmetric quantum Rabi models

Abstract

The asymmetric quantum Rabi model (AQRM) has a broken Z 2 symmetry, with generally a nondegenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the Z 2 -symmetric quantum Rabi model are recovered, however, without any obvious paritylike symmetry. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. Here, we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunneling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunneling.

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

“…Here it should be mentioned that the word "hidden" is more used for asymmetric QRM with bias where the parity symmetry is generally broken in the model but there are certain points of bias strength that regain some symmetry. [67][68][69] Here our case is reverse in some sense, the parity symmetry is never broken either for the model or in the GS, but there is a symmetry breaking which is little noticed. Let us decompose the parity into two parts, P = P𝜎 Px where P𝜎 = 𝜎 x reverses the spin while Px = (−1) a † a effectively inverses the spatial space x → −x.…”

Generalized adiabatic approximation to the quantum Rabi model

“…1. This interpretation is known as the displaced oscillator picture and has been extensively used in lightmatter interaction models [24][25][26][27].…”

Entanglement resonance in the asymmetric quantum Rabi model

“…Actually, the reappearance of the energy quasidegeneracies in the A-QRM is caused by another symmetry in the A-QRM occurring when = mω/2. Such symmetry is called the hidden symmetry of the A-QRM [42][43][44][45][46]. Very recently, its symmetry operators for m = 1 and 2 are rigorously derived [44,61] and a general scheme to obtain the symmetry operators has been proposed [62].…”

“…Among the generations, the asymmetric quantum Rabi model (A-QRM) has attracted much attention recently [42][43][44][45][46]. The A-QRM contains an extra driving term σ x compare to the standard QRM [29].…”

“…The interesting thing is that A-QRM seems to recover the symmetry at some certain values of [29,42,50,51]. Many scholars found that the A-QRM has a hidden symmetry [42][43][44][45]. More recently, an analysis of the energy spectrum of the A-QRM from a numerical point of view reveals that the hidden symmetry manifesting the energy level crossover happens for the driving amplitude equaling to an integer times half of the photon frequency ω [46].…”