Generalized adiabatic approximation to the asymmetric quantum Rabi model: conical intersections and geometric phases

Abstract

The asymmetric quantum Rabi model (AQRM), which describes the interaction between a quantum harmonic oscillator and a biased qubit, arises naturally in circuit quantum electrodynamic circuits and devices. The existence of hidden symmetry in the AQRM leads to a rich energy landscape of conical intersections (CIs) and thus to interesting topological properties. However, current approximations to the AQRM fail to reproduce these CIs correctly. To overcome these limitations we propose a generalized adiabatic approximation (GAA) to describe the energy spectrum of the AQRM. This is achieved by combining the perturbative adiabatic approximation and the exact exceptional solutions to the AQRM. The GAA provides substantial improvement to the existing approaches and pushes the limit of the perturbative treatment into non-perturbative regimes. As a preliminary example of the application of the GAA we calculate the geometric phases around CIs associated with the AQRM.

Remarks on the hidden symmetry of the asymmetric quantum Rabi model

“…These regimes have been under intense investigation by experimental and theoretical groups over the last decade [10,28]. Due to the hidden symmetry, the energy landscape of the AQRM features intersections resembling Dirac cones with quantized Berry phase [7,21]. Because the asymmetry parameter can be tuned freely in several platforms, notably circuit QED, these topological phases may be utilized as information storage with enhanced stability against noise.…”

Nodes and Spin Windings for Topological Transitions in Light–Matter Interactions

“…Indeed, although the QRM has been proposed for more than 80 years, [ 24,63 ] studies on the QRM and its extensions are still continuing. [ 1–62 ] In the following we will provide some novel insights for the level crossings and anticrossings from topological point of view.…”

“…Among the intensive dialogue between mathematics and physics [ 1–62 ] triggered by the milestone work of D. Braak [ 1 ] who revealed the integrability of the quantum Rabi model (QRM), [ 24,63,64 ] few‐body quantum phase transitions (QPTs) [ 4,13–23 ] have recently attracted a special attention in the context of light–matter interactions. [ 3,4,60,65 ] In reality, the continuing experimental enhancements of couplings have brought the era of ultra‐strong [ 5,6,66–77 ] and even deep‐strong couplings, [ 77,78 ] which makes few‐body QPTs practically relevant.…”

Symmetry operators of the asymmetric two-photon quantum Rabi model

“…Nevertheless, it exhibits the phenomenon of energy level crossings, i.e. double degeneracy [22][23][24], certainly due to the hidden symmetry beyond any known symmetry. To explore the hidden symmetry, a numerical study [25] was proposed that the symmetry operator commuting with the Hamiltonian must depend on the different system parameters unlike the symmetric case.…”