# The asymmetric quantum Rabi model in the polaron picture

## TL;DR

This paper extends the polaron concept to the asymmetric quantum Rabi model, analyzing the competition between polarons and anti-polarons influenced by coupling strength and asymmetry, revealing conditions where anti-polarons dominate.

## Contribution

It systematically explores the anti-polaron phenomenon in the asymmetric Rabi model, highlighting conditions for anti-polaron overweighting and proposing experimental detection methods.

## Key findings

- Anti-polaron can surpass the polaron in weight under certain conditions.
- Overweighted anti-polaron occurs beyond a critical coupling strength when asymmetry is small.
- Displacement transition from negative to positive indicates anti-polaron dominance.

## Abstract

The concept of the polaron in condensed matter physics has been extended to the Rabi model, where polarons resulting from the coupling between a two-level system and single-mode photons represent two oppositely displaced oscillators. Interestingly, tunneling between these two displaced oscillators can induce an anti-polaron, which has not been systematically explored in the literature, especially in the presence of an asymmetric term. In this paper, we present a systematic analysis of the competition between the polaron and anti-polaron under the interplay of the coupling strength and the asymmetric term. While intuitively the anti-polaron should be secondary owing to its higher potential energy, we find that, under certain conditions, the minor anti-polaron may gain a reversal in the weight over the major polaron. If the asymmetric amplitude $\epsilon$ is smaller than the harmonic frequency $\omega$, such an overweighted anti-polaron can occur beyond a critical value of the coupling strength $g$; if $\epsilon$ is larger, the anti-polaron can even be always overweighted at any $g$. We propose that the explicit occurrence of the overweighted anti-polaron can be monitored by a displacement transition from negative to positive values. This displacement is an experimentally accessible observable, which can be measured by quantum optical methods, such as balanced Homodyne detection.