The asymmetric quantum Rabi model in the polaron picture

Abstract

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