Linear Absorption Spectrum of a Quantum Two-Dimensional Rotator Calculated Using a Rotationally Invariant System-Bath Hamiltonian

TL;DR

This paper introduces a rotationally invariant system-bath model for a quantum two-dimensional rotator, enabling the calculation of absorption spectra that reveal quantized rotational bands and their collapse, addressing limitations of previous models.

Contribution

The authors develop a new RISB model that preserves rotational symmetry and accurately captures spectral features, improving upon existing non-invariant models.

Findings

Spectral profiles show a transition from quantized rotational bands to a single peak.

The RISB model differs significantly from the RCL model in dynamics due to energy discretization.

Both models reduce to the Langevin equation in the classical limit.

Abstract

We consider a two-dimensional rigid rotator system coupled to a two-dimensional heat bath. The Caldeira-Leggett (Brownian) model for the rotator and the spin-Boson model have been used to describe such systems, but they do not possess rotational symmetry, they cannot describe the discretized rotational bands in absorption and emission spectra that have been found experimentally. Here, to address this problem, we introduce a rotationally invariant system-bath (RISB) model that is described by two sets of harmonic-oscillator baths independently coupled to the rigid rotator as sine and cosine functions of the rotator angle. Due to a difference in the energy discretization of the total Hamiltonian, the dynamics described by the RISB model differ significantly from those described by the rotational Caldeira-Legget (RCL) model, while both models reduce to the Langevin equation for a rotator in the classical limit. To demonstrate this point, we compute the rotational absorption spectrum defined by the linear response function of a rotator dipole. For this purpose, we derive a quantum master equation for the RISB model in the high-temperature Markovian case. We find that the spectral profiles of the calculated signals exhibit a transition from quantized rotational bands to a single peak after spectrum collapse. This is a significant finding, because previous approaches cannot describe such phenomena in a unified manner.