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arXiv:2211.08070 · The Journal of Chemical Physics

Variational theory of angulons and their rotational spectroscopy

Zhongda Zeng, Enderalp Yakaboylu, Mikhail Lemeshko, Tao Shi, Richard Schmidt

Published Mar 10, 2023• 4 citations
arXivHTMLPDF

Abstract

The angulon, a quasiparticle formed by a quantum rotor dressed by the excitations of a many-body bath, can be used to describe an impurity rotating in a fluid or solid environment. Here, we propose a coherent state ansatz in the co-rotating frame, which provides a comprehensive theoretical description of angulons. We reveal the quasiparticle properties, such as energies, quasiparticle weights, and spectral functions, and show that our ansatz yields a persistent decrease in the impurity's rotational constant due to many-body dressing, which is consistent with experimental observations. From our study, a picture of the angulon emerges as an effective spin interacting with a magnetic field that is self-consistently generated by the molecule's rotation. Moreover, we discuss rotational spectroscopy, which focuses on the response of rotating molecules to a laser perturbation in the linear response regime. Importantly, we take into account initial-state interactions that have been neglected in prior studies and reveal their impact on the excitation spectrum. To examine the angulon instability regime, we use a single-excitation ansatz and obtain results consistent with experiments, in which a broadening of spectral lines is observed while phonon wings remain highly suppressed due to initial-state interactions.

DOI
10.1063/5.0135893

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The angulon, a quasiparticle formed by a quantum rotor dressed by the excitations of a many-body bath, can be used to describe an impurity rotating in a fluid or solid environment. Here, we propose a coherent state ansatz in the co-rotating frame, which provides a comprehensive theoretical description of angulons. We reveal the quasiparticle properties, such as energies, quasiparticle weights, and spectral functions, and show that our ansatz yields a persistent decrease in the impurity's rotational constant due to many-body dressing, which is consistent with experimental observations. From our study, a picture of the angulon emerges as an effective spin interacting with a magnetic field that is self-consistently generated by the molecule's rotation. Moreover, we discuss rotational spectroscopy, which focuses on the response of rotating molecules to a laser perturbation in the linear response regime. Importantly, we take into account initial-state interactions that have been neglected in prior studies and reveal their impact on the excitation spectrum. To examine the angulon instability regime, we use a single-excitation ansatz and obtain results consistent with experiments, in which a broadening of spectral lines is observed while phonon wings remain highly suppressed due to initial-state interactions.
We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an "angulon"-a quantum rotor dressed by a quantum field-and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalization of the impurity rotational structure, such as that observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.
The oft-quoted dictum by Arthur Schawlow: ``A diatomic molecule has one atom too many'' has been disavowed. Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the rotation of coupled cold molecules in the presence of a many-body environment. In this thesis, we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron - a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon - a quasiparticle formed out of a rotating molecule in a bosonic bath. With this theoretical toolbox, we reveal the self-localization transition for the angulon quasiparticle. We show that, unlike for polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. For the system containing multiple impurities, by analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system from the strong-coupling regime to the weak molecule-bath interaction regime. We show that the molecules tend to have a strong alignment in the ground state, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. Finally, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.
Impurity motion in a many-body environment has been a central issue in the field of low-temperature physics for decades. In bosonic quantum fluids, the onset of a drag force experienced by point-like objects is due to collective environment excitations, driven by the exchange of linear momentum between the impurity and the many-body bath. In this work we consider a rotating impurity, with the aim of exploring how angular momentum is exchanged with the surrounding bosonic environment. In order to elucidate these issues, we employ a quasiparticle approach based on the angulon theory, which allows us to effectively deal with the non-trivial algebra of quantized angular momentum in the presence of a many-body environment. We uncover how impurity dressing by environmental excitations can establish an exchange channel, whose effectiveness crucially depends on the initial state of the impurity. Remarkably, we find that there is a critical value of initial angular momentum, above which this channel effectively freezes.
Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born–Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.
Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born-Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.
We investigate a molecular quantum rotor in a two-dimensional Bose-Einstein condensate. The focus is on studying the angulon quasiparticle concept in the crossover from few- to many-body physics. To this end, we formulate the problem in real space and solve it with a mean-field approach in the frame co-rotating with the impurity. We show that the system starts to feature angulon characteristics when the size of the bosonic cloud is large enough to screen the rotor. More importantly, we demonstrate the departure from the angulon picture for large system sizes or large angular momenta where the properties of the system are determined by collective excitations of the Bose gas.