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Rotation of coupled cold molecules in the presence of a many-body environment

Xiang Li

Published Jan 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.15479/at:ista:8958

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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.
The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 84 years ago. Here we reveal the self-localization transition for the rotational analog of the polaron---the angulon quasiparticle. We show that, unlike for the 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. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates.
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.
Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper 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. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.
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.