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RSC theoretical and computational chemistry series

CHAPTER 9. Molecular Impurities Interacting with a Many-particle Environment: From Ultracold Gases to Helium Nanodroplets

Mikhail Lemeshko, Richard Schmidt

Published Jan 1, 2017• 14 citations
Publisher

Abstract

In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.

DOI
10.1039/9781782626800-00444

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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.

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In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.
In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem - that based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose-Einstein Condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows not only to tremendously simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.
Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here, we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.203001]. Most important, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian. The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species. These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle.
Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations.Here, we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)].Most important, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian.The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species.These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle.
The formation of vortices is usually considered to be the main mechanism of angular momentum disposal in superfluids. Recently, it was predicted that a superfluid can acquire angular momentum via an alternative, microscopic route, namely, through interaction with rotating impurities, forming so-called ``angulon quasiparticles'' [R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114, 203001 (2015)]. The angulon instabilities correspond to transfer of a small number of angular momentum quanta from the impurity to the superfluid, as opposed to vortex instabilities, where angular momentum is quantized in units of $\ensuremath{\hbar}$ per atom. Furthermore, since conventional impurities (such as molecules) represent three-dimensional (3D) rotors, the angular momentum transferred is intrinsically 3D as well, as opposed to a merely planar rotation which is inherent to vortices. Herein we show that the angulon theory can explain the anomalous broadening of the spectroscopic lines observed for CH3{\mathrm{CH}}_{3}CH3​ and NH3{\mathrm{NH}}_{3}NH3​ molecules in superfluid helium nanodroplets, thereby providing a fingerprint of the emerging angulon instabilities in experiment.
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.
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.