Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment

Abstract

Recently it was shown that an impurity exchanging orbital angular momentum with a surrounding bath can be described in terms of the angulon quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. The angulon consists of a quantum rotor dressed by a many-particle field of boson excitations, and can be formed out of, for example, a molecule or a nonspherical atom in superfluid helium, or out of an electron coupled to lattice phonons or a Bose condensate. Here we develop an approach to the angulon based on the path-integral formalism, which sets the ground for a systematic, perturbative treatment of the angulon problem. The resulting perturbation series can be interpreted in terms of Feynman diagrams, from which, in turn, one can derive a set of diagrammatic rules. These rules extend the machinery of the graphical theory of angular momentum - well known from theoretical atomic spectroscopy - to the case where an environment with an infinite number of degrees of freedom is present. In particular, we show that each diagram can be interpreted as a 'skeleton', which enforces angular momentum conservation, dressed by an additional many-body contribution. This connection between the angulon theory and the graphical theory of angular momentum is particularly important as it allows to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the 1- and 2-loop contributions to the angulon self-energy, the spectral function, and the quasiparticle weight. The diagrammatic theory we develop paves the way to investigate next-to-leading order quantities in a more compact way compared to the variational approaches.

17 pages, 5 figures

References in corpus (21)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state
• Ultracold Dipolar Gas of Fermionic ${}^{23}$Na${}^{40}$K Molecules in their Absolute Ground State
• Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate
• Attractive and repulsive Fermi polarons in two dimensions
• Bose polarons in the strongly interacting regime
• Ultrafast many-body interferometry of impurities coupled to a Fermi sea
• Quantum transport through a Tonks-Girardeau gas
• Normal state of highly polarized Fermi gases: Full many-body treatment
• Rotation of quantum impurities in the presence of a many-body environment
• Coherent Microwave Control of Ultracold ${}^{23}$Na${}^{40}$K Molecules
• Quasiparticle approach to molecules interacting with quantum solvents
• Femtosecond x-ray absorption spectroscopy of spin and orbital angular momentum in photoexcited Ni films during ultrafast demagnetization
• Laser-induced rotation of iodine molecules in He-nanodroplets: revivals and breaking-free
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Quantum decoherence of a charge qubit in a spin-fermion model
• Rotation of cold molecular ions inside a Bose-Einstein condensate
• Vertex corrections for positive-definite spectral functions of simple metals
• Anomalous screening of quantum impurities by a neutral environment
• Angular self-localization of impurities rotating in a bosonic bath
• Molecular impurities interacting with a many-particle environment: from helium droplets to ultracold gases

Cited by in corpus (12)

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• Strong coupling Bose polarons out of equilibrium: Dynamical RG approach
• An impurity in a heteronuclear two-component Bose mixture
• Theory of Electron-Phonon-Dislon Interacting System - Toward a Quantized Theory of Dislocations
• Theory of the Rotating Polaron: Spectrum and Self-Localization
• Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems
• Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon
• A simple model for high rotational excitations of molecules in a superfluid
• Variational theory of angulons and their rotational spectroscopy
• Synthetic spin-orbit coupling mediated by a bosonic environment
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling