Bose polaron in spherically symmetric trap potentials: Ground states with zero and lower angular momenta

Abstract

Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators, ${\hat{J}}^2$ and ${\hat{J}}_z$, of the system, using a cranking gauge-transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value $⟨\widehat{J^2}⟩$ is shown to be shared in impurity and bosons, but the value $⟨{\hat{J}}_z⟩$ is carried by the impurity due to the rotational symmetry. We also analyze the ground-state properties numerically obtained in this variational method for the system of the attractive impurity-boson interaction, and find that excited boson distributions around the impurity overlap largely with impurity's wave function in their quantum-number spaces and also in the real space because of the attractive interaction employed.

31 pages, 6 figures. Some comments, references, and new figures in Fig.3 have been added

References in corpus (20)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Attractive and repulsive Fermi polarons in two dimensions
• Phase diagram of a two-component Fermi gas with resonant interactions
• Repulsive Fermi polarons in a resonant mixture of ultracold ${}^6$Li atoms
• Radiofrequency spectroscopy of a strongly interacting two-dimensional Fermi gas
• Excitation spectra and rf-response near the polaron-to-molecule transition from the functional renormalization group
• Variational study of polarons in Bose-Einstein condensates
• Rotation of quantum impurities in the presence of a many-body environment
• Self-localized impurities embedded in a one dimensional Bose-Einstein condensate and their quantum fluctuations
• Diagrammatic Monte Carlo study of the acoustic and the BEC polaron
• Polarons in Ultracold Fermi Superfluids
• Transport of strong-coupling polarons in optical lattices
• Finite-temperature behavior of the Bose polaron
• Universality of the unitary Fermi gas: A few-body perspective
• The p-wave polaron
• Finite-size and confinement effects in spin-polarized trapped Fermi gases
• Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation
• The self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength
• Impurity coupled to an artificial magnetic field in a Fermi gas in a ring trap

Cited by in corpus (1)

• Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium