Analytical approach to the Bose polaron \\ via $q$-deformed Lie algebra
- URL: http://arxiv.org/abs/2203.14340v2
- Date: Tue, 13 Sep 2022 11:42:01 GMT
- Title: Analytical approach to the Bose polaron \\ via $q$-deformed Lie algebra
- Authors: Enderalp Yakaboylu
- Abstract summary: We present a novel approach to the Bose polaron based on the notion of quantum groups, also known as $q$-deformed Lie algebras.
We derive its ground state energy in the phonon branch of the Bogoliubov dispersion.
Our approach has the potential to open up new avenues in polaron physics by connecting it with seemingly unrelated research topics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a novel approach to the Bose polaron based on the notion of
quantum groups, also known as $q$-deformed Lie algebras. In this approach, a
mobile impurity can be depicted as a deformation of the Lie algebra of the
bosonic creation and annihilation operators of the bath, in which the impurity
is immersed. Accordingly, the Bose polaron can be described as a bath of
noninteracting $q$-deformed bosons, which allows us to provide an analytical
formulation of the Bose polaron at arbitrary couplings. Particularly, we derive
its ground state energy in the phonon branch of the Bogoliubov dispersion and
demonstrate that the previously observed transition from a repulsive to an
attractive polaron occurs at the vicinity where the quantum group symmetry is
broken. Furthermore, our approach has the potential to open up new avenues in
polaron physics by connecting it with seemingly unrelated research topics where
quantum groups play an essential role, such as anyons.
Related papers
- Impurities and polarons in bosonic quantum gases: a review on recent progress [0.0]
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas.
The latter can be realized by a Bose-Einstein condensate (BEC) of ultracold atoms, or of exciton polaritons in a semiconductor.
arXiv Detail & Related papers (2024-10-12T07:44:01Z) - A unified theory of strong coupling Bose polarons: From repulsive
polarons to non-Gaussian many-body bound states [0.0]
We show that the interplay of impurity-induced instability and stabilization by repulsive boson-boson interactions results in a discrete set of metastable many-body bound states.
This work provides a unified theory of attractive and repulsive Bose polarons on the repulsive side of the Feshbach resonance.
arXiv Detail & Related papers (2023-05-01T14:05:11Z) - Manipulating Generalized Dirac Cones In Quantum Metasurfaces [68.8204255655161]
We consider a collection of single quantum emitters arranged in a honeycomb lattice with subwavelength periodicity.
We show that introducing uniaxial anisotropy in the lattice results in modified dispersion relations.
arXiv Detail & Related papers (2022-03-21T17:59:58Z) - Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings.
We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z) - Self-stabilized Bose polarons [0.0]
We show a solution of the Bose polaron problem beyond the Bogoliubov approximation.
We show that the Bose polaron energy remains bounded from below across the resonance.
Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding.
arXiv Detail & Related papers (2021-02-26T17:35:00Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the
Strong Coupling Regime [0.0]
We present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a non-perturbative theory.
We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings.
arXiv Detail & Related papers (2021-01-28T13:50:03Z) - Quantum chaos driven by long-range waveguide-mediated interactions [125.99533416395765]
We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide.
Our calculation reveals two-polariton eigenstates that have a highly irregular wave-function in real space.
arXiv Detail & Related papers (2020-11-24T07:06:36Z) - Sub-bosonic (deformed) ladder operators [62.997667081978825]
We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness.
This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states.
In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
arXiv Detail & Related papers (2020-09-10T20:53:58Z) - Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems [0.0]
We extend the nonequilibrium bosonic Dynamical Mean Field Theory to Markovian open quantum systems.
As a first application, we address the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump.
arXiv Detail & Related papers (2020-08-06T10:35:26Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.