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Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to…

We review ultralong-range Rydberg molecules (ULRM), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple…

Obtaining full control over the internal and external quantum states of molecules is the central goal of ultracold chemistry and allows for the study of coherent molecular dynamics, collisions and tests of fundamental laws of physics. When…

Molecular bonds can be divided into four primary types: ionic, covalent, van der Waals and hydrogen bonds. At ultralow temperatures a novel binding type emerges paving the way for novel molecules and ultracold chemistry [1,2]. The…

We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at large internuclear distance. The binding mechanism is based on Stark shifts and level crossings which are induced in the…

We explore the external electric field control of a species of ultralong-range molecules that emerge from the interaction of a ground state polar molecule with a Rydberg atom. The external field mixes the Rydberg electronic states and…

A generalized class of ultra-long-range Rydberg molecules is proposed which consist of a multichannel Rydberg atom whose outermost electron creates a chemical bond with a distant ground state atom. Such multichannel Rydberg molecules…

Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy…

Quantum reflection is a pure wave phenomena that predicts reflection of a particle at a changing potential for cases where complete transmission occurs classically. For a chemical bond, we find that this effect can lead to non-classical…

Sufficiently high densities in Bose-Einstein condensates provide favorable conditions for the production of ultralong-range polyatomic molecules consisting of one Rydberg atom and a number of neutral ground state atoms. The chemical binding…

We investigate the electronic structure of a triatomic Rydberg molecule formed by a Rydberg atom and two neutral ground-state atoms. Taking into account the $s$-wave and $p$-wave interactions we perform electronic structure calculations and…

The "trilobite" type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The…

The internal electric field of a Rydberg atom electron can bind a polar molecule to form a giant ultralong-range stable polyatomic molecule. Such molecules not only share their properties with Rydberg atoms, they possess huge permanent…

We investigate the structure and features of an ultralong-range triatomic Rydberg molecule formed by a Rb Rydberg atom and a KRb diatomic molecule. In our numerical description, we perform a realistic treatment of the internal rotational…

We investigate properties of ultralong-range polyatomic molecules formed with a Rb Rydberg atom and several ground-state atoms whose distance from the Rydberg atom is of the order of n^2a_0, where n is the principle quantum number of the…

A ground state atom immersed in the wave function of the valence electron of a Rydberg atom can generate a long-range Rydberg molecule (LRRM). In this work, using the multipole expansion of the electrostatic interaction in prolate…

Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a…

A Rydberg and a ground-state atom can form ultralong range diatomic molecules provided the interaction between the ground-state atom and the Rydberg electron is attractive [C. H. Greene, et al., Phys. Rev. Lett. 85, 2458 (2000)]. A…

Controlling molecular binding at the level of single atoms is one of the holy grails of quantum chemistry. Rydberg macrodimers -- bound states between highly excited Rydberg atoms -- provide a novel perspective in this direction. Resulting…

We unravel some peculiar properties of ultralong-range Rydberg molecules formed by an $s$-state $^{87}$Rb Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be…