Rydberg Electrons in a Bose-Einstein Condensate

Abstract

We investigate a hybrid system composed of ultracold Rydberg atoms immersed in an atomic Bose-Einstein condensate (BEC). The coupling between the Rydberg electrons and BEC atoms leads to the excitation of phonons, the exchange of which induces Yukawa interaction between Rydberg atoms. Due to the small electron mass, the effective charge associated with this quasiparticle-mediated interaction can be large, while its range is equal to the healing length of the BEC, which can be tuned by adjusting the scattering length of the BEC atoms. We find that for small healing lengths, the distortion of the BEC can "image" the wave function density of the Rydberg electron, while large healing lengths induce an attractive Yukawa potential between the two Rydberg atoms that can form a new type of ultra-long-range molecule. We discuss both cases for a realistic system.Impurities in a Bose-Einstein condensate (BEC) have attracted much attention and motivated the investigation of a wide range of phenomena. For example, the motion of a single impurity in a BEC can probe the superfluid dynamics [1][2][3], while an ionic impurity in a BEC can form a mesoscopic molecular ion [4]. Due to the selfenergy induced by phonons (excitations of the BEC), a neutral impurity can self-localize in both a homogeneous and a harmonically trapped BEC [5][6][7], which sheds light on polaron physics [8,9]. Exchanging phonons between multiple impurities induces an attractive Yukawa potential between each pair of impurities [10,11], which leads to the so called "co-self-localization" [12] and is related to forming bipolarons and multipolarons [13]. Recent experiments, where an atom of a BEC is excited into a Rydberg state [14] to study phonon excitations and collective oscillations, open the door to exploration of the electron-phonon coupling in ultracold degenerate gases, a phenomenon responsible for the formation of Cooper pairs of two repelling electrons in BCS superconductivity [15].In this Letter, we study Rydberg atoms immersed in a homogeneous BEC, as sketched in Fig. 1(a). Rydberg atoms consist of an ion core and a highly excited electron with its oscillatory wave function Ψ e extending to large distances of the order of ∼n 2 a 0 (n: principle quantum number, a 0 : Bohr radius). As pointed out by Fermi [16], the interaction between the quasi-free electron at x and a ground state atom at r can be approximated at low scattering energies by a contact interaction parametrized by an energy-dependent s-wave scattering lengthWhile the s-wave approximation is valid for qualitative analysis, we include higher-partial wave contributions for quantitative results [17]. A s (k) depends on the scattering energy via the local wave number k(r) given by where R y is the Rydberg constant, 0 the vacuum permittivity, e and m e the charge and mass, respectively, of the electron with angular momentum e and quantum defect δ e . For low-e state, Eq. (1) gives an effective interaction between Rydberg and ground state atoms aswhich leads to an attraction and formation of ...

Production ofNaCa+molecular ions in the ground state from cold atom-ion mixtures by photoassociation via an intermediate state

“…Ions immersed in a Bose-Einstein condensate were proposed as a medium for exploring the physics of mesoscopic particles [14], polarons [15], and electronphonon coupling [16,17]. Hybrid atom-ions systems are also discussed as possible implementations of quantum gates [18,19].…”

Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas

“…The evolution of the perturbing neutral atom wavefunction in the shape resonance potential is a new aspect to utilizing Rydberg excitations in dense, cold media. These dynamics must be considered for future proposals relying on utilizing a Rydberg atom in a BEC [33][34][35]. We have shown that the line broadening of the Rydberg levels in an ultracold and dense media is a direct manifestation of the underlying Rydberg-perturber PECs, by accounting only for elastic e --Rb(5S) scattering.…”

Ultralong-range Rydberg molecules

“…Generalized versions of (7) include energy dependent scattering lengths, p-wave contributions as well as inhomogenous densities and have been employed successfully to describe the spectral response of single Rydberg impurities immersed in a dense BEC [87]. An intriguing application of Rydberg impurities in ultracold atomic gases is the production of textbook-like images of atomic orbitals by imprinting the shape of the Rydberg orbital onto the BEC density, which has been proposed theoretically in [75,76]. Another application is the creation of ionic impurities in BECs, which can be excited in the limit of large principal quantum numbers, typically n ∼ 160, when the Rydberg orbit exceeds the size of the atomic cloud [22].…”