Rydberg Macrodimers Research Articles

Microwave photo-association of fine-structure-induced Rydberg (n+2)D5/2nFJ macro-dimer molecules of cesium

Long-range (n+2)D5/2nFJ Rydberg macro-dimers are observed in an ultracold cesium Rydberg gas for 39≤n≤48. Strong dipolar flip (〈D5/2F5/2|V̂dd|F5/2D5/2〉, 〈D5/2F7/2|V̂dd|F7/2D5/2〉) and cross (〈D5/2F7/2|V̂dd|F5/2D5/2〉) couplings lead to bound, fine-structure-mixed (n+2)D5/2nFJ macro-dimers at energies between the FJ fine-structure levels. The (n+2)D5/2nFJ macro-dimers are measured by microwave photo-association from optically prepared [(n+2)D5/2]2 Rydberg-pair precursor states. Calculated adiabatic potential curves are used to elucidate the underlying physics and to model the macro-dimer spectra, with good overall agreement. Microwave photo-association allows Franck-Condon tuning, which we have studied by varying the detuning of a Rydberg-atom excitation laser. Further, in Stark spectroscopy, we have measured molecular DC electric polarizabilities that are considerably larger than those of the atomic states. The large molecular polarizabilities are unexpected and may be caused by high-ℓ mixing. The observed linewidths of the Stark-shifted molecular lines provide initial evidence for intramolecular induced-dipole-dipole interaction. Published by the American Physical Society 2024

Rydberg Macrodimers: Diatomic Molecules on the Micrometer Scale.

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 from binding potentials formed by the strong, long-range interactions of Rydberg states, Rydberg macrodimers feature bond lengths in the micrometer regime, exceeding those of conventional molecules by orders of magnitude. Using single-atom control in quantum gas microscopes, the unique properties of these exotic states can be studied with unprecedented control, including the response to magnetic fields or the polarization of light in their photoassociation. The high accuracy achieved in spectroscopic studies of macrodimers makes them an ideal testbed to benchmark Rydberg interactions, with direct relevance to quantum computing and information protocols where these are employed. This review provides a historic overview and summarizes the recent findings in the field of Rydberg macrodimers. Furthermore, it presents new data on interactions between macrodimers, leading to a phenomenon analogous to Rydberg blockade at the level of molecules, opening the path toward studying many-body systems of ultralong-range Rydberg molecules.

Microscopic electronic structure tomography of Rydberg macrodimers

Precise control and study of molecules is challenging due to the variety of internal degrees of freedom and local coordinates that are typically not controlled in an experiment. Employing quantum gas microscopy to position and resolve the atoms in Rydberg macrodimer states solves almost all of these challenges and enables unique access to the molecular frame. Here, we demonstrate the power of this approach and present first photoassociation studies for different molecular symmetries in which the molecular orientation relative to an applied magnetic field, the polarization of the excitation light and the initial atomic state are fully controlled. The observed characteristic dependencies allow for an electronic structure tomography of the molecular state. We additionally observe an orientation-dependent Zeeman shift and reveal a significant influence on it caused by the hyperfine interaction of the macrodimer state. Finally, we demonstrate controlled engineering of the electrostatic binding potential by opening a gap in the energetic vicinity of two crossing pair potentials.

Casimir-Polder-induced Rydberg macrodimers

We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir--Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances $d_s \lesssim 4\,\mu$m, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e. Rydberg macrodimers, with groundstate energies of up to $E = -68\,$MHz and radial expectation values of the order of several $\mu$m.

Adiabatic potentials of cesium (nDJ)2 Rydberg–Rydberg macrodimers

Electrostatic multipole interactions generate long-range Rydberg–Rydberg macrodimers. We calculate the adiabatic potentials of cesium Rydberg macrodimers for principal quantum numbers n ranging from 56 to 62, for J = 3/2 and 5/2, and for the allowed values of the conserved sum of the atomic angular-momentum components along the internuclear axis, M. For most combinations (n, M, J) exactly one binding potential exists, which should give rise to Rydberg macrodimer states. We study the dependence of the adiabatic potentials on the size of the two-body basis sets used in the calculation, and on the maximal order, qmax, of the multipole terms included in the calculation. We determine the binding energies and lengths of the binding adiabatic potentials, investigate their scaling behaviors as a function of the effective principal quantum number, and discuss vibrational-state wave functions. We consider the applicability of the calculated potentials and excitation rates to an experimental scheme for preparing Rydberg-atom macrodimers using two-color double-resonant photoassociation.

Long-range Rydberg molecules, Rydberg macrodimers and Rydberg aggregates in an ultracold Cs gas

We present an overview of our recent investigations of long-range interactions in an ultracold Cs Rydberg gas. These interactions are studied by high-resolution photoassociation spectroscopy, using excitation close to one-photon transitions into np3/2 Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs2 molecules. We observe two types of molecular resonances. The first type originates from the correlated excitation of two atoms into Rydberg-atom-pair states interacting at long range via multipole-multipole interactions. The second type results from the interaction of one atom excited to a Rydberg state with one atom in the electronic ground state. Which type of resonances is observed in the experiments depends on the laser intensity and frequency and on the pulse sequences used to prepare the Rydberg states. We obtain insights into both types of molecular resonances by modelling the interaction potentials, using a multipole expansion of the long-range interaction for the first type of resonances and a Fermi-contact pseudo-potential for the second type of resonances. We analyse the relation of these long-range molecular resonances to molecular Rydberg states and ion-pair states, and discuss their decay channels into atomic and molecular ions. In experiments carried out with a two-colour two-photon excitation scheme, we observe a large enhancement of Rydberg-excitation probability, which we interpret as a saturable autocatalytic antiblockade phenomenon.

Observation of Rydberg-Atom Macrodimers: Micrometer-Sized Diatomic Molecules.

Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme is employed to form these molecules in states, which correlate to np(n+1)s dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair states. We show that a full model is required to accurately predict the occurrence of bound Rydberg macrodimers. The macrodimers are distinguished from repulsive molecular states by their behavior with respect to spontaneous ionization and possible decay channels are discussed.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n{p}_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22--36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n{p}_{3/2}+n{p}_{3/2}$ dissociation asymptotes, but also to $n{s}_{1/2}+(n+1){s}_{1/2}, n{s}_{1/2}+{n}^{\ensuremath{'}}{f}_{j}$, and $(n\ensuremath{-}4){f}_{j}+(n\ensuremath{-}3){f}_{j}\phantom{\rule{4pt}{0ex}}(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole and higher-order long-range-interaction terms between the Rydberg atoms on the basis of (i) their spectral positions, (ii) their response to static and pulsed electric fields, and (iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom-pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 15 $\ensuremath{\mu}\mathrm{s}$ following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation-blockade effects.

Pulsed excitation of Rydberg-atom-pair states in an ultracold Cs gas

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n$p$_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22-36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n$p$_{3/2}+n$p$_{3/2}$ dissociation asymptotes, but also to $n$s$_{1/2}+(n+1)$s$_{1/2}$, $n$s$_{1/2}+n'$f$_{j}$, and $(n-4)$f$_{j}+(n-3)$f$_{j}$ $(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole, and higher-order long-range-interaction terms between the Rydberg atoms on the basis of i) their spectral positions, ii) their response to static and pulsed electric fields, and iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom--pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 10 $\mu$s following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation blockade effects.

Formation and properties of Rydberg macrodimers

We investigate the interaction between two rubidium atoms in highly excited Rydberg states, and find that very long-range potential wells exist. These wells are shown to support many bound states. We calculate the properties of the wells and bound levels, and show that their lifetimes are limited by that of the constituent Rydberg atoms. We also show how these micrometer-sized bound states can be populated via photoassociation (PA), and how the signature of the admixing of various l characters producing the potential wells could be probed. We discuss sharp variations of the PA rate, which could act as a switching mechanism with potential application to quantum information processing.