Ultralong-range Rydberg Molecules Research Articles

Nonadiabatic interaction effects in the spectra of ultralong-range Rydberg molecules

Nonadiabatic interaction effects in the spectra of ultralong-range Rydberg molecules

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.

Measuring nonlocal three-body spatial correlations with Rydberg trimers in ultracold quantum gases

We measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic ($^{84}\mathrm{Sr}$) and spin-polarized fermionic ($^{87}\mathrm{Sr}$) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of 6 (3!), in the case of bosonic $^{84}\mathrm{Sr}$ due to bunching and a marked reduction for spin-polarized fermionic $^{87}\mathrm{Sr}$ due to antibunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to in situ studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.

Vibronic interactions in trilobite and butterfly Rydberg molecules

Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.

Charged ultralong-range Rydberg trimers

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterised by their unique electronic structures resulting from the ion-induced admixture of quantum defect-split Rydberg $n$P states with different low-field seeking high-$l$ states. We predict that in both cases these diatomic molecular states can bind additional ground state atoms lying within the orbit of the Rydberg electron, thereby forming charged ultralong-range Rydberg molecules (ULRM) with binding energies similar to that of conventional non-polar ULRM. To demonstrate this, we consider a Rydberg atom interacting with a single ground state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalisation over a finite basis and the vibrational structure is determined using the Multi-Configuration Time-Dependent Hartree method. Due to the lobe-like structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.

Observation of Vibrational Dynamics of Orientated Rydberg-Atom-Ion Molecules.

Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few millivolts per centimeter, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenching the electric field. A high resolution ion microscope allows us to detect the molecule's orientation and its temporal vibrational dynamics in real space. Our study opens the door to the control of molecular dynamics in Rydberg molecules.

Photoassociation spectra of cesium 31D<sub>5/2</sub>+6S<sub>1/2</sub>(<i>F</i> = 4) ultra-long range Rydberg molecules

In this paper, we conduct the experiment and simulation on 31D<sub>5/2</sub>+6S<sub>1/2</sub>(<i>F</i> = 4) Cs<sub>2</sub> ULRMs. These molecules are prepared by employing a two-photon photoassociation scheme. Two distinct ultralong-range Rydberg molecular signals are observed at the detuning −162.8MHz and −66.6MHz of 31D<sub>5/2</sub> atomic resonant line, which are bound by the pure triplet potential and mixed singlet-triplet potential, respectively. We use the model of scattering interaction between the Rydberg electron and ground-state atom to perform the simulation. The molecular potential-energy curves are obtained by solving the Hamiltonian on a grid of intermolecular distances <i>R</i>. The calculations of the binding energy of pure triplet and mixed singlet-triplet <i>v</i> = 0 vibrational states are compared with the experimental measurements. The calculated and measured values of the binding energy are in good agreement. The <i>s</i>-wave pure triplet and singlet zero-energy scattering length are obtained to be<inline-formula><tex-math id="M3">\begin{document}$ {a}_{{\rm{s}}}^{{\rm{T}}}\left(\text{0}\right)=-\text{19.16}{a}_{0} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M3.png"/></alternatives></inline-formula> and<inline-formula><tex-math id="M4">\begin{document}$ {a}_{{\rm{s}}}^{{\rm{S}}}\left(0\right)=-\text{1.92}{a}_{0} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M4.png"/></alternatives></inline-formula>, respectively. This kind of molecule with large size, abundant vibrational states and large permanent electric dipole moment is an excellent candidate for studying low-energy collision dynamics. The study of these molecules will further deepen and enrich the understanding of the special binding mechanism and exotic properties of the ULRMs.

Resolving rotationally excited states of ultralong-range Rydberg molecules

We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of $^{86}\mathrm{Sr}$. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state $^{86}\mathrm{Sr}$ atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for $^{84}\mathrm{Sr}$, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large $s$-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.

Dressed Ion-Pair States of an Ultralong-Range Rydberg Molecule

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than R_{∞}/2.

A protocol to realize triatomic ultralong range Rydberg molecules in an ultracold KRb gas

We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N = 0 and N = 2 rotational levels, is engineered which exploits the unique Rydberg electron–molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck–Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.

Observation of spin-orbit-dependent electron scattering using long-range Rydberg molecules

We present experimental evidence for spin-orbit interaction of an electron as it scatters from a neutral atom. The scattering process takes place within a Rb$_2$ ultralong-range Rydberg molecule, consisting of a Rydberg atomic core, a Rydberg electron, and a ground state atom. The spin-orbit interaction leads to characteristic level splittings of vibrational molecular lines which we directly observe via photoassociation spectroscopy. We benefit from the fact that molecular states dominated by resonant $p$-wave interaction are particularly sensitive to the spin-orbit interaction. Our work paves the way for studying novel spin dynamics in ultralong-range Rydberg molecules. Furthermore, it shows that the molecular setup can serve as a microlaboratory to perform precise scattering experiments in the low-energy regime of a few meV.

Excitation of vibrationally-excited ultralong-range strontium Rydberg molecules in quantum gases

SynopsisThe photoexcitation rate for ultralong-range Rydberg molecules is sensitive to the initial spatial sepa-ration of the atoms from which they are formed. Here we explore the photoexcitation of different molecular vibrational states as a probe of spatial correlations in a cold atomic gas.

Rydberg polyatomic molecules: Electronic structure and experimental proposal for their creation

SynopsisWe describe the electronic structure and main features of ultralong range Rydberg molecules formed by a Rydberg atom, either Rb or K, and the heteronuclear diatomic molecule KRb. By analyzing their electronic structure, we propose a protocol to create these molecules experimentally from a mixture of ultracold atoms and ultracold molecules.

Measurements of spatial correlations in quantum gases using ultralong-range strontium Rydberg molecules

SynopsisThe photoexcitation of ultralong-range Rydberg molecules is demonstrated as a probe of spatial cor-relations in a quantum gas on previously inaccessible length scales of 1400-3200 a 0. Measurements using cold (∼1 μK) (fermionic) 87Sr and (bosonic) 84Sr reveal the effects of quantum statistics on the pair correlation function g (2)(R).

Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of 87Sr

Photoexcitation rates for creation of ultralong-range Rydberg molecules with 31 ≲ n ≲ 41 in both ground and excited vibrational levels in cold (T ∼ 900 nK) gases of polarized and unpolarized 87Sr are presented. The measured production rates of the ν = 0, 1 and 2 vibrational levels reveal rather different n dependences which are analyzed by evaluating the Franck–Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wave functions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited ν = 1 molecules can furnish a probe of pair correlations over intermediate length scales.

Precision Spectroscopy of Negative-Ion Resonances in Ultralong-Range Rydberg Molecules.

The level structure of negative ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system that is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so-far unobserved fine structure of the ^{3}P_{J} triplet of Rb^{-} and allows us to extract parameters of the associated p-wave scattering resonances that deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.

Formation of ultralong-range fermionic Rydberg molecules in 87Sr: role of quantum statistics

ABSTRACTMeasurements of ultralong-range Rydberg molecule formation in cold gases of fermionic 87Sr atoms are presented. Measurements undertaken using polarised and unpolarised cold atom samples demonstrate that studies of Rydberg molecule formation can provide a window into the important role played by quantum statistics in determining the pair-correlation function, , and, more generally, can furnish a sensitive probe of spatial correlations in quantum gases that is suitable for use in a number of different applications.

Alignment of s -state Rydberg molecules in magnetic fields

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 influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizeable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the $s$-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open novel possibilities to access the physics of relativistic electron-atom scattering experimentally.

Photoassociation of rotating ultra-long range Rydberg molecules

We discuss the rotational structure of ultra-long range Rydberg molecules and their angular nuclear wave function. Expressing the complete molecular wave function in a laboratory fixed frame, we derive the transition matrix elements for the photoassociation of free ground state atoms. The coupling strength depends on the angular momentum coupling in the Rydberg molecule, which differs for the various types of Rydberg molecules. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be transferred to other Rydberg molecules involving different atomic species or molecular coupling cases.

Spin-interaction effects for ultralong-range Rydberg molecules in a magnetic field

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a $^{87}$Rb Rydberg atom whose outer electron interacts via spin-dependent $s$- and p-wave scattering with a polarizable $^{87}$Rb ground state atom. Our model includes also the hyperfine structure of the ground state atom as well as spin-orbit couplings of the Rydberg and ground state atom. We focus on $d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gau{\ss}. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both, weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.