Lifetimes of ultralong-range Rydberg molecules in vibrational ground and excited state
Björn Butscher, Vera Bendkowsky, Johannes Nipper, Jonathan B. Balewski, Ludmila Kukota, Robert Löw, Tilman Pfau, Weibin Li, Thomas Pohl, Jan Michael Rost
Since their first experimental observation, ultralong-range Rydberg molecules consisting of a highly excited Rydberg atom and a ground state atom have attracted the interest in the field of ultracold chemistry. Especially the intriguing properties like size, polarizability and type of binding they inherit from the Rydberg atom are of interest. An open question in the field is the reduced lifetime of the molecules compared to the corresponding atomic Rydberg states. In this letter we present an experimental study on the lifetimes of the ^3Σ(5s-35s) molecule in its vibrational ground state and in an excited state. We show that the lifetimes depends on the density of ground state atoms and that this can be described in the frame of a classical scattering between the molecules and ground state atoms. We also find that the excited molecular state has an even more reduced lifetime compared to the ground state which can be attributed to an inward penetration of the bound atomic pair due to imperfect quantum reflection that takes place in the special shape of the molecular potential.
We predict that ultralong-range Rydberg bi-molecules form in collisions between polar molecules in cold and ultracold settings. The collision of $Λ$-doublet nitric oxide (NO) with long-lived Rydberg NO($nf$, $ng$) molecules forms ultralong-range Rydberg bi-molecules with GHz energies and kilo-Debye permanent electric dipole moments. The Hamiltonian includes both the anisotropic charge-molecular dipole interaction and the electron-NO scattering. The rotational constant for the Rydberg bi-molecules is in the MHz range, allowing for microwave spectroscopy of rotational transitions in Rydberg bi-m…
We explore the electronic structure of ultralong-range pentaatomic Rydberg molecules from a merger of a Rydberg atom and two ground state heteronuclear diatomic molecules. Our focus is on the interaction of Rb($23s$) and Rb($n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the pentaatomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and ori…
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 analyze the adiabatic electronic potentials evolving from the Rb$(n=35, l\ge 3)$ Rydberg degenerate manifold. We hereby focus on three different classes of geometries of the Rydberg molecules, including symmetric, asymmetric and planar configurations. The metamorphosis of these potential energy surfaces in the presence of an external electric field is explo…
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 motion of the diatomic molecule, and take into account the Rb($n, l\ge 3$) Rydberg degenerate manifold and the energetically closest neighboring levels with principal quantum numbers $n'>n$ and orbital quantum number $l\le2$. We focus here on the adiabatic electronic potentials evolving from the Rb($n, l\ge 3$) and Rb($n=26, l=2$) manifolds. The directional pr…
We explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on interaction of Rb($27s$) Rydberg atom with KRb($N=0$) diatomic polar molecule. There's significant electronic hybridization of Rb($n=24$, $l\ge 3$) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born-Oppenheimer potential curves, ess…
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 …
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.
We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the ground Cs perturber atoms by including the full set of spin-resolved ${}^{1,3}S_J$ and ${}^{1,3}P_J$ scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet (S=1) spin states through Rydberg electron spin-orbit and ground electron hyperfine interactions. Excellent agreement with observed data in Saßmannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and …
Vibrational properties of ultralong Rydberg Cs$_2$ molecules are investigated on corresponding potential curves obtained by perturbation theory. The Rydberg Cs$_2$ molecules are associated by a Rydberg Cs($nS/nP$) atom $(n=30-70)$ and a ground state Cs($6s$) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential curves is to generate accurate atomic Rydberg states from realistic {\it ab initio} effective core potential. The calculated results have similar characteristics with available experimental and theoretical investigations on Rydberg Rb$_2$ m…
We investigate polyatomic ultralong-range Rydberg molecules consisting of three ground state atoms bound to a Rydberg atom via $s$- and $p$-wave interactions. By employing the finite basis set representation of the unperturbed Rydberg electron Green's function we reduce the computational effort to solve the electronic problem substantially. This method is subsequently applied to determine the potential energy surfaces of triatomic systems in electronic $s$- and $p$-Rydberg states. Their molecular geometry and resulting vibrational structure are analyzed within an adiabatic approach that separa…
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 therefore strongly alters the electric field seen by the polar diatomic molecule due to the Rydberg electron. As a consequence, the adiabatic potential energy curves responsible for the molecular binding can be tuned in such a way that an intersection with neighboring curves occurs. The latter leads to admixture of s-wave character in the Rydberg wave function an…
We study long range interactions between two Rydberg atoms and predict the existence of ultralong range Rydberg dimers with equilibrium distances of many thousand Bohr radii. We calculate the dispersion coefficients $C_{5}$, $C_{6}$ and $C_{8}$ for two rubidium atoms in the same excited level $np$, and find that they scale like $n^{8}$, $n^{11}$ and $n^{15}$, respectively. We show that for certain molecular symmetries, these coefficients lead to long range potential wells that can support molecular bound levels. Such macrodimers would be very sensitive to their environment, and could probe wea…
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 electric dipole moments and in addition allow for coherent control of the polar molecule orientation. In this work, we include additional Rydberg manifolds which couple to the nearly degenerate set of Rydberg states employed in [S. T. Rittenhouse and H. R. Sadeghpour, Phys. Rev. Lett. 104, 243002 (2010)]. The coupling of a set of $(n+3)s$ Rydberg states with the…
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…
We report the creation of ultralong-range Sr$_2$ molecules comprising one ground-state $5s^2$ $^1S_0$ atom and one atom in a $5sns$ $^3S_1$ Rydberg state for $n$ ranging from 29 to 36. Molecules are created in a trapped ultracold atomic gas using two-photon excitation near resonant with the $5s5p$ $^3P_1$ intermediate state, and their formation is detected through ground-state atom loss from the trap. The observed molecular binding energies are fit with the aid of first-order perturbation theory that utilizes a Fermi pseudopotential with effective $s$-wave and $p$-wave scattering lengths to de…
We observe ultralong-range blue-shifted Cs$_{2}$ molecular states near $ns_{1/2}$ Rydberg states in an optical dipole trap, where $31\leq n\leq34$. The accidental near degeneracy of $(n-4)l$ and $ns$ Rydberg states for $l>2$ in Cs, due to the small fractional $ns$ quantum defect, leads to non-adiabatic coupling among these states, producing potential wells above the $ns$ thresholds. Two important consequences of admixing high angular momentum states with $ns$ states are the formation of large permanent dipole moments, $\sim 15-100\,$Debye, and accessibility of these states via two-photon assoc…
A detailed theoretical framework for highly excited Rydberg molecules is developed based on the generalized local frame transformation. Our approach avoids the use of pseudopotentials and yields analytical expressions for the body-frame reaction matrix. The latter is used to obtain the molecular potential energy curves, but equally it can be employed for photodissociation, photoionization, or other processes. To illustrate the reliability and accuracy of our treatment we consider the Rb$^*-$Rb Rydberg molecule and compare our treatment with state-of-the-art alternative approaches. As a second …
We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an $s$-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the…
We study the impact of Rydberg molecule formation on the storage and retrieval of Rydberg polaritons in an ultracold atomic medium. We observe coherent revivals appearing in the retrieval efficiency of stored photons that originate from simultaneous excitation of Rydberg atoms and Rydberg molecules in the system with subsequent interference between the possible storage paths. We show that over a large range of principal quantum numbers the observed results can be described by a two-state model including only the atomic Rydberg state and the Rydberg dimer molecule state. At higher principal qua…
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 electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interat…
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration taking into account both the $s$-wave and $p$-wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the $p$-wave interaction on the ultralong-range molecular states for a pure $B$-field configuration. In the presence of external fields the angular degrees of freedom acquires vibrational character and we encounter two- and three-dimensional…
Photoexcitation rates for creation of ultralong-range Rydberg molecules (ULRM) with 31$\lesssim n \lesssim41$ in both ground and excited vibrational levels in cold ($T\sim900$~nK) gases of polarized and unpolarized $^{87}$Sr 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 q…
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 which 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 $^3P_J$ triplet of Rb$^-$ and allow us to extract parameters of the associated $p$-wave…
We investigate the impact of an electric field on the structure of ultralong-range polar diatomic Rydberg molecules. Both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows to shift the corresponding potential wells in such a m…
The lifetimes and decay channels of ultralong-range Rydberg molecules created in a dense BEC are examined by monitoring the time evolution of the Rydberg population using field ionization. Studies of molecules with values of principal quantum number, $n$, in the range $n=49$ to $n=72$ that contain tens to hundreds of ground state atoms within the Rydberg electron orbit show that their presence leads to marked changes in the field ionization characteristics. The Rydberg molecules have lifetimes of $\sim1-5\,μ$s, their destruction being attributed to two main processes: formation of Sr$^+_2$ ion…
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 fr…
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 non-adiabatic 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 non-adiabatic trapping and decay of molecular states found near pronounced avoided crossings in…
Ultracold Rydberg molecules have been extensively studied both theoretically and ex-perimentally. Here the authors review the recent realizations of various ultralong-range Rydberg molecules and macrodimers, and explore their potential for current and future applications in spectroscopy, few- and many-body interactions and quantum information processing.
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 mV/cm, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenchi…
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…
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 repulsive interaction does not support bound states. However, as we will show, adding a second ground-state atom, a bound triatomic molecule becomes possible constituting a Borromean Rydberg system.
The formation of ultralong-range Rydberg molecules is a result of the attractive interaction between Rydberg electron and polarizable ground state atom in an ultracold gas. In the nondegenerate case the backaction of the polarizable atom on the electronic orbital is minimal. Here we demonstrate, how controlled degeneracy of the respective electronic orbitals maximizes this backaction and leads to stronger binding energies and lower symmetry of the bound dimers. Consequently, the Rydberg orbitals hybridize due to the molecular bond.
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 Rydberg electron. In particular, we put emphasis on the splitting of the energy levels, and elucidate the nature of the splitting via the construction of symmetry-adapted orbitals.
We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using the Born-Oppenheimer approximation including s- and p-wave scattering, reproduces the measured binding energies. The calculated molecular wavefunctions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or anti-alig…
We report on the observation of ultralong range interactions in a gas of cold Rubidium Rydberg atoms. The van-der-Waals interaction between a pair of Rydberg atoms separated as far as 100,000 Bohr radii features two important effects: Spectral broadening of the resonance lines and suppression of excitation with increasing density. The density dependence of these effects is investigated in detail for the S- and P- Rydberg states with main quantum numbers n ~ 60 and n ~ 80 excited by narrow-band continuous-wave laser light. The density-dependent suppression of excitation can be interpreted as th…
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…
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 properties and electronic wave functions of these exotic molecules are investigated analytically via hybridized diatomic states. The effects of the molecular geometry on the system's properties are studied through comparisons of the adiabatic potential curves and electronic structures for both symmetric and randomly configured molecular geometries. General …
The lifetimes of the lower-lying vibrational states of ultralong-range strontium Rydberg molecules comprising one ground-state 5s2 1S0 atom and one Rydberg atom in the 5s38s 3S1 state are reported. The molecules are created in an ultracold gas held in an optical dipole trap and their numbers determined using field ionization, the product electrons being detected by a microchannel plate. The measurements show that, in marked contrast to earlier measurements involving rubidium Rydberg molecules, the lifetimes of the low-lying molecular vibrational states are very similar to those of the parent R…
We observe "trilobite-like" states of ultracold 85Rb2 molecules, in which a ground-state atom is bound by the electronic wavefunction of its Rydberg-atom partner. We populate these states through the ultraviolet excitation of weakly-bound molecules, and access a regime of trilobite-like states at low principal quantum numbers and with vibrational turning points around 35 Bohr radii. This demonstrates that, unlike previous studies that used free-to-bound transitions, trilobite-like states can also be excited through bound-to-bound transitions. This approach provides high excitation probabilitie…
In high orbital angular momentum ($\ell \geq 3$) Rydberg states, the centrifugal barrier hinders close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-$\ell$ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular …
We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-range molecules with giant (kilo-Debye) permanent electric dipole moments form. Large molecular permanent electric dipole moments are challenging to experimentally realize. Meeting this challenge has garnered significant interest because permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions and realization of strongly correlated many-body quantum systems. These ne…
A remarkable property of Rydberg atoms is the possibility to create molecules formed by one highly excited atom and another atom in the ground state. The first realisation of such a Rydberg molecule has opened an active field of physical investigations, and showed that its basic properties can be described within a simple model regarding the ground state atom as a small perturber that is bound by a low-energy scattering process with the Rydberg electron [C. H. Greene et al, Phys. Rev. Lett., 85: 2458 (2000)]. Besides the good agreement between theory and the experiment concerning the vibration…
Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behaviour in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We i…
We report the creation of heteronuclear ultralong-range Rydberg-molecule dimers by excitation of minority $^{88}\text{Sr}$ atoms to $5sns\,^3S_1$ Rydberg states ($n=31-39$) in a dense background of $^{84}\text{Sr}$. We observe an isotope shift of the $ν=0$ vibrational state over this range of $n$ and compare our measurements with a theoretical prediction and a simple scaling argument. With the appropriate choice of principal quantum number the isotope shift is sufficiently large to produce heteronuclear dimers with almost perfect fidelity. When the spectral selectivity is limited, we obtain a …
We investigate the interaction between three rubidium atoms in highly excited ($58p$) Rydberg states lying along a common axis and calculate the potential energy surfaces (PES) between the three atoms. We find that three-body long-range potential wells exist in some of these surfaces, indicating the existence of very extended bound states that we label \textit{macrotrimers}. We calculate the lowest vibrational eigenmodes and the resulting energy levels and show that the corresponding vibrational periods are rapid enough to be detected spectroscopically.
