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 $n$p$_{3/2}$ Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs$_2$ 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.
Electrostatic multipole interactions generate long-range Rydberg-Rydberg macrodimer. We calculate the adiabatic potentials of cesium $(nD_{J})_2$ 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 ca…
A microscopic understanding of molecules is essential for many fields of natural sciences but their tiny size hinders direct optical access to their constituents. Rydberg macrodimers - bound states of two highly-excited Rydberg atoms - feature bond lengths easily exceeding optical wavelengths. Here we report on the direct microscopic observation and detailed characterization of such macrodimers in a gas of ultracold atoms in an optical lattice. The size of about 0.7 micrometers, comparable to the size of small bacteria, matches the diagonal distance of the lattice. By exciting pairs in the ini…
Long-range macrodimers formed by D-state cesium Rydberg atoms are studied in experiments and in calculations. Cesium 62DJ-62DJ Rydberg-atom macrodimers, bonded via long-range multipole interaction, are prepared by two-color photo-association in a cesium atom trap. The first color (pulse A) resonantly excites seed Rydberg atoms, while the second (pulse B, detuned by the molecular binding energy) resonantly excites the Rydberg-atom macrodimer states below the 62DJ pair asymptotes. The Rydberg-atom molecules are measured by extraction of auto-ionization products and Rydberg-atom electric-field io…
We show that sizeable Abelian and non-Abelian gauge fields arise in the relative motion of two dipole-dipole interacting Rydberg atoms. Our system exhibits two magnetic monopoles for adiabatic motion in one internal two-atom state. These monopoles occur at a characteristic distance between the atoms that is of the order of one micron. The deflection of the relative motion due to the Lorentz force gives rise to a clear signature of the effective magnetic field. In addition, we consider non-adiabatic transitions between two near-degenerate internal states and show that the associated gauge field…
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…
We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy surfaces (PES) for various symmetries of doubly excited ns and np rubidium atoms. We show that the PES for these symmetries exhibit deep (~GHz) potential wells, which can support very extended (~micrometers) bound vibrational states (macrodimers). We present n-scaling relations for both the depth De of the wells and the equilibrium separations Re of these macrodimers, and explore their response to small electric fields and stability with resp…
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 was 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…
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 $d_s \lesssim 4\,μ$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 =…
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 $μ$m-size bound states can be populated {\it via} photoassociation (PA), and how the signature of the ad-mixing of various $\ell$-character producing the potential wells could be probed. We discuss how sharp variations of the PA rate %to…
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 lig…
We report the observation of cold Cs Rydberg atom molecules bound at internuclear separations of R~3-9 um. The bound states result from avoided crossings between Rydberg atom pair interaction potentials in an applied electric field. The molecular states can be modified by changing the applied electric field. The molecules are observed by mapping the radial separation of the two Rydberg atoms as a function of time delay between excitation and detection using the Coulomb repulsion of the ions after pulsed field ionization. Measurements were performed for 63D+65D, 64D+66D, 65D+67D, and 66D+68D pa…
Extended Hubbard models have proven to bear novel quantum states, but their experimental realization remains challenging. In this work we propose to use bosonic quantum gases dressed with molecular bound states in Rydberg interaction potentials for the observation of these quantum states. We study the molecular Rabi coupling with respect to principal quantum number and trapping frequency of the ground state atoms for various molecular potentials of Rubidium and Potassium, and the hereby resulting dressed interaction strength. Additionally, we propose a two-color excitation scheme which signifi…
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.
We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser excitation cycle as a function of the laser detuning provides a measure for the Rydberg interaction coefficient. With the lattice spacing precisely known, the proposed scheme only relies on the measurement of the number of Rydberg atoms and thus circumvents the necessity to map the interaction potential by varying the interparticle separation.
Ultracold Rb atoms were used to demonstrate non-degenerate four-wave mixing through a Rydberg state. Continuous 5S-5P-nD two-photon excitation to the Rydberg state was combined with an nD-6P tuned laser in a phase matched geometry. The angular dependence, spatial profile, and dependence on detuning were investigated, showing good agreement with theory. Under optimum conditions 50 percent of the radiation was emitted into the phase-matched direction.
We show that ultracold chemical reactions can be manipulated and controlled by using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasi-bound) states exist near the collision threshold. We investigate how, by Rydberg-dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmar…
We propose a new approach to excite ion-pair states of ultracold dimers. The central idea is a two-step process where first long-range Rydberg molecules are formed by photoassociation, which are then driven by stimulated emission towards the ion-pair state, a process bearing features of a photo-induced harpooning reaction. We assess the feasibility of this approach through a detailed experimental and theoretical study on a specific system, p-wave-scattering dominated long-range Rydberg molecules in caesium, and discuss potential applications for the study of strongly correlated plasmas consist…
We investigate static properties of laser-driven, ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and discussed.
We study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in t…
We measure nonlocal third-order spatial correlations in non-degenerate ultracold gases of bosonic ($^{84}$Sr) and spin-polarized fermionic ($^{87}$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 six (3!) in the case of bosonic $^{84}$Sr due to bunching, and a marked reduction for spin-polarized fermionic $^{87}$Sr due to anti-bunching. The experimental results are compared to theoretical predictions an…
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-ord…
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 pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For…
We present a versatile laser system which provides more than 1.5W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial Titanium-Sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we…
We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the pr…
We have studied the behavior of cold Rydberg atoms embedded in an ultracold plasma. We demonstrate that even deeply bound Rydberg atoms are completely ionized in such an environment, due to electron collisions. Using a fast pulse extraction of the electrons from the plasma we found that the number of excess positive charges, which is directly related to the electron temperature Te, is not strongly affected by the ionization of the Rydberg atoms. Assuming a Michie-King equilibrium distribution, in analogy with globular star cluster dynamics, we estimate Te. Without concluding on heating or cool…
We present a combined experimental and theoretical study of the effects of Rydberg interactions on Autler-Townes spectra of ultracold gases of atomic strontium. Realizing two-photon Rydberg excitation via a long-lived triplet state allows us to probe the thus far unexplored regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atom-loss spectra. The experiment is analyzed within a one-body density matrix approach, accounting for interaction-induced level shifts and de…
Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms such as giant dipole states are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence t…
We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold quantum Rydberg gas.
In excited molecules, the interaction between the covalent Rydberg and ion-pair channels forms a unique class of excited Rydberg states, in which the infinite manifold of vibrational levels are the equivalent of atomic Rydberg states with a heavy electron mass. Production of the ion pair states usually requires excitation through one or several interacting Rydberg states; these interacting channels are pathways for loss of flux, diminishing the rate of ion pair production. Here, we develop an analytical, asymptotic charge transfer model for the interaction between ultracold Rydberg molecular s…
We show that the excitation of long-range Rydberg molecules in a three-dimensional optical lattice can be used as a position- and time-sensitive probe of the site occupancy in the system. To this end, we detect the ions which are continuously generated by the decay of the formed Rydberg molecules. While a superfluid gas shows molecule formation for all parameters, a Mott insulator with $n=1$ filling reveals a strong suppression of the number of formed molecules. In the limit of weak probing, the technique can be used to probe the superfluid to Mott-insulator transition in real-time. Our method…
In the laser excitation of ultracold atoms to Rydberg states, we observe a dramatic suppression caused by van der Waals interactions. This behavior is interpreted as a local excitation blockade: Rydberg atoms strongly inhibit excitation of their neighbors. We measure suppression, relative to isolated atom excitation, by up to a factor of 6.4. The dependence of this suppression on both laser irradiance and atomic density are in good agreement with a mean-field model. These results are an important step towards using ultracold Rydberg atoms in quantum information processing.
Rubidium Rydberg atoms in either $|m_j|$-sublevel of the $36p_{3/2}$ state can exchange energy via Stark-tuned Förster resonances, including two-, three-, and four-body dipole-dipole interactions. Three-body interactions of this type were first reported and categorized by Faoro, \textit{et al.}~[Nat.\ Commun.\ \textbf{6}, 8173 (2015)] and their Borromean nature was confirmed by Tretyakov, \textit{et al.}~[Phys.\ Rev.\ Lett. \textbf{119}, 173402 (2017)]. We report the time dependence of the $N$-body Förster resonance $N\times 36p_{3/2,|m_j|=1/2}\rightarrow 36s_{1/2}+37s_{1/2}+(N-2)\times 36p_{3…
We explore how the extraordinary properties of Rydberg atoms can be employed to impact the motion of ultracold ground state atoms. Specifically, we use an off-resonant two-photon laser dressing to map features of the Rydberg states on ground state atoms. It is demonstrated that the interplay between the spatially varying quantization axis of the considered Ioffe-Pritchard field and the fixed polarizations of the laser transitions provides the possibility of substantially manipulating the ground state trapping potential.
We propose a scheme to realize a heavy Rydberg system (HRS), a bound pair of oppositely charged ions, from a gas of ultracold atoms. The intermediate step to achieve large internuclear separations is the creation of a unique class of ultra-long-range Rydberg molecules bound in a stairwell potential energy curve. Here, a ground-state atom is bound to a Rydberg atom in an oscillatory potential emerging due to attractive singlet $p$-wave electron scattering. The utility of our approach originates in the large electronic dipole transition element between the Rydberg- and the ionic molecule, while …
We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schroedinger equation of the system within a given n-manifold and show that for a sufficiently large Ioffe field strength the 2n^2-dimensional system of coupled Schroedinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center…
We present time-resolved spectroscopic measurements of Rydberg-Rydberg interactions in an ultracold gas, revealing the pair dynamics induced by long-range van der Waals interactions between the atoms. By detuning the excitation laser, a specific pair distribution is prepared. Penning ionization on a microsecond timescale serves as a probe for the pair dynamics under the influence of the attractive long-range forces. Comparison with a Monte Carlo model not only explains all spectroscopic features but also gives quantitative information about the interaction potentials. The results imply that th…
We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about three orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the …
We predict the existence of a class of ultracold giant molecules formed from trapped ultracold Rydberg atoms and polar molecules. The interaction which leads to the formation of such molecules is the anisotropic charge-dipole interaction ($a/R^2$). We show that prominent candidate molecules such as KRb and deuterated hydroxyl (OD) should bind to Rydberg rubidium atoms, with energies $E_b\simeq 5-25$ GHz at distances $R\simeq 0.1-1 \ μ$m. These molecules form in double wells, mimicking chiral molecules, with each well containing a particular dipole orientation. We prepare a set of correlated dr…
We demonstrate the interaction-induced blockade effect in an ultracold $^{88}$Sr gas via studying the time dynamics of a two-photon excitation to the triplet Rydberg series $5\mathrm{s}n\mathrm{s}\, ^3\textrm{S}_1$ for five different principle quantum numbers $n$ ranging from 19 to 37. By using a multi-pulse excitation sequence to increase the detection sensitivity we could identify Rydberg-excitation-induced atom losses as low as $<1\%$. Based on an optical Bloch equation formalism, treating the Rydberg-Rydberg interaction on a mean-field level, the van der Waals coefficients are extracted fr…
The Rydberg excitation blockade has been at the heart of an impressive array of recent achievements; however, state-mixing interactions can compromise its efficiency. When ultracold atoms are excited to Rydberg states near Förster resonance, up to $\sim 50\%$ of atoms can be found in dipole coupled product states within tens of ns after excitation. There has been disagreement in the literature regarding the mechanism by which this mixing occurs. We use state-selective field ionization spectroscopy to measure, on a shot-by-shot basis, the distribution of Rydberg states populated during narrowba…
An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from $300\,$K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance …
We present the experimental observation of the antiblockade in an ultracold Rydberg gas recently proposed by Ates et al. [Phys. Rev. Lett. 98, 023002 (2007)]. Our approach allows the control of the pair distribution in the gas and is based on a strong coupling of one transition in an atomic three-level system, while introducing specific detunings of the other transition. When the coupling energy matches the interaction energy of the Rydberg long-range interactions, the otherwise blocked excitation of close pairs becomes possible. A time-resolved spectroscopic measurement of the Penning ionizat…
Clouds of ultracold strontium 5s48s 1S0 or 5s47d 1D2 Rydberg atoms are created by two photon excitation of laser cooled 5s2 1S0 atoms. The spontaneous evolution of the cloud of low orbital angular momentum (low-l) Rydberg states towards an ultracold neutral plasma is observed by imaging resonant light scattered from core ions, a technique that provides both spatial and temporal resolution. Evolution is observed to be faster for the S-states, which display isotropic attractive interactions, than for the D-states, which exhibit anisotropic, principally repulsive interactions. Immersion of the at…
Recent experiments have demonstrated the spontaneous evolution of a gas of ultracold Rydberg atoms into an expanding ultracold plasma, as well as the reverse process of plasma recombination into highly excited atomic states. Treating the evolution of the plasma on the basis of kinetic equations, while ionization/excitation and recombination are incorporated using rate equations, we have investigated theoretically the Rydberg-to-plasma transition. Including the influence of spatial correlations on the plasma dynamics in an approximate way we find that ionic correlations change the results only …
We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential energy curves. The wide parameter range accessible by combining the various properties of different alkali atoms often leads to hybridized electronic states accessible via one or two photon ex…
It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the Rydberg blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is observab…
We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. Key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wavefunction, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initi…
