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.
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…
Trilobites are exotic giant dimers with enormous dipole moments. They consist of a Rydberg atom and a distant ground-state atom bound together by short-range electron-neutral attraction. We show that highly polar, polyatomic trilobite states unexpectedly persist and thrive in a dense ultracold gas of randomly positioned atoms. This is caused by perturbation-induced quantum scarring and the localization of electron density on randomly occurring atom clusters. At certain densities these states also mix with a s-state, overcoming selection rules that hinder the photoassociation of ordinary trilob…
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 explore the feasibility of optically forming long-range tetratomic and larger polyatomic molecules in their ground electronic state from ultracold pairs of polar molecules aligned by external fields. Depending on the relative orientation of the interacting diatomic molecules, we find that a tetratomic can be formed either as a weakly bound complex in a very extended halo state or as a pure long-range molecule composed of collinear or nearly-collinear diatomic molecules. The latter is a novel type of tetratomic molecule comprised of two diatomic molecules bound at long intermolecular range a…
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.
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 …
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…
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.
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 …
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…
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.
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…
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…
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.
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 …
The rich internal structure and long-range dipole-dipole interactions establish polar molecules as unique instruments for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where a plethora of effects is predicted in many-body physics, quantum information science, ultracold chemistry, and physics beyond the standard model. These objectives have inspired the development of a wide range of methods to produce cold molecular ensembles. However, cooling polyatomic molecules to ultracold temperatures has until now seemed intractab…
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 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…
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 report the observation of dipole-forbidden, but quadrupole-allowed, one-photon transitions to high Rydberg states in Rb. Using pulsed UV excitation of ultracold atoms in a magneto-optical trap, we excite $5s \to nd$ transitions over a range of principal quantum numbers $n=27-59$. Compared to dipole-allowed (E1) transitions from $5s \to np$, these E2 transitions are weaker by a factor of approximately 2000. We also report measurements of the anomalous $np_{3/2} : np_{1/2}$ fine-structure transition strength ratio for $n=28-75$. Both results are in agreement with theoretical predictions.
We theoretically investigate the quantum properties of nS, nP, and nD Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to point-like particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schroedinger equation. In addition to the electronic propert…
We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases, with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation-scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in q…
Within a dense environment ($ρ\approx 10^{14}\,$atoms/cm$^3$) at ultracold temperatures ($T < 1\,μ\text{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ $^{87}$Rb Rydberg states and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydb…
We have studied the associative ionization of a Rydberg atom and a ground state atom in an ultracold Rydberg gas. The measured scattering cross section is three orders of magnitude larger than the geometrical size of the produced molecule. This giant enhancement of the reaction kinetics is due to an efficient directed mass transport which is mediated by the Rydberg electron. We also find that the total inelastic scattering cross section is given by the geometrical size of the Rydberg electron's wavefunction.
We have calculated long-range molecular potentials of the $0_g^{+}$, $0_u^{-}$ and $1_u$ symmetries between highly-excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ Rydberg states. Long-range molecular resonances are such phenomena and they were first reported in S.M. Farooqi {\it et al.}, Phys. Rev. Lett. {\bf 91} 183002. One class of these resonances occurs at energies corresponding to excited atom pairs $(n-1)d+ns$. Such resonances are attributed to $\ell$-mixin…
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, and significant differences are observed. We discuss the conditions for blockaded Rydberg excitation an…
We investigate the spectral properties of a finite laser-driven lattice of ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with variable spacings are considered. In the case of a weak laser coupling, we find a multitude of many-body Rydberg states with well-defined excitation properties which are adiabatically accessible starting from the ground state. A comprehensive analysis of the degeneracies of the spectrum as well as of the single and pair excitations numbers of the eigenstates is perform…
We have experimentally demonstrated both heating and cooling of electrons in an ultracold neutral plasma (UNP) by embedding Rydberg atoms into the plasma soon after its creation. We have determined the relationship between the initial electron temperature, $T_{e,i}$, and the binding energy of the added Rydberg atoms, $E_b$, at the crossover between heating and cooling behaviors (that is, the binding energy of the atoms, which, when they are added to the plasma, neither accelerate or slow down the plasma expansion). Specifically, this condition is $|E_b| \approx 2.7 \times k_B T_{e,i}$ when the…
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 characterize the two-photon excitation of an ultracold gas of Rubidium atoms to Rydberg states analysing the induced atomic losses from an optical dipole trap. Extending the duration of the Rydberg excitation to several ms, the ground state atoms are continuously coupled to the formed positively charged plasma. In this regime we measure the $n$-dependence of the blockade effect and we characterise the interaction of the excited states and the ground state with the plasma. We also investigate the influence of the quasi-electrostatic trapping potential on the system, confirming the validity o…
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 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 interaction…
We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as 80 cm$^{-1}$ below the lowest ionization threshold. The density of excited molecules in the illuminated volume is as high as 1 x 10$^{13}$ cm$^{-3}$. This population evolves to produce prompt free electrons and a durable cold plasma of electrons and intact NO$^{+}$ ions.
We describe a quantum information architecture consisting of a hybrid array of optically-trapped molecules and atoms. This design leverages the large transition dipole moments of Rydberg atoms to mediate fast, high-fidelity gates between qubits encoded in coherent molecular degrees of freedom. Error channels of detuning, decay, pulse area noise, and leakage to other molecular states are discussed. The molecule-Rydberg interaction can also be used to enable nondestructive molecule detection and rotational state readout. We consider a specific near-term implementation of this scheme using NaCs m…
We propose and analyze a new scheme to produce ultracold neutral plasmas deep in the strongly coupled regime. The method exploits the interaction blockade between cold atoms excited to high-lying Rydberg states and therefore does not require substantial extensions of current ultracold plasma experiments. Extensive simulations reveal a universal behavior of the resulting Coulomb coupling parameter, providing a direct connection between the physics of strongly correlated Rydberg gases and ultracold plasmas. The approach is shown to reduce currently accessible temperatures by more than an order o…
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…
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…
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…
We report on the behaviour of the ionization avalanche in an ensemble of ultracold 87Rb atoms coupled to a high lying Rydberg state and investigate extensions to the current model by including the effects of three-body recombination and plasma expansion. To separate the two effects we study the time dependence of the plasma formation at various densities as well as for different nS and nD states. At medium densities and low n we observe the onset of the avalanche as has been reported in other experiments, as well as a subsequent turn-off of the avalanche for longer excitation times, which we a…
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…
