Observation of blueshifted ultralong-range Cs2 Rydberg molecules

Dissociation of ultracold cesium Rydberg-ground molecules

We report the experimental measurements of the decay rate of polar cesium nD5/2 - 6S1/2 Rydberg-ground molecules with a large principal quantum number range of 35 ≤ n ≤ 40. Rydberg molecules are prepared employing the method of two-photon photoassociation and the molecular (atomic) ions, due to autoionization (blackbody photoionization), are detected with a microchannel plate detector. The decay rate Γ of the vibrational ground state of the deep and shadow bound molecules for triplet (TΣ) and mixed singlet-triplet (S,TΣ) are measured by fitting the molecular population with the exponential function. Comparing with the parent atom, the decay rate of the polar Rydberg-ground molecule shows an obvious increase with a magnitude of a few μs. The possible dissociation mechanism of polar Rydberg-ground molecules including a collisional decay, blackbody induced decay, and coupling of adjacent Rydberg states and tunneling decay are discussed in detail. The theoretical model is induced to simulate the measurements, showing agreement.

Heteronuclear Long-Range Rydberg Molecules

We present the formation of homonuclear Cs_{2}, K_{2}, and heteronuclear CsK long-range Rydberg molecules in a dual-species magneto-optical trap for ^{39}K and ^{133}Cs by one-photon UV photoassociation. The different ground-state-density dependence of homo- and heteronuclear photoassociation rates and the detection of stable molecular ions resulting from autoionization provide an unambiguous assignment. We perform bound-bound millimeter-wave spectroscopy of long-range Rydberg molecules to access molecular states not accessible by one-photon photoassociation. Calculations based on the most recent theoretical model and atomic parameters do not reproduce the full set of data from homo- and heteronuclear long-range Rydberg molecules consistently. This shows that photoassociation and millimeter-wave spectroscopy of heteronuclear long-range Rydberg molecules provide a benchmark for the development of theoretical models.

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.

Observation of photoassociation spectroscopy of ultralong 37D5/2 + 6S1/2Cs2 Rydberg molecules

We present an experimental observation of 37D_5/2 + 6S_1/2Cs₂ Rydberg-ground molecules by employing a two-photon photoassociation method. Two distinct Rydberg-ground molecular signals, deep and shallow bound molecules, are observed at the red detuning of atomic line. In theory, the model of scattering interaction between the Rydberg electron and ground-state atom is used to simulate the experiments. Two potential energy curves with energy minimum, deep pure triplet ³Σ and shallow hyperfine-mixed singlet-triplet ^1,3Σ potentials, refer to the attained Rydberg-ground molecular signals, respectively. Calculations of the binding energy of triplet ³Σ and mixed ^1,3Σv = 0 states are compared with the measurements. The agreement between the calculated and measured values of the binding energy yields zero-energy scattering lengths a_s ^T(0) = -19.2a₀ and a_s ^S(0) = -1.3a₀, respectively.

Theoretical Prediction of the Creation and Observation of a Ghost Trilobite Chemical Bond

The "trilobite"-type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The ultralong-range chemical bond between the two atoms is a nonperturbative linear combination of the many degenerate electronic states associated with high principal quantum numbers, and the resulting electron probability distribution closely resembles a fossil trilobite from antiquity. We show how to coherently engineer this same long-range orbital through a sequence of electric and magnetic field pulses even when the ground-state atom is not present and propose several methods to observe the resulting orbital. The existence of such a ghost chemical bond in which an electron reaches out from one atom to a nonexistent second atom is a consequence of the high level degeneracy.

Ultracold Rydberg molecules

Ultracold molecules formed from association of a single Rydberg atom with surrounding atoms or molecules and those from double Rydberg excitations are discussed in this review. Ultralong-range Rydberg molecules possess a novel molecular bond resulting from scattering of the Rydberg electron from the perturber atoms or molecules. The strong interactions between Rydberg atoms in ultracold gases may lead to formation of macroscopic Rydberg macrodimers. The exquisite control over the properties of the Rydberg electron means that interesting and unusual few-body and quantum many-body features can be realized in such systems.

Rydberg molecules have been extensively studied both theoretically and experimentally. Here the authors review the recent developments in the study of various types of Rydberg molecules and their potential for future applications in spectroscopy, sensing and quantum information.

Polyatomic Trilobite Rydberg Molecules in a Dense Random Gas

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 an s state, overcoming selection rules that hinder the photoassociation of ordinary trilobites.

Atom-Based Sensing of Weak Radio Frequency Electric Fields Using Homodyne Readout

We utilize a homodyne detection technique to achieve a new sensitivity limit for atom-based, absolute radio-frequency electric field sensing of 5 μV cm⁻¹ Hz^−1/2. A Mach-Zehnder interferometer is used for the homodyne detection. With the increased sensitivity, we investigate the dominant dephasing mechanisms that affect the performance of the sensor. In particular, we present data on power broadening, collisional broadening and transit time broadening. Our results are compared to density matrix calculations. We show that photon shot noise in the signal readout is currently a limiting factor. We suggest that new approaches with superior readout with respect to photon shot noise are needed to increase the sensitivity further.

Theory of Ultralong-Range Rydberg Molecule Formation Incorporating Spin-Dependent Relativistic Effects: Cs(6s)-Cs(np) as Case Study

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules that form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the 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 state electron hyperfine interactions. Excellent agreement with observed data in Saßmannshausen et al. [Phys. Rev. Lett. 2015, 113, 133201] in line positions and profiles is obtained. We also determine the spin-dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules for which all of the relativistic contributions are accounted.

Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segrè in 1934, but a line shape that changes with the principal quantum number n. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet p-wave shape resonance in the e^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14}  cm^{-3}, and therefore an interparticle spacing of 1300 a_{0} within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion-neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

Molecular physics. Production of trilobite Rydberg molecule dimers with kilo-Debye permanent electric dipole moments

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. However, large molecular permanent electric dipole moments are challenging to realize experimentally. We report the observation of ultralong-range Rydberg molecules with bond lengths of ~100 nanometers and kilo-Debye permanent electric dipole moments that form when an ultracold ground-state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit. The electronic character of this hybrid class of "trilobite" molecules is dominated by degenerate Rydberg manifolds, making them difficult to produce by conventional photoassociation. We used detailed coupled-channel calculations to reproduce their properties quantitatively. Our findings may lead to progress in ultracold chemistry and strongly correlated many-body physics.

Experimental characterization of singlet scattering channels in long-range Rydberg molecules

We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.

From molecular spectra to a density shift in dense Rydberg gases

In Rydberg atoms, at least one electron is excited to a state with a high principal quantum number. In an ultracold environment, this low-energy electron can scatter off a ground state atom allowing for the formation of a Rydberg molecule consisting of one Rydberg atom and several ground state atoms. Here we investigate those Rydberg molecules created by photoassociation for the spherically symmetric S-states. A step by step increase of the principal quantum number up to n=111 enables us to go beyond the previously observed dimer and trimer states up to a molecule, where four ground state atoms are bound by one Rydberg atom. The increase of bound atoms and the decreasing binding potential per atom with principal quantum number results finally in an overlap of spectral lines. The associated density-dependent line broadening sets a fundamental limit, for example, for the optical thickness per blockade volume in Rydberg quantum optics experiments.

Ultracold Rydberg atoms — atoms with highly excited electrons — can form molecules with ground state atoms. By tuning the principal quantum number of the Rydberg state, Gaj et al. study the transition from resolvable molecular lines to the mean shift regime, where indistinguishable lines form a band.

Dynamics of heavy-Rydberg ion-pair formation in K(14p,20p)-SF6, CCl4 collisions

The dynamics of formation of heavy-Rydberg ion-pair states through electron transfer in K(np)-SF6, CCl4 collisions is examined by measuring the velocity, angular, and binding energy distributions of the product ion pairs. The results are analyzed with the aid of a Monte Carlo collision code that models both the initial electron capture and the subsequent evolution of the ion pairs. The model simulations are in good agreement with the experimental data and highlight the factors such as Rydberg atom size, the kinetic energy of relative motion of the Rydberg atom and target particle, and (in the case of attaching targets that dissociate) the energetics of dissociation that can be used to control the properties of the product ion-pair states.

Photoassociation of long-range nD Rydberg molecules

We observe long-range homonuclear diatomic nD Rydberg molecules photoassociated out of an ultracold gas of Rb87 atoms for 34≤n≤40. The measured ground-state binding energies of Rb87(nD+5S1/2) molecular states are larger than those of their Rb87(nS+5S1/2) counterparts, which shows the dependence of the molecular bond on the angular momentum of the Rydberg atom. We exhibit the transition of Rb87(nD+5S1/2) molecules from a molecular-binding-dominant regime at low n to a fine-structure-dominant regime at high n [akin to Hund's cases (a) and (c), respectively]. In the analysis, the fine structure of the nD Rydberg atom and the hyperfine structure of the 5S1/2 atom are included.

Alignment of D-state Rydberg molecules

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 a Fermi pseudopotential approach including s- and p-wave scattering terms, reproduces the measured binding energies. The calculated molecular wave functions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or antialignment with respect to the magnetic field axis.

Excitation of weakly bound molecules to trilobitelike Rydberg states

We observe "trilobitelike" states of ultracold (85)Rb(2) molecules, in which a ground-state atom is bound by the electronic wave function of its Rydberg-atom partner. We populate these states through the ultraviolet excitation of weakly bound molecules, and access a regime of trilobitelike 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, trilobitelike states can also be excited through bound-to-bound transitions. This approach provides high excitation probabilities without requiring high-density samples, and affords the ability to control the excitation radius by selection of the initial-state vibrational level.