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 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.
We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to princip…
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…
In this paper we demonstrate the detection of millimeter waves via Autler-Townes splitting in 85Rb Rydberg atoms. This method may provide an independent, atom-based, SI-traceable method for measuring mm-wave electric fields, which addresses a gap in current calibration techniques in the mm-wave regime. The electric- field amplitude within a rubidium vapor cell in the WR-10 waveguide band is measured for frequencies of 93 GHz, and 104 GHz. Relevant aspects of Autler-Townes splitting originating from a four-level electromagnetically induced transparency scheme are discussed. We measure the E-fie…
We report on the measurement of Stark shifted energy levels of $^{87}$Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500V/cm, ranging beyond the classical ionisation threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers $n=35$ and $n=70$ have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in [M. L. Zimmerman et al., Phys. Rev. A 20, 2251 (1979)], which…
We present a precise measurement of the rubidium ionic core polarizability. The results can be useful for interpreting experiments such as parity violation or black-body radiation shifts in atomic clocks since the ionic core electrons contribute significantly to the total electrical polarizability of rubidium. We report a dipole polarizability $α_d$ = $9.116 \pm 0.009$ $a_0^3$ and quadrupole polarizability $α_q$ = $38.4 \pm 0.6$ $a_{0}^{5}$ derived from microwave and radio-frequency spectroscopy measurements of Rydberg states with large angular momentum. By using a relatively low principal qua…
We have measured the radiative lifetimes of ns, np and nd Rydberg states of rubidium in the range 28 < n < 45. To enable long-lived states to be measured, our experiment uses slow-moving Rb atoms in a magneto-optical trap (MOT). Two experimental techniques have been adopted to reduce random and systematic errors. First, a narrow-bandwidth pulsed laser is used to excite the target Rydberg state, resulting in minimal shot-to-shot variation in the initial state population. Second, we monitor the target state population as a function of time delay from the laser pulse using a short-duration, milli…
We present the direct measurements of electric-dipole moments for $5P_{3/2}\to nD_{5/2}$ transitions with $20<n<48$ for Rubidium atoms. The measurements were performed in an ultracold sample via observation of the Autler-Townes splitting in a three-level ladder scheme, commonly used for 2-photon excitation of Rydberg states. To the best of our knowledge, this is the first systematic measurement of the electric dipole moments for transitions from low excited states of rubidium to Rydberg states. Due to its simplicity and versatility, this method can be easily extended to other transitions and o…
It is clearly important to pursue atomic standards for quantities like electromagnetic fields, time, length and gravity. We have recently shown, using Rydberg states, that Rb atoms in a vapor cell can serve as a practical, compact standard for microwave electric field strength. Here, we demonstrate, for the first time, that Rb atoms excited in a vapor cell can also be used for vector microwave electrometry by using Rydberg atom electromagnetically induced transparency. We describe the measurements necessary to obtain an arbitrary microwave electric field polarization at a resolution of $0.5^\c…
We investigate the electronic structure and properties of Rydberg atoms exposed to a magnetic quadrupole field. It is shown that the spatial as well as generalized time reversal symmetries lead to a two-fold degeneracy of the electronic states in the presence of the external field. A delicate interplay between the Coulomb and magnetic interactions in the inhomogeneous field leads to an unusual weak field splitting of the energy levels as well as complex spatial patterns of the corresponding spin polarization density of individual Rydberg states. Remarkably the magnetic quadrupole field induces…
Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and…
We investigate the phenomenon of optical bistability in a driven ensemble of Rydberg atoms. By performing two experiments with thermal vapors of rubidium and cesium, we are able to shed light onto the underlying interaction mechanisms causing such a non-linear behavior. Due to the different properties of these two atomic species, we conclude that the large polarizability of Rydberg states in combination with electric fields of spontaneously ionized Rydberg atoms is the relevant interaction mechanism. In the case of rubidium, we directly measure the electric field in a bistable situation via tw…
Three body resonant interactions between Rydberg atoms are considered in order to perform few-body quantum gates. So far, the resonances found in cesium or rubidium atoms relied on an adjacent two-body resonance which ceases to exist for principal quantum numbers above $n \simeq 40$. We have proposed recently a new class of 3-body interaction resonances in alkali-metal Rydberg atoms [P. Cheinet \textit{et al.}, Quant. Elect. \textbf{50}, 213 (2020)], which circumvienes this limit. We investigate here the relative strength between this new class of 3-body interaction resonance and quasi-forbidd…
We have experimentally produced rubidium Bose-Einstein condensate in an optically-plugged magnetic quadrupole (OPQ) trap. A far blue-detuned focused laser beam with a wavelength of 532 nm is plugged in the center of the magnetic quadrupole trap to increase the number of trapped atoms and suppress the heating. A radio frequency (RF) evaporative cooling in the magneto-optical hybrid trap is applied to decrease the atom temperature into degeneracy. The atom number of the condensate is $1.2(0.4)\times10^5$ and the temperature is below 100 nK. We have also studied characteristic behaviors of the co…
The exquisite properties of Rydberg levels make them particularly appealing for emerging quantum technologies. The lifetime of low-angular-momentum laser-accessible levels is however limited to a few $100\,μ\mathrm{s}$ by optical transitions and microwave blackbody radiation (BBR) induced transfers at room temperature. A considerable improvement would be obtained with the few $10\,\mathrm{ms}$ lifetime of circular Rydberg levels in a cryogenic environment reducing the BBR temperature. We demonstrate the preparation of long-lived circular Rydberg levels of laser-cooled Rubidium atoms in a cryos…
We observe the direct excitation of pairs of Cs atoms from the ground state to molecular states correlating asymptotically to $ns\,n'f$ asymptotes. The molecular resonances are interpreted as originating from the dipole-quadrupole interaction between the $ns\,n'f$ pair states and close-by $np\,np$ asymptotes ($22\leq n \leq 32$). This interpretation is supported by Stark spectroscopy of the pair states and a detailed modeling of the interaction potentials. The dipole-quadrupole interaction mixes electronic states of opposite parity and thus requires a coupling between electronic and nuclear mo…
The structure and photoexcitation dynamics of high lying doubly excited states of the strontium atom with high angular momenta are studied in the vicinity of the Sr$^+(N=5)$ threshold. The spectra recorded using resonant multiphoton isolated core excitation are analyzed with calculations based on configuration interaction with exterior complex scaling, which treats the correlated motion of the two valence electrons of Sr from first principles. The results are rationalized with a model based on multichannel quantum-defect theory and transition dipole moments calculated with a perturbative treat…
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric dipole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single…
We explore the possibility to trap Rydberg atoms in tightly confining magnetic microtraps. The trapping frequencies for Rydberg atoms are expected to be influenced strongly by magnetic field gradients. We show that there are regimes where Rydberg atoms can be trapped. Moreover, we show that so-called magic trapping conditions can be found for certain states of rubidium, where both Rydberg atoms and ground state atoms have the same trapping frequencies. Magic trapping is highly beneficial for implementing quantum gate operations that require long operation times.
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show…
Experiments on the spectroscopy of the Förster resonance Rb(37P)+Rb(37P) -> Rb(37S)+Rb(38S) and microwave transitions nP -> n'S, n'D between Rydberg states of cold Rb atoms in a magneto-optical trap have been performed. Under ordinary conditions, all spectra exhibited a 2-3 MHz line width independently of the interaction time of atoms with each other or with microwave radiation, although the ultimate resonance width should be defined by the inverse interaction time. Analysis of the experimental conditions has shown that the main source of the line broadening was the inhomogeneous electric fiel…
We have measured the AC-Stark shift of the $14D_{5/2}$ Rydberg state of rubidium 87 in an optical dipole trap formed by a focussed CO$_2$-laser. We find good quantitative agreement with the model of a free electron experiencing a ponderomotive potential in the light field. In order to reproduce the observed spectra we take into account the broadening of the Rydberg state due to photoionization. The extracted cross-section is compatible with previous measurements on neighboring Rydberg states.
Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms …
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 report on measurements on the 5S-6P rubidium transition frequencies for rubidium isotopes with an absolute uncertainty of better than \SI{450}{kHz} for the 5S $\rightarrow$ 6P$_{1/2}$ transition and \SI{20}{kHz} for the 5S $\rightarrow$ 6P$_{3/2}$ transition, achieved by saturation absorption spectroscopy. From the results we derive the hyperfine splitting with an accuracy of \SI{460}{kHz} and \SI{30}{kHz}, respectively. We also verify the literature values for the isotope shifts as well as magnetic dipole constant and the electric quadrupole constant.
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…
The structure of the Cooper minima in the transition probabilities and photoionization cross-sections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found.
The electron signals from the field ionization of two closely-spaced Rydberg states of \mbox{rubidium-85} are separated using quantum control. In selective field ionization, the state distribution of a collection of Rydberg atoms is measured by ionizing the atoms with a ramped electric field. Generally, atoms in higher energy states ionize at lower fields, so ionized electrons which are detected earlier in time can be correlated with higher energy Rydberg states. However, the resolution of this technique is limited by the Stark effect. As the electric field is increased, the electron encounter…
The decay of Rydberg-atom-ion molecules (RAIMs) due to non-adiabatic couplings between electronic potential energy surfaces is investigated. We employ the Born-Huang representation and perform numerical simulations using a Crank-Nicolson algorithm. The non-adiabatic lifetimes of rubidium RAIMs for the lowest ten vibrational states, $ν$, are computed for selected Rydberg principal quantum numbers, $n$. The non-adiabatic lifetimes are found to generally exceed the radiative Rydberg-atom lifetimes. We observe and explain a trend of the lifetimes as a function of $ν$ and $n$, and attribute irregul…
We have measured the asymptotic expansion velocities of ultra-cold plasmas (UNPs) which evolve from cold, dense, samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the initial plasma electron temperature as functions of the original Rydberg atom density and binding energy. Our results show that the electron temperature is determined principally by the plasma environment when the UNP decouples from the Rydberg atoms, which occurs when the plasma electrons become too cold to ionize the remaining Rydberg population. Furthermore, the dep…
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…
We observe the shift of Rydberg levels of rubidium close to a copper surface when atomic clouds are repeatedly deposited on it. We measure transition frequencies of rubidium to S and D Rydberg states with principal quantum numbers n between 31 and 48 using the technique of electromagnetically induced transparency. The spectroscopic measurement shows a strong increase of electric fields towards the surface that evolves with the deposition of atoms. Starting with a clean surface, we measure the evolution of electrostatic fields in the range between 30 and 300 \mum from the surface. We find that …
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 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…
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 measure strong radio-frequency (RF) electric fields using rubidium Rydberg atoms prepared in a room-temperature vapor cell as field sensors. Electromagnetically induced transparency is employed as an optical readout. We RF-modulate the 60$S_{1/2}$ and 58$D_{5/2}$ Rydberg states with 50~MHz and 100~MHz fields, respectively. For weak to moderate RF fields, the Rydberg levels become Stark-shifted, and sidebands appear at even multiples of the driving frequency. In high fields, the adjacent hydrogenic manifold begins to intersect the shifted levels, providing rich spectroscopic structure suitab…
We present evidence for Rydberg-Rydberg interaction in a gas of rubidium atoms above room temperature. Rabi oscillations on the nanosecond timescale to different Rydberg states are investigated in a vapor cell experiment. Analyzing the atomic time evolution and comparing to a dephasing model we find a scaling with the Rydberg quantum number n that is consistent with van der Waals interaction. Our results show that the interaction strength can be larger than the kinetic energy scale (Doppler width) which is the requirement for realization of thermal quantum devices in the GHz regime.
Measurements of the loss rates for strontium n$^{3}$S$_{1}$ Rydberg atoms excited in a dense BEC are presented for values of principal quantum number $n$ in the range $49\lesssim n \lesssim 150$ and local atom densities of $\sim1$ to $3\times10^{14}$cm$^{-3}$. Two main processes contribute to loss, associative ionization and state-changing. The relative importance of these two loss channels is investigated and their $n$- and density-dependences are discussed using a model in which Rydberg atom loss is presumed to involve a close collision between the Rydberg core ion and ground-state atoms. Th…
We report the measurement of absolute excitation frequencies of 87Rb to nS and nD Rydberg states. The Rydberg transition frequencies are obtained by observing electromagnetically induced transparency on a rubidium vapor cell. The accuracy of the measurement of each state is < 1 MHz, which is achieved by frequency stabilizing the two diode lasers employed for the spectroscopy to a frequency comb and a frequency comb calibrated wavelength meter, respectively. Based on the spectroscopic data we determine the quantum defects of 87Rb, and compare it with previous measurements on 85Rb. We determine …
We demonstrate how Rydberg atoms and the phenomena of electromagnetically induced transparency can be used to aid in the recording of a musical instrument in real time as it is played. Also, by using two different atomic species (cesium and rubidium) in the same vapor cell, we demonstrate the ability to record two guitars simultaneously, where each atomic species detects and allows for the recording of each guitar separately. The approach shows how audio data (the musical composition) can be detected with a quantum system, illustrating how we can control ensembles of atoms to such an extent th…
We provide an experimental demonstration of a direct fiber-optic link for RF transmission ("radio-over-fiber") using a sensitive optical antenna based on a rubidium vapor cell. The scheme relies on measuring the transmission of laser light at an electromagnetically-induced transparency resonance that involves highly-excited Rydberg states. By dressing pairs of Rydberg states using microwave fields that act as local oscillators, we encoded RF signals in the optical frequency domain. The light carrying the information is linked via a virtually lossless optical fiber to a photodetector where the …
We present a novel spectroscopic method for probing the \insitu~density of quantum gases. We exploit the density-dependent energy shift of highly excited {Rydberg} states, which is of the order $10$\MHz\,/\,1E14\,cm$^{\text{-3}}$ for \rubidium~for triplet s-wave scattering. The energy shift combined with a density gradient can be used to localize Rydberg atoms in density shells with a spatial resolution less than optical wavelengths, as demonstrated by scanning the excitation laser spatially across the density distribution. We use this Rydberg spectroscopy to measure the mean density addressed…
We report on the guided transport of an atomic sample along an optical waveguide up to a room-temperature dielectric surface. The technique exploits a simple hybrid trap consisting of a single beam dipole trap positioned ~125 μm below the field zero of a magnetic quadrupole potential. Transportation is realised by applying a moderate bias field (<12 G) to displace the magnetic field zero along the axis of the dipole trap. We use the technique to demonstrate that atomic gases may be precisely positioned at controlled distances from the surface with negligible heating or loss. This work forms an…
Long-range dipole-dipole and quadrupole-quadrupole interactions between pairs of Rydberg atoms are calculated perturbatively for calcium, strontium and ytterbium within the Coulomb approximation. Quantum defects, obtained by fitting existing laser spectroscopic data, are provided for all $S$, $P$, $D$ and $F$ series of strontium and for the $^3P_2$ series of calcium. The results show qualitative differences with the alkali metal atoms, including isotropically attractive interactions of the strontium $^1S_0$ states and a greater rarity of Förster resonances. Only two such resonances are identif…
We present a very sensitive and scalable method to measure the population of highly excited Rydberg states in a thermal vapor cell of rubidium atoms. We detect the Rydberg ionization current in a 5 mm electrically contacted cell. The measured current is found to be in excellent agreement with a theory for the Rydberg population based on a master equation for the three level problem including an ionization channel and the full Doppler distributions at the corresponding temperatures. The signal-to-noise ratio of the current detection is substantially better than purely optical techniques.
