High resolution studies of the fine structure pattern in high-L n=37 levels of Th3+ have been carried out using radio-frequency (rf) spectroscopy detected with Resonant Excitation Stark Ionization Spectroscopy (RESIS). Intervals separating L=9 to L=15 levels have been measured, and the results analyzed with the long-range effective potential model. The dipole polarizability of Th4+is determined to be aD= 7.720(7) a.u.. The quadrupole polarizability is found to be 21.5(3.9) a.u. Both measurements represent significant tests of a-priori theoretical descriptions of this highly relativistic ion.
Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali atoms, Rb and Cs, for the $nS$, $nP_{1/2, 3/2}$, and $nD_{3/2, 5/2}$ states with large principal quantum numbers up to $n = 50$. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semi-empirical core-polarization potential. The obtained results are compared with those from a simpler semi-empirical approach and with available experimental data.
Intensity modulated optical lattice potentials can change sign for an alkali metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO$_2$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential seen by the Rydberg atom can be made to vanish for atoms in \targeted" Rydberg states. Such state selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices.…
We present an experimental study of the Rydberg $^1S_0$- and $^1P_1$- series of ytterbium for principal quantum numbers in the range of $n=70$ to $90$. The study is performed using trap loss spectroscopy in a magneto-optical trap operating on the $6^1S_0 \rightarrow 6^1P_1$ transition at $399\,\text{nm}$. Compared to the commonly used Rydberg spectroscopy method using field-ionization and ion detection, trap loss spectroscopy is significantly simpler and requires a less sophisticated experimental setup. Using this method we determine relative values of the scalar and tensor electric polarizabi…
We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for the…
We employ doubly-resonant two-photon excitation into the 74S Rydberg state to spectroscopically measure the dynamic scalar polarizability, alpha 0, and tensor polarizability, alpha 2, of rubidium 5P3/2. To reach the necessary high intensities, we employ a cavity-generated 1064 nm optical-lattice light field, allowing us to obtain intensities near 2x10^11 W/m^2. In the evaluation of the data we use a self-referencing method that renders the polarizability measurement largely free from the intensity calibration of the laser light field. We obtain experimental values alpha 0 =-1149 (pm 2.5 percen…
Highly excited Rydberg states are usually extremely polarizable and exceedingly sensitive to electric fields. Because of this Rydberg ions confined in electric fields have state-dependent trapping potentials. We engineer a Rydberg state that is insensitive to electric fields by coupling two Rydberg states with static polarizabilities of opposite sign, in this way we achieve state-independent magic trapping. We show that the magically-trapped ion can be coherently excited to the Rydberg state without the need for control of the ion's motion.
This article presents a review of the most recent theoretical and experimental results in hydrogen. We particularly emphasize the methods used to deduce the Rydberg constant $R_\infty$ and we consider the prospects for future improvements in the precision of $R_\infty$.
The phase noise of incident light fields can be converted into amplitude noise via absorption and dispersion effects in media under electromagnetically induced transparency. The conversion process is sensitive to two-photon detuning. This effect can be used to perform a novel type of Rydberg spectroscopy. We present experimental measurements of the phase noise spectrum (PNS) with Rydberg atoms in a cesium vapor cell. Furthermore, to explore microwave field measurements, a modulation-enhanced PNS approach is proposed.
We present a study of a cold strontium Rydberg gas. The narrowband laser excitation of Rydberg states in the range n=20-80 from a 6~mK cloud of strontium atoms is detected using the spontaneous ionization of the Rydberg atoms. Using a high-resolution step-scanning technique, we perform detailed measurements of the Stark maps of selected Rydberg states. We find excellent agreement between the measured Stark maps and a numerical calculation based on an independent-electron model. Finally we show that excitation of the second valence electron can be used to probe the dynamics of the Rydberg gas w…
We study Rydberg atoms modulated by strong radio-frequency (RF) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the RF field increases from the weak- into the strong-field regime, the range of observed RF-induced phenomena progresses from AC level shifts through increasingly pronounced and numerous RF-modulation sidebands to complex state-mixing and level-crossings with high-l hydrogen-like states. Weak anharmonic admixtures in the RF field generate …
Rydberg states of atomic helium with principal quantum numbers ranging from n=20 to n=100 have been prepared by non-resonance-enhanced single-color two-photon excitation from the metastable 2 {^3}S{_1} state. Photoexcitation was carried out using linearly and circularly polarized pulsed laser radiation. In the case of excitation with circularly polarized radiation, Rydberg states with azimuthal quantum number |m_{\ell}|=2 were prepared in zero electric field, and in homogeneous electric fields oriented parallel to the propagation axis of the laser radiation. In sufficiently strong electric fie…
We present experimental results on the controlled de-excitation of Rydberg states in a cold gas of Rb atoms. The effect of the van der Waals interactions between the Rydberg atoms is clearly seen in the de-excitation spectrum and dynamics. Our observations are confirmed by numerical simulations. In particular, for off-resonant (facilitated) excitation we find that the de-excitation spectrum reflects the spatial arrangement of the atoms in the quasi one-dimensional geometry of our experiment. We discuss future applications of this technique and implications for detection and controlled dissipat…
We develop a theoretical understanding of trapping divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wavefunctions. Optical potential is proportional to the ac Stark polarizability. We find that in the independent particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usua…
We experimentally investigate trap-loss spectra of the cesium 6S1/2(F=4)-71P3/2 Rydberg state by combining the cesium atomic magneto-optical trap with the narrow-linewidth, continuously-tunable 318.6 nm ultraviolet laser. That is, the atoms in the magneto-optical trap are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which leads to the reduction of atomic fluorescence. Based on the trap-loss spectroscopy technology, the Autler-Townes splitting due to strong cooling laser is observed, and the parameter dependence of the AT splitting interval of trap-l…
The theoretical treatment of Rydberg states in one-electron ions is facilitated by the virtual absence of the nuclear-size correction, and fundamental constants like the Rydberg constant may be in the reach of planned high-precision spectroscopic experiments. The dominant nuclear effect that shifts transition energies among Rydberg states therefore is due to the nuclear mass. As a consequence, spectroscopic measurements of Rydberg transitions can be used in order to precisely deduce nuclear masses. A possible application of this approach to the hydrogen and deuterium, and hydrogen-like lithium…
Multi-step laser resonance ionization spectroscopy of lutetium (Lu) has been performed at TRIUMF's off-line laser ion source test stand. The even-parity Rydberg series $6s^2nd$ $^2D_{3/2}$, $6s^2nd$ $^2D_{5/2}$ and $6s^2ns$ $^2S_{1/2}$ were observed converging to the 6s$^2$ ionization potential. The experimental results has been compared to previous work. 51 levels of Rydberg series $6s^2nd$ $^2D_{5/2}$ and 52 levels of Rydberg series $6s^2ns$ $^2S_{1/2}$ were reported new. Additionally six even-parity autoionization (AI) series converging to Lu ionic states $5d6s$ $^3D_1$ and $5d6s$ $^3D_2$ w…
The $1\mathrm{s}n\mathrm{p}\,^3\mathrm{P}_J$ fine structure of high Rydberg states in helium has been measured by microwave spectroscopy of single-photon transitions from $1\mathrm{s}n\mathrm{s}\,^3\mathrm{S}_1$ levels in pulsed supersonic beams. For states with principal quantum numbers in the range from $n=34$ to 36, the $J = 0 \rightarrow 2$ and $J = 1 \rightarrow 2$ fine structure intervals were both observed. For values of $n$ between 45 and 51 only the larger $J = 0 \rightarrow 2$ interval was resolved. The experimental results are in good agreement with theoretical predictions. Detailed…
Binding energies of high-L Rydberg states (L^3 7) of Th2+ with n=27-29 were studied using the Resonant Excitation Stark Ionization Spectroscopy (RESIS) method. The core of the Th2+ Rydberg ion is the Fr-like ion Th3+ whose ground state is a 5 2F5/2 level. The large core angular momentum results in a complex Rydberg fine structure pattern consisting of six levels for each value of L that is only partially resolved in the RESIS excitation spectrum. The pattern is further complicated, especially for the relatively low L levels, by strong non-adiabatic effects due to the low-lying 6d levels. Analy…
We demonstrate the single-photon Rydberg excitation of cesium atoms in a magneto-optical trap (MOT). We excite atoms directly from ${{6S}_{1/2}}$ ground state to ${{nP}_{3/2}}(n=70-100)$ Rydberg state with a narrow-linewidth 319 nm ultra-violet laser. The detection of Rydberg states is performed by monitoring the reduction of fluorescence signal of the MOT as partial population on ${{6S}_{1/2}} (F = 4)$ ground state are transferred to Rydberg state. We clearly observe Autler-Townes doublet in the trap-loss spectra due to the cooling lights. Utilizing the large electric polarizibility of Rydber…
We experimentally studied the Rydberg level shift caused by the electric field, which is generated by Rydberg atom collision induced ionization in a cesium atomic ensemble. The density of charged particles caused by collisions between Rydberg atoms is changed by controlling the ground-state atomic density and optical excitation process. We measured the Rydberg level shift using Rydberg electromagnetically-induced-transparency (EIT) spectroscopy, and interpreted the physical origin using a semi-classical model. The experimental results are in good agreement with the numerical simulation. These …
We report on the atom loss spectroscopy of strontium Rydberg atoms in a magneto-optical trap, using a two-photon excitation scheme through the intermediate state $5\mathrm{s}5\mathrm{p} \, ^3\mathrm{P}_1$. Energies of the $5\mathrm{s}n\mathrm{s} \, ^3\mathrm{S}_1$ and $5\mathrm{s}n\mathrm{d} \, ^3\mathrm{D}_{1,2}$ Rydberg series of $^{88}$Sr in the range $13 \leq n \leq 50$ are determined with an absolute accuracy of 10 MHz, including the perturbed region where the $5\mathrm{s}n\mathrm{d} \, ^3\mathrm{D}_{2}$ series couples to the $5\mathrm{s}n\mathrm{d} \, ^1\mathrm{D}_{2}$ series. This repre…
We report new frequency-comb-based measurements of Ca Rydberg energy levels. Counter-propagating laser beams at 390 nm and 423 nm excite Ca atoms from the $4s^2~^1\mbox{S}_0$ ground state to $4sns~^1\mbox{S}_0$ Rydberg levels with $n$ ranging from 40 to 110. Near-resonant two-photon two-color excitation of atoms in a thermal beam makes it possible to eliminate the first-order Doppler shift. The resulting lineshapes are symmetric and Gaussian. We verify laser metrology and absolute accuracy by reproducing measurements of well-known transitions in Cs, close to the fundamental wavelengths of our …
Coupling by the resonant dipole-dipole energy transfer between cold cesium Rydberg atoms is investigated using time-resolved narrow-band de-excitation spectroscopy. This technique combines the advantage of efficient Rydberg excitation with high-resolution spectroscopy at variable interaction times. The coherent character of the process is studied by back and forth transfer in the np+np <--> ns+(n+1)s reaction. Decoherence in the ensemble has two different origins: the atom motion induced by dipole-dipole interaction and the migration of the s-Rydberg excitation in the environment of p-Rydberg …
New measurements of high-lying even parity $6sns\, {}^1 \! S_0$ and $6snd\,{}^{3,1}\!D_2$ levels of neutral $^{174}$Yb are presented in this paper. Spectroscopy is performed by a two-step laser excitation from the ground state $4f^{14}6s^2 \, {}^1 \! S_0$, and the Rydberg levels are detected by using the field ionization method. Additional two-photon microwave spectroscopy is used to improve the relative energy accuracy where possible. The spectroscopic measurements are complemented by a multichannel quantum defect theory (MQDT) analysis for the J=0 and the two-coupled J=2 even parity series. …
We present a solid-state laser system that generates over 200 mW of continuous-wave, narrowband light, tunable from 316.3 nm - 317.7 nm and 318.0 nm - 319.3 nm. The laser is based on commercially available fiber amplifiers and optical frequency doubling technology, along with sum frequency generation in a periodically poled stoichiometric lithium tantalate crystal. The laser frequency is stabilized to an atomic-referenced high finesse optical transfer cavity. Using a GPS-referenced optical frequency comb we measure a long term frequency instability of $<$35 kHz for timescales between $10^{-3}$…
We use the sensitive response to electric fields of Rydberg atoms to characterize all three vector components of the local electric field close to an atom-chip surface. We measured Stark-Zeeman maps of $S$ and $D$ Rydberg states using an elongated cloud of ultracold Rubidium atoms ($T\sim2.5$ $μ$K) trapped magnetically $100$ $μ$m from the chip surface. The spectroscopy of $S$ states yields a calibration for the generated local electric field at the position of the atoms. The values for different components of the field are extracted from the more complex response of $D$ states to the combined …
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…
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.
A velocity-selective spectroscopy technique for studying the spectra from hot Rydberg gases is presented. This method provides high-resolution measurement of the spectrum interval. Based on this method, the velocity-selective hyperfine splitting of intermediate states is measured, as well as the Doppler-free fine-structure splitting of the Rydberg states via two-photon Rydberg excitation in a room-temperature 133Cs vapor cell. The experiment data and theoretical predictions show excellent agreement.
A combined experimental and theoretical spectroscopic study of high-$n$, ${30 \lesssim n \lesssim 100}$, triplet $\text{S}$ and $\text{D}$ Rydberg states in $^{87}\text{Sr}$ is presented. $^{87}\text{Sr}$ has a large nuclear spin, ${I=9/2}$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n$ $\text{S}$ states, the hyperfine shifts are evaluated non-perturbatively taking advantage of earlier spectroscopic data for …
Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2Σ_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were ob…
Precision spectroscopy of the fine and hyperfine structures of high molecular Rydberg-Stark states: Metrology of molecular hydrogen ions
ETH Zürich（苏黎世联邦理工学院）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Université Paris-Saclay（巴黎萨克雷大学）；Centre National de la Recherche Scientifique（法国国家科学研究中心）
We show that optical spectroscopy of Rydberg states can provide accurate {\em in situ} thermometry at room-temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25 to 30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the Strontium clock transition. We demonstrate that magic wavelength lattices exist for both Strontium and Ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with $10^{-16}$ accuracy provide $10 \, \mathrm{mK}$ resolution and yield a blac…
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 demonstrate a single-photon Rydberg excitation spectroscopy of cesium (Cs) atoms in a room-temperature vapor cell. Cs atoms are excited directly from 6S1/2 ground state to nP3/2 (n = 70 - 100) Rydberg states with a 318.6 nm ultraviolet (UV) laser,and Rydberg excitation spectra are obtained by transmission enhancement of a probe beam resonant to Cs 6S1/2, F = 4 - 6P3/2, F' = 5 transition as partial population on F = 4 ground state are transferred to Rydberg state .Analysis reveals that the observed spectra are velocity-selective spectroscopy of Rydberg state, from which the amplitude and lin…
We investigated the Autler-Townes splitting produced by microwave transitions between atomic Rydberg states explored by optical spectroscopy from the ground electronic state. The laser-atom Hamiltonian describing the double irradiation of such a multilevel system is analysed on the basis of the Morris-Shore transformation. The application of this transformation to the microwave-dressed atomic system allows the identification of bright, dark, and spectator states associated with different configurations of atomic states and microwave polarisation. We derived synthetic spectra that show the main…
We report on the measurement of electron emission after the interaction of strong laser pulses with atoms and molecules. These electrons originate from high-lying Rydberg states with quantum numbers up to $n \lesssim 120$ formed by frustrated field ionization. Simulations show that both tunneling ionization by a weak dc field and photoionization by the black-body radiation contribute to delayed electron emission on the nano- to microsecond scale. We measured ionization rates from these Rydberg states by coincidence spectroscopy. Further, the dependence of the Rydberg-state production on the el…
This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions i…
Trapping a Rydberg atom close to a surface is an important step towards the realisation of many proposals of quantum information or hybrid quantum systems. One of the challenges in these experiments is to overcome the electric field emanating from contaminations on the surface. Here we report on measurements of an electric field created by $^{87}$Rb atoms absorbed on a 25$\,$nm thick layer of SiO$_2$, covering a 90$\,$nm layer of Au. The electric field is measured using a two-photon transition to the 23$D_{5/2}$ and 25$S_{1/2}$ state. The electric field value that we measure is higher than typ…
We report measurements of the absolute excitation frequencies of $^{165}$Ho $4f^{11}6sns$ and $4f^{11}6snd$ odd-parity Rydberg series. The states are detected through depletion of a magneto-optical trap via a two-photon excitation scheme. Measurements of 162 Rydberg levels in the range $n=40-101$ yield quantum defects well described by the Rydberg-Ritz formula. We observe a strong perturbation in the $ns$ series around $n=51$ due to an unidentified interloper at 48515.47(4) cm$^{-1}$. From the series convergence, we determine the first ionization potential $E_\mathrm{IP}=48565.939(4)$ cm$^{-1}…
We report measurements of the $^{115}$In $7p_{1/2}$ and $7p_{3/2}$ scalar and tensor polarizabilities using two-step diode laser spectroscopy in an atomic beam. The scalar polarizabilities are one to two orders of magnitude larger than for lower lying indium states due to the close proximity of the $7p$ and $6d$ states. For the scalar polarizabilities, we find values (in atomic units) of $1.811(4) \times 10^5$ $a_0^3$ and $2.876(6) \times 10^5$ $a_0^3$ for the $7p_{1/2}$ and $7p_{3/2}$ states respectively. We estimate the smaller tensor polarizability component of the $7p_{3/2}$ state to be $-…
Two-dimensional (2D) spectroscopy uses multiple electromagnetic pulses to infer the properties of a complex system. A paradigmatic class of target systems are molecular aggregates, for which one can obtain information on the eigenstates, various types of static and dynamic disorder and on relaxation processes. However, two-dimensional spectra can be difficult to interpret without precise knowledge of how the signal components relate to microscopic Hamiltonian parameters and system-bath interactions. Here we show that two-dimensional spectroscopy can be mapped in the microwave domain to highly …
Photoionization spectra of Se have been studied by step-wise resonance laser ionization. The Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_{0,1,2}$ and 4s$^2$4p$^3$($^4$S)np $^5$P$_{1,2,3}$ were measured via different excitation schemes. Using the Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_2$ with n=15-33, the ionization potential of Se was determined with improved precision to 76658.15(2)$_{stat}$(4)$_{sys}$ cm$^{-1}$, which resolved the discrepancy in previous literatures. Autoionizing (AI) spectra between the IP and two neighboring converging limits of the Se ionic states 4s$^2$4p$^3$($^2$D$…
We present the derivation of the frequency dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom 5s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5s ground state sub-levels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far-detuned from the atomic resonance and the total electronic angular momentu…
We develop and study quantum and semi-classical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in any other spectroscopic scheme, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a novel type of sub-Doppler mechanism, which we explain in detail. In our exact quantum model, we solve the time-dependent Schrödinger equation in the product space of center-of-mass (COM)…
