Experimental study of bound and autoionizing Rydberg states of the europium atom

An isolated-core-excitation （ICE） scheme and stepwise excitation are employed to study the highly excited states of the europium atom. The bound europium spectrum with odd parity in a region of 42400-43500 cm^-1 is measured, from which spectral information on 38 transitions, such as level position and relative intensity, can be deduced. Combined with information about excitation calibration and the error estimation process, the selection rules enable us to determine the possible values of total angular momentum J for the observed states. The autoionization spectra of atomic europium, belonging to the 4f^76pnl（l = 0, 2） configurations, are systematically investigated by using the three-step laser resonance ionization spectroscopy （RIS） approach. With the ICE scheme, all the experimental spectra of the autoionizing states have nearly symmetric profiles whose peak positions and widths can be easily obtained. A comparison between our results and those from the relevant literature shows that our work not only confirms many reported states, but also discovers 14 bound states and 16 autoionizing states.

Investigation of odd-parity Rydberg states of Eu I with autoionization detection

Isolated-core-excitation （ICE） scheme and autoionization detection are employed to study the bound Rydberg states of europium atom. The high-lying states with odd parity have been measured using the autoionization detection method with three different excitation paths via 4f76s6p[8Ph/2], 4f76s6p[8P7/2] and 4f76s6p[SP9/2] intermediate states, respectively. In this paper the spectra of bound Rydberg states of Eu atom are reported, which cover the energy regions from 36000 cm-1 to 38250 cm-1 and from 38900 cm-1 to 39500 cm-1. The study provides the information about level energy, the possible J values and relative line intensity as well as the effective principal quantum number n＊ for these states. This work not only confirms the previous results of many states, but also discovers 11 new Rydberg states of Eu atom.

Lifetimes of Rydberg states of Eu atoms

The radiative lifetimes of the Eu 4f76snp（8^PJ or10^PJ） Rydberg states with J = 5/2 and 11/2 are investigated with a combination of multi-step laser excitation and pulsed electric field ionization, from which their dependence on the effective principal quantum number is observed. The lifetimes of 21 states are reported along with an evaluation of their experimental uncertainty. The influence of blackbody radiation, due to the oven temperature, on the lifetime of the higher-n states is detected. The non-hydrogen behavior of the investigated states is also observed.

Field ionization process of Eu 4f^76snp Rydberg states

The field ionization process of the Eu 4f76snp Rydberg states, converging to the first ionization limit, 4f76s 954, is systematically investigated. The spectra of the Eu 4f76snp Rydberg states are populated with three-step laser excitation, and detected by electric field ionization （EFI） method. Two different kinds of the EFI pulses are applied after laser excitation to observe the possible impacts on the EFI process. The exact EFI ionization thresholds for the 4f76snp Rydberg states can be determined by observing the corresponding EFI spectra. In particular, some structures above the EFI threshold are found in the EFI spectra, which may be interpreted as the effect from black body radiation （BBR）. Finally, the scaling law of the EFI threshold for the Eu 4f76snp Rydberg states with the effective quantum number is built.

Stark spectra of Rydberg states in atomic cesium in the vicinity of n=18

The Stark structures in a cesium atom around n=18 are numerically calculated. The results show that the components of 20D states with a small azimuthal quantum number ｜m｜ shift upward a lot, and those with a large ｜m｜ shift downward a little within 1100 V/cm. All components of P states shift downward. Experimental work has been performed in ultracold atomic cesium. Atoms initially in 6P3/2 state are excited to high-n Rydberg states by a polarization light perpendicular to the field, and Stark spectra with ｜m｜=1/2,3/2,5/2 are simultaneously observed with a large linewidth for the first time. The observed spectra are analyzed in detail. The relative transition probability is calculated. The experimental results are in good agreement with our numerical computation.

Energy level analyses of even-parity J=1 and 2 Rydberg states of Sn I by multichannel quantum defect theory

This paper analyzes the energy levels along the even-parity J = 1 and 2 Rydberg series of Sn I by multichannel quantum defect theory. A good agreement between theoretical and experimental energy levels was achieved. Below 59198 cm^-1, a total of 85 and 23 new energy levels, respectively, in the J = 1 and J = 2 series, which cannot be measured previously by experiments, are predicted in this work. Based on the calculated admixture coefficients of each channel, interchannel interactions were discussed in detail. The results are helpful to understand the characteristics of configuration interaction among even-parity levels in Sn I.

Photoelectron imaging on vibrational excitation and Rydberg intermediate states in multi-photon ionization process of NH3 molecule

The ionization processes of NH3 molecule are studied by photoelectron velocity map imaging technique in a linearly polarized 400-nm femtosecond laser field. The two-dimensional photoelectron images from ammonia molecules under different laser intensities are obtained. In the slow electron region, the values of kinetic energy of photoelectrons corresponding to peaks 1, 2, 3, and 4 are 0.27, 0.86, 1.16, and 1.6 eV, respectively. With both the kinetic energy and angular distribution of photoelectrons from NH3 molecules, we can confirm that the two-photon excited intermediate Rydberg state is A^1 A2" (v2'=3) state for photoelectron peaks 2, 3, 4, and the three peaks are marked as 1223 (2 + 2), 1123 (2 + 2), and 1023 (2 + 2) multi-photon processes, respectively. Then, peak 1 is found by adding a hexapole between the source chamber and the detection chamber to realize the rotational state selection and beam focusing. Peak 1 is labeled as the 1323 (3 + 1) multi-photon process through the intermediate Rydberg state E^1A1'. The phenomena of channel switching are found in the slow electron kinetic energy distributions. Our calculations and experimental results indicate that the stretching vibrational mode of ammonia molecules varies with channels, while the umbrella vibration does not. In addition, we consider and discuss the ac-Stark effect in a strong laser field. Peaks 5 and 6 are marked as (2 + 2 + 1) and (2 + 2 + 2) above threshold ionization processes in the fast electron region.

Two-Photon Excited State Dynamics of Dark Rydberg and Bright Valence States in Furan

Two-photon absorption in systems with parity permits access to states that cannot be directly prepared by one-photon absorption. Here we investigate ultrafast internal conversion （IC） dynamics of furan by using this strategy in combination with femtosecond time-resolved photoelectron imaging. The dark Rydberg S1 and bright valence S2 states are simultaneously excited by two photons of 405 nm, and then ionized by two photons of 800nm. The IC from S2 to S1 is clearly observed and extracted from the time dependence of the higher photoelectron kinetic energy （PKE） component. More importantly, the internal conversions to hot So from directly-prepared S1 and secondarily-populated S1 are unambiguously identified by the time-dependence of the lower PKE component. The average lifetime of the S2 and S1 states is measured to be 29 fs. The internal conversions of S2 to S1, S1 to hot So occur on estimated timescales of 15.4 fs and 38 fs, respectively.

Experimental study of highly excited even-parity bound states of the Sm atom

In this work, a three-step autoionization detection method and direct photoionization detection method are employed to measure the highly excited even-parity states of the Sm atom in the energy region between 36360 cm^-1 and 40800 cm^-1. Comparisons between the results from the two detection techniques enable us to discriminate the Rydberg states from the valence states in the same energy region with the information of level energies, possible J values and their relative intensities. Furthermore, in the experiment two different excitation schemes are designed to obtain the spectra of highly excited even-parity states of the Sm atom. With a detailed analysis of the experimental data, this work not only confirms the results about many spectral data from the literature with different excitation schemes, but also reports new spectral data on 29 Rydberg states and 23 valence states.

Nonlinear spectroscopy of three-photon excitation of cesium Rydberg atoms in vapor cell

We present nonlinear spectra of four-level ladder cesium atoms employing 6 S1/2→6 P3/2→7 S1/2→30 P3/2 scheme of a room temperature vapor cell.A coupling laser drives Rydberg transition,a dressing laser couples two intermediate levels,and a probe laser optically probes the nonlinear spectra via electromagnetically induced transparency(EIT).Nonlinear spectra are detected as a function of coupling laser frequency.The observed spectra exhibit an enhanced absorption(EA) signal at coupling laser resonance to Rydberg transition and enhanced transmission(ET) signals at detunings to the transition.We define the enhanced absorption(transmission) strength,HEA(HET),and distance between two ET peaks,γET,to describe the spectral feature of the four-level atoms.The enhanced absorption signal HEA is found to have a maximum value when we vary the dressing laser Rabi frequency Ωd,corresponding Rabi frequency is defined as a separatrix point,ΩdSe.The values of ΩdSe and further η=ΩdSe/Ωc are found to depend on the probe and coupling Rabi frequency but not the atomic density.Based on ΩdSe,the spectra can be separated into two regimes,weak and strong dressing ranges,Ωd≤ΩdSe and Ωd≥QdSe,respectively.The spectroscopies display different features at these two regimes.A four-level theoretical model is developed that agrees well with the experimental results in terms of the probe-beam absorption behavior of Rabi frequency-dependent dressed states.

Spectral filtering of dual lasers with a high-finesse length-tunable cavity for rubidium atom Rydberg excitation

We propose and demonstrate an alternative method for spectral filtering and frequency stabilization of both 780-nm and 960-nm lasers using a high-finesse length-tunable cavity(HFLTC).Firstly,the length of HFLTC is stabilized to a commercial frequency reference.Then,the two lasers are locked to this HFLTC using the Pound–Drever–Hall(PDH)method which can narrow the linewidths and stabilize the frequencies of both lasers simultaneously.Finally,the transmitted lasers of HFLTC with each power up to about 100μW,which act as seed lasers,are amplified using the injection locking method for single-atom Rydberg excitation.The linewidths of obtained lasers are narrowed to be less than 1 k Hz,meanwhile the obtained lasers'phase noise around 750 k Hz are suppressed about 30 d B.With the spectrally filtered lasers,we demonstrate a Rabi oscillation between the ground state and Rydberg state of single-atoms in an optical trap tweezer with a decay time of(67±37)μs,which is almost not affected by laser phase noise.We found that the maximum short-term laser frequency fluctuation of a single excitation lasers is at~3.3 k Hz and the maximum long-term laser frequency drift of a single laser is~46 k Hz during one month.Our work develops a stable and repeatable method to provide multiple laser sources of ultra-low phase noise,narrow linewidth,and excellent frequency stability,which is essential for high precision atomic experiments,such as neutral atom quantum computing,quantum simulation,quantum metrology,and so on.

Measurement of the argon-gas-induced broadening and line shifting of the barium Rydberg level 6s24d 1^D2 by two-photon resonant nondegenerate four-wave mixing

We apply two-photon resonant nondegenerate four-wave mixing with a resonant intermediate state to the obser-vation of the broadening and shifting of the barium Rydberg level 6s24d 1^D2 by collision with argon. The collision broadening and shifting cross sections are measured. This technique is purely optical, and can investigate the pressure dependence of the transverse relaxation rate-P21 between the Rydberg state and an intermediate state, as well as the transverse relaxation rate F20 between the Rydberg state and the ground state.

A sensitive detection of high Rydberg atom with large dipole moment

We report a sensitive detection of high Rydberg atom with large dipole moment utilizing its deflection near a pair of parallel cylindrical copper rods which are oppositely charged. When the low-field seeking state Rydberg atoms fly across the gradient electric field formed by the pair of rods, they will be pushed away from the rods while the high-field seeking state ones will be attracted towards the rods. These atoms will form different patterns on an ion imaging system placed downwards at the end of the rods. The spatial distribution of the deflected atoms on the imaging system is also simulated, in good agreement with the experimental results, from which we can deduce the quantum state information of the excited atoms. This state resolvable Rydberg atom detection can be used for the dynamics research of the dipole-dipole interaction between atoms with large dipole moments.

Theoretical Analysis of Rydberg and Autoionizing State Spectra of Antimony

We calculate the Rydberg and autoionization Rydberg spectra of antimony （Sb） from first principles by relativistic multichannel theory within the framework of multichannel quantum defect theory. Our calculation can be used to classify and assign the atomic states described in recently reported three Rydberg series and four autoionizing states. The perturbation effects on line intensity, variation and line profile are discussed. Assignments of the perturber states and autoionizing states are presented.

Importance of Relativistic Effects for Intermediate-Z Elements： Photoionization Process of Excited Na

Using a modified R-matrix code, the fine-structure-resolved partial photoionization cross sections of excited Na （Z = 11） are calculated within the Breit-Pauli approximation. Our calculated energy levels of Na＋ and Na are in good agreement with the experimental values within 1% and the branching ratios of the J-resolved partial cross sections are consistent with the recent measurements within the experimental uncertainties. The agreements are impossible to be obtained without adequately taking into account the relativistic effects and the electron correlations together. Therefore, even for the intermediate-Z elements （e.g. Na with Z = 11）, the relativistic effects （mainly the spin-orbit interactions） should not be neglected.

Photoelectron angular distributions of H ionization in low energy regime:Comparison between different potentials

We theoretically investigate the low energy part of the photoelectron spectra in the tunneling ionization regime by numerically solving the time-dependent Schrdinger equation for different atomic potentials at various wavelengths.We find that the shift of the first above-threshold ionization（ATI） peak is closely related to the interferences between electron wave packets,which are controlled by the laser field and largely independent of the potential.By gradually changing the short-range potential to the long-range Coulomb potential,we show that the long-range potential＇s effect is mainly to focus the electrons along the laser＇s polarization and to generate the spider structure by enhancing the rescattering process with the parent ion.In addition,we find that the intermediate transitions and the Rydberg states have important influences on the number and the shape of the lobes near the threshold.

Rydberg electromagnetically induced transparency in^(40)K ultracold Fermi gases

We report the measurement of the electromagnetically induced transparency(EIT)with Rydberg states in ultracold^(40)K Fermi gases,which is obtained through a two-photon process with the ladder scheme.Rydberg–EIT lines are obtained by measuring the atomic losses instead of the transmitted probe beam.Based on the laser frequency stabilization locking to the superstable cavity,we study the Rydberg–EIT line shapes for the 37s and 35d states.We experimentally demonstrate the significant change in the Rydberg–EIT spectrum by changing the principal quantum number of the Rydberg state(n=37/52 and l=0).Moreover,the transparency peak position shift is observed,which may be induced by the interaction of the Rydberg atoms.This work provides a platform to explore many interesting behaviors involving Rydberg states in ultracold Fermi gases.

Classical Dynamics of Muonic-Electronic Helium and Heliumlike Ions: The Allowance for the Eccentricity of the Muon and Nucleus Orbits

In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than the electron motion. Assuming that the muon and nucleus orbits are circular, he applied the analytical method based on separating rapid and slow subsystems. He showed that the electron moves in an effective potential that is mathematically equivalent to the potential of a satellite orbiting an oblate planet like the Earth. He also showed that the “unperturbed” elliptical orbit of the electron engages in two precessions simultaneously: the precession of the electron orbit in the plane of the orbit and the precession of the orbital plane of the electron around the axis perpendicular to the plane of the muon and nuclear orbits. The problem remained whether or not the allowance for the ellipticity of the orbit could significantly change the results. In the present paper, we address this problem: we study how the allowance for a relatively low eccentricity ε of the muon and nucleus orbits affects the motion of the electron. We derive an additional, ε-dependent term in the effective potential for the motion of the electron. We show analytically that in the particular case of the planar geometry (where the electron orbit is in the plane of the muon and nucleus orbits), it leads to an additional contribution to the frequency of the precession of the electron orbit. We demonstrate that this additional, ε-depen- dent contribution to the precession frequency of the electron orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Therefore, the results of our paper seem to be important not only qualitatively, but also quantitatively.

Rydberg state excitation in molecules manipulated by bicircular two-color laser pulses

Multiphoton resonant excitation and frustrated tunneling ionization,manifesting the photonic and optical nature of the driving light via direct excitation and electron recapture,respectively,are complementary mechanisms to access Rydberg state excitation(RSE)of atoms and molecules in an intense laser field.However,clear identification and manipulation of their individual contributions in the light-induced RSE process remain experimentally challenging.Here,we bridge this gap by exploring the dissociative and nondissociative RSE of H2 molecules using bicircular two-color laser pulses.Depending on the relative field strength and polarization helicity of the two colors,the RSE probability can be boosted by more than one order of magnitude by exploiting the laser waveform-dependent field effect.The role of the photon effect is readily strengthened with increasing relative strength of the second-harmonic field of the two colors regardless of the polarization helicity.As compared to the nondissociative RSE forming H2
,the field effect in producing the dissociative RSE channel of eHt;H
T is moderately suppressed,which is primarily accessed via a three-step sequential process separated by molecular bond stretching.Our work paves the way toward a comprehensive understanding of the interplay of the underlying field and photon effects in the strong-field RSE process,as well as facilitating the generation of Rydberg states optimized with tailored characteristics.

Rydberg quantum computation with nuclear spins in two-electron neutral atoms

Alkaline-earth-like(AEL)atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing.Typical AEL ground states possess no hyperfine splitting,but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation.Though strong magnetic fields can induce a GHz-scale splitting,weak fields are desirable to avoid noise in experiments.Here,we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes.In the first theory,the two nuclear spin qubit states∣0〉and∣1〉are excited to Rydberg states∣r〉with detuningΔand 0,respectively,where a MHz-scale detuningΔarises from a weak magnetic field on the order of 1 G.With a proper ratio betweenΔandΩ,the qubit state∣1〉can be fully excited to the Rydberg state while∣0〉remains there.In the second theory,we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state.The second theory is applicable whatever the magnitude of the magnetic field is.These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.