Rydberg States Research Articles

Photofragmentation of cyclobutanone at 200nm: TDDFT vs CASSCF electron diffraction.

To simulate a 200nm photoexcitation in cyclobutanone to the n-3s Rydberg state, classical trajectories were excited from a Wigner distribution to the singlet state manifold based on excitation energies and oscillator strengths. Twelve singlet and 12 triplet states are treated using TD-B3LYP-D3/6-31+G** for the electronic structure, and the nuclei are propagated with the Tully surface hopping method. Using time-dependent density functional theory, we are able to predict the bond cleavage that takes place on the S1 surface as well as the ultrafast deactivation from the Rydberg n-3s state to the nπ*. After showing that triplet states and higher-lying singlet states do not play any crucial role during the early dynamics (i.e., the first 300fs), the SA(6)-CASSCF(8,11)/aug-cc-pVDZ method is used as an electronic structure and the outcome of the non-adiabatic dynamic simulations is recomputed. Gas-phase ultrafast electron diffraction spectra are computed for both electronic structure methods, showing significantly different results.

Collisional shift and broadening of Rydberg states in nitric oxide at room temperature

Collisional shift and broadening of Rydberg states in nitric oxide at room temperature

Control and Entanglement of Individual Rydberg Atoms near a Nanoscale Device.

Coherent control of Rydberg atoms near dielectric surfaces is a major challenge due to the large sensitivity of Rydberg states to electric fields. We demonstrate coherent single-atom operations and two-qubit entanglement as close as 100 μm from a nanophotonic device. Using the individual atom control enabled by optical tweezers to study the spatial and temporal properties of the electric field from the surface, we employ dynamical decoupling techniques to characterize and cancel the electric-field noise with submicrosecond temporal resolution. We further use entanglement-assisted sensing to accurately map magnitude and direction of electric-field gradients on a micrometer scale. Our observations open a path for integration of Rydberg arrays with micro- and nanoscale devices for applications in quantum networking and quantum information science.

Coherent interface between optical and microwave photons on an integrated superconducting atom chip

Sub-wavelength arrays of atoms exhibit remarkable optical properties, analogous to those of phased array antennas, such as collimated directional emission or nearly perfect reflection of light near the collective resonance frequency. We propose to use a single-sheet sub-wavelength array of atoms as a switchable mirror to achieve a coherent interface between propagating optical photons and microwave photons in a superconducting coplanar waveguide resonator. In the proposed setup, the atomic array is located near the surface of the integrated superconducting chip containing the microwave cavity and optical waveguide. A driving laser couples the excited atomic state to Rydberg states with strong microwave transition. Then the presence or absence of a microwave photon in the superconducting cavity makes the atomic array transparent or reflective to the incoming optical pulses of proper frequency and finite bandwidth.

Electrostatic Trapping of N_{2} Molecules in High Rydberg States.

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

Wave packet dynamics and control in excited states of molecular nitrogen.

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle.

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2 V cm^{-1}, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 ^{2}S_{1/2}(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)-1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.203001; A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.230801] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)NATUAS0028-083610.1038/229110a0], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)_{stat}(1.8)_{syst} kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)-2P_{1/2}(1) interval [N. Bezginov et al., Science 365, 1007 (2019)SCIEAS0036-807510.1126/science.aau7807], we determine the Rydberg frequency to be cR_{∞}=3 289 841 960 204(15)_{stat}(7)_{syst}(13)_{2S-2P} kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.

Ion core switching during photodissociation dynamics via the Rydberg states of XeAr

The heterodimer, XeAr, is a classic example of a weakly bound van der Waals molecule, which has a variety of accessible bound excited states that exhibit complex interactions. In this study, XeAr has been investigated in the 77,500–81,500 cm−1 region using a combination of Resonance Enhanced Multi-Photon Ionization (REMPI) spectroscopy and Velocity Map Imaging (VMI). By monitoring REMPI and photodissociative product channels across the spectrum, several novel excited states, product channels, excited state symmetries and lifetimes, as well as highly localized perturbations were observed and characterized, including the first VMI study of Ar* dissociating from XeAr Rydberg states accessed by two-photon excitation. In this work we have analyzed 38 vibronic bands representing nine different electronic transitions, and we provide new assignments for two 0+←0+ electronic transitions dissociating to the Xe* 5d [3/2]02 (ca. 80,323 cm−1) and Xe* 5d [7/2]03 (ca. 80,970 cm−1) limits. Several new predissociation product channels were identified at the two- and three-photon levels, including production of Xe* 5p[5/2]3, Xe* 6s'[1/2]o1, Xe* 6p[1/2]1, Ar* 4p[1/2]0, Ar* 4p'[3/2]1, Ar* 4p'[1/2]1, and Ar* 4p[5/2]3. Using the multidimensional analysis offered by VMI, we explore interesting photophysics whereby a resonant state that is reached after absorbing two photons can predissociate to yield Xe*, but which also can absorb a 3rd photon, yielding super-excited Ar*Xe that predissociates to Ar* limits. The ground state dissociation energy for XeAr was determined to be D0 = 114.4 ± 2.7 cm−1, in excellent agreement with previous measurements.

Excitation and ionization of OCS molecules in strong UV and NIR laser fields

Abstract Rydberg state excitation (RSE) is a highly non-linear physical phenomenon that is induced by the ionization of atoms or molecules in strong femtosecond laser fields. Here we observe that both parent and fragments (S, C, OC) of the tri-atomic molecule carbonyl sulfide (OCS) can survive strong 800 nm or 400 nm laser fields in high Rydberg states. The dependence of parent and fragment RSE yields on laser intensity and ellipticity is investigated in both laser fields, and the results are compared with those for strong-field ionization. Distinctly different tendencies for laser intensity and ellipticity are observed for fragment RSE compared with the corresponding ions. The mechanisms of RSE and strong-field ionization of OCS molecules in different laser fields are discussed based on the experimental results. Our study sheds some light on the strong-field excitation and ionization of molecules irradiated by femtosecond NIR and UV laser fields.

Giant microwave–optical Kerr nonlinearity via Rydberg excitons in cuprous oxide

Microwave–optical conversion is key to future networks of quantum devices, such as those based on superconducting technology. Conversion at the single quantum level requires strong nonlinearity, high bandwidth, and compatibility with a millikelvin environment. A large nonlinearity is observed in Rydberg atoms, but combining atomic gases with dilution refrigerators is technically challenging. Here, we demonstrate a strong microwave–optical nonlinearity in a cryogenic, solid-state system by exploiting Rydberg states of excitons in Cu2O. We measure a microwave–optical cross-Kerr coefficient of B0 = 0.022 ± 0.008 m V−2 at 4 K, which is several orders of magnitude larger than other solid-state systems. The results are in quantitative agreement with a nonlinear susceptibility model based on the giant microwave dipole moment between nearby excitonic states. Our results highlight the potential of Rydberg excitons for nonlinear optics and form the basis for a microwave–optical frequency converter based on Cu2O.

Microwave coupled Zeeman splitting spectroscopy of a cesium nPJ Rydberg atom.

We perform measurements of microwave spectra of cesium Rydberg 51S1/2 → 51PJ transitions with the linewidth approaching the Fourier limit. A two-photon scheme excites the ground-state atoms to the Rydberg 51S1/2 state, and a weak microwave photon couples the Rydberg transition of 51S1/2 → 51PJ. The hyperfine structure of 51P1/2 can be clearly resolved with a narrow linewidth microwave spectra by using the method of ion detection. Furthermore, we investigate the Zeeman effect of the 51P1/2,3/2 state. The theoretical calculations reproduce the measurement well. Our experimental measurements provide a reliable technical solution for the investigation of high angular momentum Rydberg states, which is conducive to further realizing the coherent manipulation of Rydberg energy levels and improving the sensitivity of electromagnetic field measurement.

Fractional Quantum Anomalous Hall Phase for Raman Superarray of Rydberg Atoms

AbstractRydberg atom arrays offer promising platforms for quantum simulation of correlated quantum matter and raise great interests. This work proposes a novel stripe‐lattice model with “Raman superarray of Rydberg atoms” to realize bosonic fractional quantum anomalous Hall (FQAH) phase. Two types of Rydberg states, arranged in a supperarray configuration and with Raman‐assisted dipole‐exchange couplings, are implemented to realize a minimal QAH model for hard‐core bosons populated into a topological flat band with large bulk gap under proper tunable experimental condition. With this the bosonic FQAH phase can be further achieved and probed feasibly. In particular, a novel quench protocol is proposed to probe the fractionalized excitations by measuring the correlated quench dynamics featured by fractional charge tunneling between bulk and chiral edge modes in the open boundary.

Valence shell electronically excited states of norbornadiene and quadricyclane.

The absolute photoabsorption cross sections of norbornadiene (NBD) and quadricyclane (QC), two isomers with chemical formula C7H8 that are attracting much interest for solar energy storage applications, have been measured from threshold up to 10.8eV using the Fourier transform spectrometer at the SOLEIL synchrotron radiation facility. The absorption spectrum of NBD exhibits some sharp structure associated with transitions into Rydberg states, superimposed on several broad bands attributable to valence excitations. Sharp structure, although less pronounced, also appears in the absorption spectrum of QC. Assignments have been proposed for some of the absorption bands using calculated vertical transition energies and oscillator strengths for the electronically excited states of NBD and QC. Natural transition orbitals indicate that some of the electronically excited states in NBD have a mixed Rydberg/valence character, whereas the first ten excited singlet states in QC are all predominantly Rydberg in the vertical region. In NBD, a comparison between the vibrational structure observed in the experimental 11B1-11A1 (3sa1 ← 5b1) band and that predicted by Franck-Condon and Herzberg-Teller modeling has necessitated a revision of the band origin and of the vibrational assignments proposed previously. Similar comparisons have encouraged a revision of the adiabatic first ionization energy of NBD. Simulations of the vibrational structure due to excitation from the 5b2 orbital in QC into 3p and 3d Rydberg states have allowed tentative assignments to be proposed for the complex structure observed in the absorption bands between ∼5.4 and 7.0eV.

Zero-Quantum-Defect Method and the Fundamental Vibrational Interval of H_{2}^{+}.

The fundamental vibrational interval of H_{2}^{+} has been determined to be ΔG_{1/2}=2191.126 614(17) cm^{-1} by continuous-wave laser spectroscopy of Stark manifolds of Rydberg states of H_{2} with the H_{2}^{+} ion core in the ground and first vibrationally excited states. Extrapolation of the Stark shifts to zero field yields the zero-quantum-defect positions -R_{H_{2}}/n^{2}, from which ionization energies can be determined. Our new result represents a 4-order-of-magnitude improvement compared to earlier measurements. It agrees, within the experimental uncertainty, with the value of 2191.126 626 344(17)(100) cm^{-1} determined in nonrelativistic quantum electrodynamic calculations [V. Korobov, L. Hilico and J.-Ph. Karr, Phys. Rev. Lett. 118, 233001 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.233001].

Enhanced microwave-atom coupling via quadrupole transition-dressed Rydberg atoms

The power broadening of a coupling laser can be converted into two-photon detuning by electromagnetically induced transparency (EIT), resulting in a residual Doppler effect. The residual Doppler effect in a ladder-type EIT in a room-temperature atom ensemble is further amplified through a wavelength mismatch effect between the probe and coupling laser beams, which reduces the atomic coupling of light or microwaves. We measured the Rydberg spectra of the electric dipole (E1) and electric quadrupole (E2) microwave transitions, demonstrating that the reduction in the Rydberg EIT signal can be recovered through far-off-resonance E2 microwave transition dressing and achieving an 8-dB enhancement in the Rydberg EIT signal. The frequency-dependent dressing of the E2 transition enables the shift of the dressed Rydberg states to be tuned, thereby providing a scalable approach to optimize the interaction between the Rydberg state and microwave field.

Ultrafast electronic relaxation pathways of the molecular photoswitch quadricyclane

The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2.

Probing Polaron Clouds by Rydberg Atom Spectroscopy.

In recent years, Rydberg excitations in atomic quantum gases have become a successful platform to explore quantum impurity problems. A single impurity immersed in a Fermi gas leads to the formation of a polaron, a quasiparticle consisting of the impurity being dressed by the surrounding medium. With a radius of about the Fermi wavelength, the density profile of a polaron cannot be explored using insitu optical imaging techniques. In this Letter, we propose a new experimental measurement technique that enables the insitu imaging of the polaron cloud in ultracold quantum gases. The impurity atom induces the formation of a polaron cloud and is then excited to a Rydberg state. Because of the mesoscopic interaction range of Rydberg excitations, which can be tuned by the principal numbers of the Rydberg state, atoms extracted from the polaron cloud form dimers with the impurity. By performing first principle calculations of the absorption spectrum based on a functional determinant approach, we show how the occupation of the dimer state can be directly observed in spectroscopy experiments and can be mapped onto the density profile of the gas particles, hence providing a direct, real-time, and insitu measure of the polaron cloud.

Superradiance of ultracold cesium Rydberg |65D5/2〉 → |66P3/2〉

We investigate Rydberg |65D5/2〉 → |66P3/2〉 superradiance in dense ultracold cesium atoms, where the ground atoms are excited to |65D5/2〉 Rydberg states via two-photon excitation in a standard magneto-optical trap. The superradiant spectrum of |65D5/2〉 → |66P3/2〉 is obtained using the state-selective field ionization technique. We observe its dynamic evolution process by varying the delay time of ionization field t d. The results show that the evolution process of |65D5/2〉 → |66P3/2〉 is much shorter than its radiation lifetime at room temperature, which verifies the superradiance effect. The dependence of the superradiance process on Rydberg atoms number N e and principal quantum number n is investigated. The results show that the superradiance becomes faster with increasing N e, while it is suppressed for stronger van der Waals (vdW) interactions. Superradiance has potential applications in quantum technologies, and the Rydberg atom is an ideal medium for superradiance. Our system is effective for studying the strong two-body interaction between Rydberg atoms.

Excitonic Rydberg States in a Trilayer to Monolayer H2-Aided CVD-Grown Large-Area MoS2 Film with Excellent UV to Visible Broad Band Photodetection Applications.

The diverse nature of optoelectronic properties of few-layer or monolayer MoS2 is generally dominated by A and B excitons. Occasionally, strong Coulombic interactions within the 2D monolayer led to the creation of hydrogen-like Rydberg states of excitons in MoS2 similar to other 2D monolayers. In this paper, a simple process is used to convert trilayer MoS2 films to a monolayer by introducing H2 gas during chemical vapor deposition. Remarkably, alongside the usual A, B excitons, and A- trion, the appearance of the Rydberg states is evidenced by photoluminescence spectra even at room temperature; also, there is an increase in their areal percentage with an increase in H2 content. The s-type excited Rydberg states up to the fourth order (n = 5) and third order (n = 4) of A and B excitons, respectively, have been probed from the photoluminescence spectra at 93 K. Unprecedentedly, the first-order derivative of room-temperature photocurrent spectrum reveals the Rydberg states concurrently and elaboratively. Furthermore, the large-area MoS2 films exhibit photoresponse in a broad UV to visible region with excellent photosensitivity (∼102) toward both UV and visible lights. Not only does this provide a profound understanding of the excitonic Rydberg states but also highlights the considerable potential of large-area monolayer MoS2 overcoming the difficulty of tiny flake-related 2D device endeavors.

Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene.

Moiré excitons are emergent optical excitations in two-dimensional semiconductors with moiré superlattice potentials. Although these excitations have been observed on several platforms, a system with dynamically tunable moiré potential to tailor their properties is yet to be realized. Here we present a continuously tunable moiré potential in monolayer WSe2, enabled by its proximity to twisted bilayer graphene (TBG) near the magic angle. By tuning local charge density via gating, TBG provides a spatially varying and dynamically tunable dielectric superlattice for modulation of monolayer WSe2 exciton wave functions. We observed emergent moiré exciton Rydberg branches with increased energy splitting following doping of TBG due to exciton wave function hybridization between bright and dark Rydberg states. In addition, emergent Rydberg states can probe strongly correlated states in TBG at the magic angle. Our study provides a new platform for engineering moiré excitons and optical accessibility to electronic states with small correlation gaps in TBG.