Rydberg States Research Articles

Multiphoton Ionization/Dissociation of Molecular Sulfur S2 in the UV Region.

The multiphoton ionization/dissociation dynamics of molecular sulfur (S2) in the ultraviolet range of 205-300 nm is studied using velocity map ion imaging (VMI). In this one-color experiment, molecular sulfur (S2) is generated in a pulsed discharge and then photodissociated by UV radiation. At the three-photon level, superexcited states are accessed via two different resonant states: the B3Σu- (v' = 8-11) valence states at the one-photon level and a Rydberg state at the two-photon level. Among the decay processes of these superexcited states, dissociation to electronically excited S atoms is dominant as compared to autoionization to ionic states S2+ (X2Πg) at wavelengths λ < 288 nm. The anisotropy parameter extracted from these images reflects the parallel character of these electronic transitions. In contrast, autoionization is found to be particularly efficient at S(1D) and S(1S) detection wavelengths around 288 nm. Information obtained from the kinetic energy distributions of S atoms has revealed the existence of vibrationally excited S2+ (X2Πg (v+ > 11)) that dissociates to ionic products following one-photon absorption. This work also reveals many interesting features of S2 photodynamics compared to those of electronically analogous O2.

Independent Rydberg atom sensing using a dual-ladder scheme

Rydberg atom-based electric field sensing can provide all-optical readout of radio frequency (RF) fields in a dielectric environment. However, because a single set of optical fields is typically used to prepare the Rydberg state and readout its response to RF fields, it is challenging to perform simultaneous and independent measurements of the RF field(s). Here, we show that using two independent schemes to prepare and readout the same Rydberg state can be used to perform independent measurements in general, which we demonstrate specifically by resolving the RF polarization. We expect this work will be useful for fiber-coupled sensor heads where spatial multiplexing is challenging as well as for complex multi-level sensing schemes.

Ultrafast photochemistry and electron-diffraction spectra in n → (3s) Rydberg excited cyclobutanone resolved at the multireference perturbative level.

We study the ultrafast time evolution of cyclobutanone excited to the singlet n → Rydberg state through non-adiabatic surface-hopping simulationsperformed at extended multi-state complete active space second-order perturbation (XMS-CASPT2) level of theory. These dynamics predict relaxation to the ground-state with a timescale of 822 ± 45fs with minimal involvement of the triplets. The major relaxation path to the ground-state involves a three-state degeneracy region and leads to a variety of fragmented photoproducts. We simulate the resulting time-resolved electron-diffraction spectra, which track the relaxation of the excited state and the formation of various photoproducts in the ground state.

Unraveling the Rich Fragmentation Dynamics Associated with S-H Bond Fission Following Photoexcitation of H2S at Wavelengths ∼129.1 nm.

H2S is being detected in the atmospheres of ever more interstellar bodies, and photolysis is an important mechanism by which it is processed. Here, we report H Rydberg atom time-of-flight measurements following the excitation of H2S molecules to selected rotational (JKaKc') levels of the 1B1 Rydberg state associated with the strong absorption feature at wavelengths of λ ∼ 129.1 nm. Analysis of the total kinetic energy release spectra derived from these data reveals that all levels predissociate to yield H atoms in conjunction with both SH(A) and SH(X) partners and that the primary SH(A)/SH(X) product branching ratio increases steeply with ⟨Jb2⟩, the square of the rotational angular momentum about the b-inertial axis in the excited state. These products arise via competing homogeneous (vibronic) and heterogeneous (Coriolis-induced) predissociation pathways that involve coupling to dissociative potential energy surfaces (PES(s)) of, respectively, 1A″ and 1A' symmetries. The present data also show H + SH(A) product formation when exciting the JKaKc' = 000 and 111 levels, for which ⟨Jb2⟩ = 0 and Coriolis coupling to the 1A' PES(s) is symmetry forbidden, implying the operation of another, hitherto unrecognized, route to forming H + SH(A) products following excitation of H2S at energies above ∼9 eV. These data can be expected to stimulate future ab initio molecular dynamic studies that test, refine, and define the currently inferred predissociation pathways available to photoexcited H2S molecules.

The photochemistry of Rydberg-excited cyclobutanone: Photoinduced processes and ground state dynamics.

Owing to ring strain, cyclic ketones exhibit complex excited state dynamics with multiple competing photochemical channels active on the ultrafast timescale. While the excited state dynamics of cyclobutanone after π* ← n excitation into the lowest-energy excited singlet (S1) state has been extensively studied, the dynamics following 3s ← n excitation into the higher-lying singlet Rydberg (S2) state are less well understood. Herein, we employ fully quantum multiconfigurational time-dependent Hartree (MCTDH) simulations using a model Hamiltonian as well as "on-the-fly" trajectory-based surface-hopping dynamics (TSHD) simulations to study the relaxation dynamics of cyclobutanone following 3s ← n excitation and to predict the ultrafast electron diffraction scattering signature of these relaxation dynamics. Our MCTDH and TSHD simulations indicate that relaxation from the initially-populated singlet Rydberg (S2) state occurs on the timescale of a few hundreds of femtoseconds to a picosecond, consistent with the symmetry-forbidden nature of the state-to-state transition involved. There is no obvious involvement of excited triplet states within the timeframe of our simulations (<2ps). After non-radiative relaxation to the electronic ground state (S0), vibrationally hot cyclobutanone has sufficient internal energy to form multiple fragmented products including C2H4 + CH2CO (C2; 20%) and C3H6 + CO (C3; 2.5%). We discuss the limitations of our MCTDH and TSHD simulations, how these may influence the excited state dynamics we observe, and-ultimately-the predictive power of the simulated experimental observable.

Theoretical study on Stark effect of Rydberg atom in super low frequency electric field measurement

AbstractSuper low frequency electric field measurements are crucial in analysing electromagnetic compatibility, assessing equipment status, and other related fields. Rydberg atom‐based super low frequency electric field measurements are performed by observing the Stark shift in the spectrum of the Rydberg state. In a specific range of field strength (E &lt; Eavoid, where Eavoid is the threshold to avoid crossing electric fields), the Rydberg atomic spectrum experiences a quadratic frequency shift in relation to the field strength, with the coefficient being determined by the atomic polarisability α. The authors establish a dynamic equation for the interaction between the external electric field and the atomic system, and present the Stark structure diagram of the Caesium Rydberg atom. The mathematical formulae for α and Eavoid in different Rydberg states are also obtained: α = A × (n*)6 + B × (n*)7 and Eavoid = C/(n*)5 + D/(n*)7, where A(B) = 2.2503 × 10−9(7.49,948 × 10−11) and C(D) = 1.68,868 × 108(2.45,991 × 109). The error of α and Eavoid compared with the experimental values does not exceed 8% and is even lower in the low Rydberg states. Accurately calculating the values of α and Eavoid is crucial in incorporating the Rydberg atom quantum coherence effect into super low frequency electric field measurements in new power systems.

Ion-core switching in Rydberg series of XeKr

We investigate XeKr in high Rydberg states by mass-resolved optical-optical double resonance excitation spectroscopy. We excite XeKr via two-photon absorption to the v* = 0 and v* = 2 vibrational levels of an intermediate electronically excited state of Xe*Kr correlated to Xe*6p[5/2]2 and excite Xe*Kr further via one-photon absorption to the high Rydberg states of Xe**Kr in the energy range of 93200–97400 cm−1. The potential energy curves and the quantum defects of the d-Rydberg and s-Rydberg series of Xe**Kr, converging the A 2Π3/2 state of XeKr+ are determined. From the kinetic energy release in the predissociation process, we conclude that the ion-core switching occurs by the interaction between the bound electronic states of Xe**Kr converging to the A 2Π3/2 state of XeKr+ and the repulsive electronic states of low-lying electronic states of XeKr**. Based on numerical simulations, we interpret the dependence of the yield of the ion-core switching on the excitation energy in terms of the population transfer from the bound electronic states of the high Rydberg states Xe**Kr, converging to the A 2Π3/2 state of XeKr+, to those converging to the electronic ground X2 Σ 1 / 2 + state of XeKr + .

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone.

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ abinitio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

20 Watt single-frequency 509 nm laser by single-pass second harmonic generation in an LBO crystal

High power 509 nm continuous-wave (CW) lasers have important applications in science and communication. Here we demonstrate a robust high-power single-frequency 509 nm laser system based on nonlinear phase demodulation technique and single-pass second harmonic generation (SHG) configuration. In experiments, the single-frequency fundamental wave at 1018 nm was linewidth-broadened by an electro-optical modulator and then amplified to 207 W in a ytterbium-doped fiber amplifier. In subsequent single-pass SHG stage, over 20 W CW single-frequency 509 nm laser was generated in a LiB3O5 crystal with a SHG efficiency of 9.7%. To the best of our knowledge, this is the highest reported power for CW single-frequency 509 nm laser, which could be used for advanced underwater optical communication and preparation of cesium Rydberg state.

Photocleavage of Aliphatic C–C Bonds in the Interstellar Medium

Ultraviolet (UV) processing in the interstellar medium (ISM) induces the dehydrogenation of hydrocarbons. Aliphatics, including alkanes, are present in different interstellar environments, being prevalently formed in evolved stars; thus, the dehydrogenation by UV photoprocessing of alkanes plays an important role in the chemistry of the ISM, leading to the formation of unsaturated hydrocarbons and eventually to aromatics, the latter ubiquitously detected in the ISM. Here, through combined experimental results and ab initio calculations, we show that UV absorption (mainly at the Lyα emission line of hydrogen at 121.6 nm) promotes an alkane to an excited Rydberg state from where it evolves toward fragmentation, inducing the formation of olefinic C=C bonds, which are necessary precursors of aromatic hydrocarbons. We show that the photochemistry of aliphatics in the ISM does not primarily produce direct hydrogen elimination but preferential C–C photocleavage. Our results provide an efficient synthetic route for the formation of unsaturated aliphatics, including propene and dienes, and suggest that aromatics could be formed in dark clouds by a bottom-up mechanism involving molecular fragments produced by UV photoprocessing of aliphatics.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Nonadiabatic Holonomic Quantum Computation Based on Rydberg Ground State Blockade

Quantum gates are crucial for quantum computation and quantum information processing. However, their effectiveness is often hindered by systematic errors and decoherence. Therefore, achieving resilient quantum gates to these factors is of great significance. We present a method to construct nonadiabatic holonomic single- and two-qubit gates in a Rydberg ground-state-blockade regime. Our approach utilizes a far-off-resonant technique for the single-qubit gate and a modified Rydberg antiblockade for the two-qubit gate. The reduction of the population of single- and two-excitation Rydberg states and the nonadiabatic holonomic process during the construction of the gates ensure robustness to decoherence and systematic errors, respectively. Numerical results demonstrate the fidelity and robustness of our scheme. The proposed scheme holds promise for future applications in quantum computation and quantum information processing tasks.

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.