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DOE OSTI2026

Autler-Townes spectroscopy of a Rydberg ladder

Ladder-type two-photon excitation of an atom from a ground state $|g\rangle$, to an intermediate excited state $|e\rangle$, and finally, to a Rydberg state $|r\rangle$ has a variety of uses from quantum information to sensing. A common scheme for detecting this transition optically is through electromagnetically induced transparency (EIT). However, in inverted wavelength schemes, where the ground-to-excited transition wavelength is shorter than the excited-to-Rydberg transition wavelength, the strength of the EIT feature on the lower-leg beam is strongly reduced in a Doppler-broadened medium. Here, in this study, we report on an alternative two-photon spectroscopic feature, which we term the two-photon Autler-Townes resonance, observed on the upper-leg beam. Compared to the EIT signal, this feature's superior signal-to-noise ratio allows one to resolve Rydberg resonances with principal quantum number as high as n=80. We also show that such a feature can be utilized to generate an error signal for stabilizing the frequency of the upper-leg beam.

Xiang, Tai [University of California, Berkeley, CA↗

DOE OSTI2023

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction. Our method uses fast, single-pulse gates based on optimal control, atomic dark states to reduce scattering and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms, error-corrected circuits and digital simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Electron beam characterization via quantum coherent electric field imaging

We demonstrate an all-optical, minimally invasive electron beam (𝑒−beam) characterization using Rydberg electrometry. An 𝑒-beam passes through a localized detector volume containing thermal Rb atoms that are optically excited in a quantum superposition of ground and Rydberg states. The 𝑒-beam's electric field perturbs atomic coherence and modifies resonance fluorescence in a narrow spectral region near the two-photon optical transition. Imaging Rb fluorescence provides a map of the electric field from the 𝑒-beam via Rydberg state Stark shifts and allows us to reconstruct the 𝑒-beam width, centroid position, and current. For an 𝑒-beam of 20 keV and electron currents of 20–40 µ⁢A, we measured the centroid position with an accuracy of ≤ 8 µ⁢m and width to within 100 µ⁢m, limited by the experimental sensitivity of electric field reconstruction of ∼0.02 V/cm. This method is suitable for a wide range of electron energies and currents, and can be adopted for nuclear and high-energy experiments for minimally invasive real-time diagnostics and profiling of charged particle beams.

Behary, Rob [College of William and Mary, Williams↗

DOE OSTI2024

Finite-Temperature Quantum Matter with Rydberg or Molecule Synthetic Dimensions

Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases—two are localized in the synthetic dimension, predicted as zero-temperature ground states, and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. Furthermore, by examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Nonresonant coherent amplitude transfer in attosecond four-wave-mixing spectroscopy

Attosecond four-wave mixing (FWM) spectroscopy using an extreme ultraviolet (XUV) pulse and two noncollinear near-infrared (NIR) pulses is employed to measure Rydberg wave packet dynamics resulting from XUV excitation of a 3s electron in atomic argon into a series of autoionizing 3s –1 np Rydberg states ~29 eV. The emitted signals from individual Rydberg states exhibit oscillatory structure and persist well beyond the expected lifetimes of the emitting Rydberg states. These results reflect substantial contributions of longer-lived Rydberg states to the FWM emission signals of each individually detected state. A wave packet decomposition analysis reveals that coherent amplitude transfer occurs predominantly from photoexcited 3s –1 (n + 1) p states to the observed 3s –1 np Rydberg states. The experimental observations are reproduced by time-dependent Schrödinger equation simulations using electronic structure and transition moment calculations. Finally, the theory highlights that coherent amplitude transfer is driven nonresonantly to the 3s –1 np states by the NIR light through 3s –1 (n + 1)s and 3s –1 (n – 1)d dark states during the FWM process.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Singularities in nearly uniform one-dimensional condensates due to quantum diffusion

Dissipative systems often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k 2 (k being the wavevector) and vanishing at long wavelengths as k→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly uniform condensate—a dispersive analog to the Kardar-Parisi-Zhang equation—which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Photon-recoil and laser-focusing limits to Rydberg gate fidelity

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schrödinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency, and the atomic mass. These limits on gate fidelity are studied for the standard π-2π-π Rydberg gate and a protocol based on a single adiabatic pulse with a Gaussian envelope.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2005

Atomic and Molecular Physics

A symposium on atomic and molecular physics was held on November 18, 2005 at Goddard Space Flight Center. There were a number of talks through the day on various topics such as threshold law of ionization, scattering of electrons from atoms and molecules, muonic physics, positron physics, Rydberg states etc. The conference was attended by a number of physicists from all over the world.

Bhatia, Anand K.↗

DOE OSTI2022

The proton charge radius

Nucleons (protons and neutrons) are the building blocks of atomic nuclei and are responsible for more than 99% of the visible matter in the Universe. Despite decades of efforts in studying its internal structure, there are still a number of puzzles surrounding the proton such as its spin and charge radius. Accurate knowledge about the proton charge radius is not only essential for understanding how QCD works in the nonperturbative region but also important for bound state QED calculations of atomic energy levels. It also has an impact on the Rydberg constant, one of the most precisely measured fundamental constants in nature. This review examines the latest situation concerning the proton charge radius in light of the new experimental results from both atomic hydrogen spectroscopy and electron-scattering measurements, with particular focus on the latter. Further, theoretical backgrounds and recent developments concerning the determination of the proton charge radius using different experimental techniques are also presented. Upcoming experiments are discussed, and the deuteron charge radius puzzle is mentioned at the end.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Spectroscopy of Rydberg states in erbium using electromagnetically induced transparency

We present a study of the Rydberg spectrum in 166 Er for series connected to the 4 f 12 ( 3 H 6 )6s, J c = 13/2 and J c = 11/2 ionic core states using an all-optical detection based on electromagnetically induced transparency in an effusive atomic beam. Identifying approximately 550 individual states, we find good agreement with a multi-channel quantum defect theory (MQDT) which allows assignment of most states to ns or nd Rydberg series. We provide an improved accuracy for the lowest two ionization thresholds to E IP, J c =13/2 = 49260:750(1) cm -1 and E IP, J c =11/2 = 49701:184(1) cm -1 as well as the corresponding quantum defects for all observed series. We identify Rydberg states in five different isotopes, and states between the two lowest ionization thresholds. Our results open the way for future applications of Rydberg states for quantum simulation using erbium and exploiting its special open-shell structure.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Transient Symmetry Controls Photo Dynamics near Conical Intersections

Excited-state chemistry lacks generalised symmetry rules. With many femtochemistry studies focused on individual cases, it is hard to build up the same level of chemical intuition for excited-states as exists for ground states. Here, we unravel the degrees of freedom involved in ultrafast internal conversion (IC) by mapping the vibrational coherence of the initial wavepacket, and the dependence on molecular symmetry in various cyclic tertiary amines. Molecular symmetry plays an important role in the preservation of vibrational coherence in the transit from one electronic state to another. We show here that it is sufficient for the molecule to simply have the possibility of a more symmetric structure to achieve the preservation of vibrational coherence. It can be transient and still lead to preservation. Furthermore, this finding provides an additional angle on how symmetry influences electronic transitions and an additional piece to the puzzle of establishing symmetry-based selection rules for excited-state processes.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Resonant x-ray absorption of strong-field-ionized CF 3 Br

We report on an experimental and theoretical study of strong-field laser ionization of CF 3 Br followed by resonant x-ray absorption at the Br K-edge. Distinct 1s -> 4p, 5p Rydberg transitions of Br q+ (q = 1-4) atomic ions are observed and identified with Hartree-Fock-Slater and relativistic configuration interaction calculations. Time-dependent density functional theory and ab initio molecular dynamics calculations were performed to simulate the dissociative ionization process and the molecular orbitals for the q = 1-4 charge states. Measurements were made with both parallel and perpendicular linear polarizations of the laser and x-rays, but dichroism was not observed, indicating negligible alignment by the laser ionization process. This result is explained by calculations on atomic Br and the molecular simulation.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Dissociation dynamics of ion-pair states accessed by low-energy electron collisions

Abstract Ion-pair (IP) states are the superexcited states of the neutral molecule that dissociate as a pair of positive and negative ions. These states are generally present near the ionization continuum of the molecule. IP states can be accessed by using photoexcitation or by using the electron collision technique. Different photoexcitation techniques are widely used over the years to study the threshold (threshold IP production spectroscopy) and the dynamics (IP imaging spectroscopy) of the IP states. However, the electron collision technique is ignored over the years and only a few studies are available. In this review, we will discuss different experimental techniques to probe IP states by using electron collision and also the dynamics of the IP states that are accessed by the electron collision.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Benchmarking and Fidelity Response Theory of High-Fidelity Rydberg Entangling Gates

The fidelity of entangling operations is a key figure of merit in quantum information processing, especially in the context of quantum error correction. High-fidelity entangling gates in neutral atoms have seen remarkable advancement recently. A full understanding of error sources and their respective contributions to gate infidelity will enable the prediction of fundamental limits on quantum gates in neutral atom platforms with realistic experimental constraints. In this work, we implement the time-optimal Rydberg controlled-Z (CZ) gate, design a circuit to benchmark its fidelity, and achieve a fidelity, averaged over symmetric input states, of 0.9971 ( 5 ) , downward corrected for leakage error, which together with our recent work [Nature 634, 321–327 (2024)] forms a new state of the art for neutral atoms. The remaining infidelity is explained by an error model, consistent with our experimental results over a range of gate speeds, with varying contributions from different error sources. Further, we develop a fidelity response theory to efficiently predict infidelity from laser noise with nontrivial power spectral densities and derive scaling laws of infidelity with gate speed. Besides its capability of predicting gate fidelity, we also utilize the fidelity response theory to compare and optimize gate protocols, to learn laser frequency noise, and to study the noise response for quantum simulation tasks. Finally, we predict that a CZ gate fidelity of ≳ 0.999 is feasible with realistic experimental upgrades. Published by the American Physical Society 2025

Tsai, Richard Bing-Shiun (ORCID:0000000286758677)↗

DOE OSTI2021

Photodissociation Dynamics of the Cyclohexyl Radical from the 3p Rydberg State at 248 nm

The photodissociation of jet-cooled cyclohexyl was studied by exciting the radicals to their 3p Rydberg state by using 248 nm laser light and detecting photoproducts by photofragment translational spectroscopy. Both H atom loss and dissociation to heavy fragment pairs are observed. The H atom loss channel exhibits a two-component translational energy distribution. The fast photoproduct component is attributed to impulsive cleavage directly from an excited state, likely the Rydberg 3s state, forming cyclohexene. The slow component is due to statistical decomposition of hot cyclohexyl radicals that internally convert to the ground electronic state prior to H atom loss. The fast and slow components are present in an ~0.7:1 ratio, similar to findings in other alkyl radicals. Internal conversion to the ground state also leads to ring-opening followed by dissociation to 1-buten-4-yl + ethene in comparable yield to H-loss, with the C 4 H 7 fragment containing enough internal energy to dissociate further to butadiene via H atom loss. A very minor ground-state C 5 H 8 + CH 3 channel is observed, attributed predominantly to 1,3-pentadiene formation. Lastly, the ground-state branching ratios agree well with RRKM calculations, which also predict C 4 H 6 + C 2 H 5 and C 3 H 6 + C 3 H 5 channels with similar yield to C 5 H 8 + CH 3 . If these channels were active, it was at levels too low to be observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

The Complete α 8 m Contributions to the 1s Lamb Shift in Hydrogen

Precision studies of simple atoms, such as hydrogen, play an essential role in tests of bound-state QED and determining fundamental constants, such as the Rydberg constant and the proton charge radius. One of the QED predictions is for the Lamb shift of hydrogenic energy levels and, in particular, of the ground state. Here, the value of the 1s Lamb shift in hydrogen and deuterium is required for an accurate determination of the Rydberg constant and the proton charge radius utilizing data from high-resolution spectroscopy of hydrogen and deuterium atoms, as well as for precision tests of bound-state QED. The dominant QED contribution to the uncertainty is due to the α 8 m external-field contributions. We discuss here our recent results on the two- and three-loop contributions, which essentially reduce the theoretical uncertainty. Combined with recent calculations of Laporta on the slope of the Dirac form factor in the three-loop level, our results allow for completion of calculations of α 8 m contributions to the Lamb shift of the ground state in the hydrogen atom.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1999

Rydberg States of Lithium and Other Systems

The interesting calculation of retardation corrections to excited atomic state energies is facilitated by the existence of good calculations of the nonrelativistic and nonretarded energies, to which retardation corrections can be added. Here I describe a perturbation method, applicable when the angular momentum is high enough which generates an asymptotic series for the energy. It makes use of generalized polarizabilities of the atomic or ionic core (numerically obtained) but otherwise is completely analytic. It is applied here to the lithium atom in detail, and its application to hydrogen molecular ions is outlined.

Drachman, Richard J.↗

NASA NTRSDate not supplied

Accelerating the Deployment of Space-Based Quantum Sensors

Quantum sensors rely on quantum mechanical properties, such as wave-particle duality, atomic energy levels, or entanglement, to measure physical, optical, or electromagnetic information from a target. Examples include Rydberg sensors, nitrogen-vacancy magnetometers, HOM (Hong-Ou-Mandel) interferometers, and SQUIDs (Superconducting Quantum Interference Devices). In general, as quantum sensors rely on interrogation at the atomic and photonic level rather than on classical mechanical measurements, these technologies promise advantages over their traditional counterparts in sensitivity, accuracy, and SWaP (Size, Weight, and Power). Conceptually, the use of quantum sensors unlocks the new phenomenology of sensor entanglement. While an ultra-low TRL (Technology Readiness Level) prospect for most sensor types, multi-sensor entanglement is a high risk, high reward strategy with a potential for exquisite sensitivity and SWaP improvements entirely inaccessible to classical sensors.

Grace Caroline Wusk↗