CyberSec Research

Laser ionization spectroscopy was performed on both neutral and singly ionized $^{232}$Th with the aim of identifying the nuclear-clock isomer in the singly charged ionic state of $^{229}$Th. A search for an efficient laser ionization scheme of $^{232}$Th$^+$ was conducted in an argon-filled gas cell. This revealed a congested spectrum due to collisional quenching effects and the presence of several auto-ionizing states, one of which has a laser ionization efficiency of at least $1.2 \%$. Using a threshold approach, the second ionization potential was determined to be $12.300(9)\,$eV. The subsequent study on atomic $^{232}$Th validated the threshold approach. Conducting spectroscopy in a hypersonic gas jet, suppressed the gas-collision-induced quenching, revealing a Rydberg series that converges to the first ionization potential, determined to be $6.306879(14)\,$eV. The gas jet also cools down the thorium, allowing for high-resolution laser spectroscopy with a resolution of $240(30)\,$MHz. Using the Multiconfigurational Dirac-Hartree-Fock (MCDHF) method, the ionization potentials were computed, showing a relative difference of 0.06\% and 0.19\% between theory and our experimental values for the ionization potentials of Th and Th$^+$ respectively. Further calculations using a pseudo-relativistic Hartree-Fock method reveal strong mixing in the used intermediate state at $26113.27\,$cm$^{-1}$ of Th. A dedicated fast-extraction gas cell with $^{233}$U recoil sources was used to study $^{229}$Th$^+$ but no photo-ionization signal could be observed.

Systematic QED calculations of ionization energies of the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the $2p_{1/2}$--$2s$ and $2p_{3/2}$--$2p_{1/2}$ transition energies are performed for Li-like ions with the nuclear charge numbers $Z = 10$--$100$. The convergence of QED perturbative expansion is improved by using the extended Furry picture, which starts from the Dirac equation with a local screening potential. An ab initio treatment is accomplished for one- and two-photon electron-structure QED effects and the one-photon screening of the self-energy and vacuum-polarization corrections. This is complemented with an approximate treatment of the two-photon QED screening and higher-order (three or more photon) electron-structure effects. As a result, the obtained theoretical predictions improve upon the accuracy achieved in previous calculations. Comparison with available experimental data shows a good agreement between theory and experiment. In most cases, the theoretical values surpass the experimental results in precision, with only a few exceptions. In the case of uranium and bismuth, the comparison provides one of the most stringent tests of bound-state QED in the strong-field regime. Alternatively, the obtained results can be employed for high-precision determinations of nuclear charge radii.

This study provides a comprehensive analysis of $S$-wave exotic hydrogen-like three-body systems ($pp\mu^-$, $pp\tau^-$, $\mu^-\mu^-p$, $\tau^-\tau^-p$, $p\mu^-\tau^-$) with spin-parity $J^P = 1/2^+$ and $3/2^+$, and four-body systems ($pp\mu^-\mu^-$, $pp\tau^-\tau^-$) with $J^P = 0^+$, $1^+$, and $2^+$. We use complex scaling and Gaussian expansion methods to solve the complex-scaled Schr\"{o}dinger equation and obtain possible bound and quasi-bound states. The resulting binding energies range from $-33.8$~keV to $-340$~eV. Notably, we present the first theoretical estimation of the bound-state energy levels of $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$, which is of significant importance for understanding exotic few-body Coulomb systems. We further analyze spin configurations and root-mean-square radii to elucidate the spatial structure of these bound and quasi-bound states. Our results reveal that $K$-type spatial configurations play a crucial role in accurately describing bound and quasi-bound states in the hydrogen-molecule-like systems $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$. Incorporating $K$-type configurations significantly alters the mass spectra of these states. Future muon colliders and muon facilities may offer promising platforms for the possible copious production of such heavy flavored hydrogen molecules and molecular ions. For instance, scattering processes such as $2\mu^- + \mathrm{H_2} \to \mathrm{H_{2\mu}} + 2e^-$, $\mu^- + \mathrm{H_2} \to \mathrm{H_{\mu e}} + e^-$, and $\mu^- + \mathrm{H_2^+} \to \mathrm{H_{2\mu}^+} + e^-$ could be utilized, facilitating detailed studies of intriguing states such as $\mathrm{H_{2\mu}}$, $\mathrm{H_{\mu e}}$, and $\mathrm{H_{2\mu}^+}$.

Efficient loading of single atoms into tightly confined traps is crucial for advancing quantum information processing and exploring atom-photon interactions. However, directly loading atoms from a magneto-optical trap (MOT) into static tweezers in cavity-based systems and hybrid atom-photon interfaces remains a challenge. Here, we demonstrate atom loading in a tightly confined optical tweezer 0.6mm away from MOT by an optical conveyor belt. By employing real-time feedback control of the atom number in the overlapping region between the conveyor belt and the tweezer, we enhance a single-atom loading probability to 77.6%. Our technique offers a versatile solution for deterministic single-atom loading in various experimental settings and paves the way for diverse applications based on hybrid photonic-atom structures.

We compute the isotope shifts of the \emph{total} electron binding energy of neutral atoms and singly charged ions up to element $Z=120$, using relativistic Hartree-Fock method including the Breit interaction. Field shift coefficients are extracted by varying the nuclear charge radius; a small quadratic term is retained to cover large radius changes relevant to superheavy nuclei. We tabulate isotope shift coefficients for closed shell systems from Ne to Og and benchmark selected open shell cases, used to test the interpolation formula. A simple power law interpolation $bZ^k$ reproduces calculated field shifts to within about 1\% across the table, with the effective exponent $k$ growing from roughly 5 near $Z \sim 50$ to about 12 at $Z \sim 118$. Due to the domination of inner shells, differences between neutrals and singly charged ions does not exceed few percent, becoming noticeable mainly when an outer $s$ electron is removed. Therefore, these results may also be used for higher charge ions.

Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms include scalability, reconfigurable connectivity, and native multi-qubit gates, making them particularly well-suited for addressing complex network problems. These problems can often be framed as graph-based tasks, which can be efficiently addressed using quantum walks. In this work, we propose a general implementation of staggered quantum walks with Rydberg atoms, with a particular focus on spatial networks. We also present an efficient algorithm for constructing the tessellations required for the staggered quantum walk. Finally, we demonstrate that our proposal achieves quadratic speedup in spatial search algorithms.

We employ an all-particle multireference Fock-space relativistic coupled-cluster (FSRCC) theory to compute the ionization potential, excitation energy, transition rate and hyperfine structure constants associated with $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^{3}P_{1}$ and $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^1P_{1}$ transitions in nobelium (No). Using our state-of-the-art calculations in conjunction with available experimental data \cite{raeder-18}, we extract the values of nuclear magnetic dipole ($\mu$) and electric quadrupole ($Q$) moments for $^{253}$No. Further, information on nuclear deformation in even-mass isotopes is extracted from the isotope shift calculations. Moreover, we employ a perturbed relativistic coupled-cluster (PRCC) theory to compute the ground state electric dipole polarizability of No. In addition, to assess the accuracy of our calculations, we compute the ionization potential and dipole polarizability of lighter homolog ytterbium (Yb). To account for strong relativistic and quantum electrodynamical (QED) effects in No, we incorporate the corrections from Breit interaction, vacuum polarization and self-energy in our calculations. The contributions from triple excitations in coupled-cluster is accounted perturbatively. Our calculations reveal a significant contribution of $\approx$10\% from the perturbative triples to the transition rate of $7s^2\;^1S_{0}\rightarrow 7s7p\;^3P_{1}$ transition. The largest cumulative contribution from Breit+QED is observed to be $\approx$4\%, to the magnetic dipole hyperfine structure constant of $7s7p\;^1P_{1}$ state. Our study provides a comprehensive understanding of atomic and nuclear properties of nobelium with valuable insights into the electron correlation and relativistic effects in superheavy elements.

We utilize few-level model systems to analyze the polarization and phase properties of below-threshold harmonics (BTH) in aligned molecules. In a two-level system (TLS), we find that the phase of emitted harmonics undergoes a distinct change. For harmonics with photon energies below the transition between the dominant field-dressed states, the phase alternates by $\pi$ between successive odd harmonic orders but remains constant above. Exploiting this behavior, we construct a four-level model composed of two uncoupled TLS subsystems aligned along orthogonal directions. We demonstrate that with selected transition frequencies lower-order harmonics follow the polarization of the linearly polarized driving field while higher-order harmonics exhibit a mirrored polarization. The model predicts that aligned systems with orthogonal transition dipoles may show analogous phase and polarization features in the BTH regime.

We analyze the zero energy collision of three identical bosons in the same internal state with total orbital angular momentum $L=2$, assuming short range interactions. By solving the Schr\"odinger equation asymptotically, we derive two expansions of the wave function when three bosons are far apart or a pair of bosons and the third boson are far apart. The scattering hypervolume $D$ is defined for this collision. Unlike the scattering hypervolume defined by one of us in 2008, whose dimension is length to the fourth power, the dimension of $D$ studied in the present paper is length to the eighth power. We then derive the expression of $D$ when the interaction potentials are weak, using the Born's expansion. We also calculate the energy shift of such three bosons with three different momenta $\hbar \mathbf{k_{1}}$, $\hbar\mathbf{k_{2}}$ and $\hbar\mathbf{k_{3}}$ in a large periodic box. The obtained energy shift depends on $D^{(0)}/\Omega^{2}$ and $D/\Omega^{2}$, where $D^{(0)}$ is the three-body scattering hypervolume defined for the three-body $L=0$ collision and $\Omega$ is the volume of the periodic box. We also calculate the contribution of $D$ to the three-body T-matrix element for low-energy collisions. We then calculate the shift of the energy and the three-body recombination rate due to $D^{(0)}$ and $D$ in the dilute homogeneous Bose gas. The contribution to the three-body recombination rate constant from $D$ is proportional to $T^2$ if the temperature $T$ is much larger than the quantum degeneracy temperature but still much lower than the temperature scale at which the thermal de Broglie wave length becomes comparable to the physical range of interaction.

Cluster states are a useful resource in quantum computation, and can be generated by applying entangling gates between next-neighbor qubits. Heralded entangling gates offer the advantage of high post-selected fidelity, and can be used to create cluster states at the expense of large space-time overheads. We propose a low-overhead protocol to generate and merge high-fidelity many-atom entangled states into a 3D cluster state that supports fault-tolerant universal logical operations. Our simulations indicate that a state-of-the-art high-finesse optical cavity is sufficient for constructing a scalable fault-tolerant cluster state with loss and Pauli errors remaining an order of magnitude below their respective thresholds. This protocol reduces the space-time resource requirements for cluster state construction, highlighting the measurement-based method as an alternative approach to achieving large-scale error-corrected quantum processing with neutral atoms.

Nuclear Schiff moments (NSMs) are sensitive probes for physics beyond the Standard Model of particle physics, signaling violations of time-reversal and parity-inversion symmetries in atomic nuclei. In this Letter, we report the first-ever calculation of a NSM in a nuclear ab initio framework, employing the no-core shell model to study the fluorine isotope $^{19}$F. We further perform quantum-chemistry calculations to evaluate the sensitivity of the hafnium monofluoride cation, HfF$^+$, to the NSM of $^{19}$F. Combined with recent high-precision measurements of the molecular electric dipole moment of HfF$^+$, our results enable the first experimental bound on the NSM of $^{19}$F.

Young's double slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which "passes through the slit". Early pioneering experiments were done with trapped ions and atom pairs created via photo-dissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this note, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.

The exceptionally low-energy isomeric transition in $^{229}$Th at around 148.4 nm offers a unique opportunity for coherent nuclear control and the realisation of a nuclear clock. Recent advances, most notably the incorporation of large ensembles of $^{229}$Th nuclei in transparent crystals and the development of pulsed vacuum-ultraviolet (VUV) lasers, have enabled initial laser spectroscopy of this transition. However, the lack of an intense, narrow-linewidth VUV laser has precluded coherent nuclear manipulation. Here we introduce and demonstrate the first continuous-wave laser at 148.4 nm, generated via four-wave mixing (FWM) in cadmium vapor. The source delivers 100 nW of power with a linewidth well below 100 Hz and supports broad wavelength tunability. This represents a five-orders-of-magnitude improvement in linewidth over all previous single-frequency lasers below 190 nm, marking a major advance in laser technology. We develop a spatially resolved homodyne technique to place a stringent upper bound on the phase noise induced by the FWM process and demonstrate sub-hertz linewidth capability. These results eliminate the final technical hurdle to a $^{229}$Th-based nuclear clock, opening new directions in quantum metrology, nuclear quantum optics and precision tests of the Standard Model. More broadly, they establish a widely tunable, ultranarrow-linewidth laser platform for applications across quantum information science, condensed matter physics, and high-resolution VUV spectroscopy.

We present a novel method for mapping in situ the spatial distribution of photon momentum across a laser beam using a Bose-Einstein condensate (BEC) as a moving probe. By displacing the BEC, we measure the photon recoil by atom interferometry at different positions in the laser beam and thus reconstruct a two-dimensional map of the local intensity and effective dispersion of the $k$ wave vector. Applied to a beam diffracted by a diaphragm, this method reveals a local extra recoil effect, which exceeds the magnitude $h\nu/c$ of the individual plane-waves over which the beam can be decomposed. This method offers a new way to precisely characterize wavefront distortions and to evaluate one of the major systematic bias sources in quantum sensors based on atom interferometry.

We report a detailed study of post-collision interaction (PCI) in a liquid medium. We investigate PCI for the Auger KLL electrons of solvated Cl$^-$, K$^+$ and Ca$^{2+}$. All three isoelectronic ions exhibit a very similar PCI behavior, which is little affected by changing the solvent from water to methanol or ethanol. The two main factors modifying the PCI interaction in condensed media is the screening of Coulombic interactions, and scattering of the electrons. The experimental results are compared with the predictions of a previously reported semi-classical PCI theory modified to account for screening and scattering. We show that a better agreement with experiment can be obtained by instead modeling scattering using electron transport Monte-Carlo simulations. We suggest that, in turn, PCI experimental data could be used as another experimental constraint to refine the currently insufficiently well-known scattering parameters of low-energy electrons in water, which are crucial in many fields.

Mercury (Hg) and superheavy element copernicium (Cn) are investigated using equation-of-motion relativistic coupled-cluster (EOM-RCC) and configuration interaction plus many-body perturbation theory (CI+MBPT) methods. Key atomic properties including ionization potentials (IP), excitation energies (EEs), isotope field shift factors (F), and static electric dipole polarizabilities ({\alpha}) are calculated for ground and low-lying excited states. To evaluate the theoretical accuracy, calculations for both Hg and Cn are performed, with experimental data of Hg serving as benchmarks. Furthermore, basis set dependence has been systematically evaluated in the EOM-RCC calculations, with corresponding uncertainty estimates having been provided. The calculated atomic properties could provide valuable insights into the electronic structure and chemical behavior of superheavy elements.

Simulating nuclear matter described by quantum chromodynamics using quantum computers is notoriously inefficient because of the assortment of quark degrees of freedom such as matter/antimatter, flavor, color, and spin. Here, we propose to address this resource efficiency challenge by encoding three qubits within individual ytterbium-171 atoms of a neutral atom quantum processor. The three qubits are encoded in three distinct sectors: an electronic "clock" transition, the spin-1/2 nucleus, and the lowest two motional states in one radial direction of the harmonic trapping potential. We develop a family of composite sideband pulses and demonstrate a universal gate set and readout protocol for this three-qubit system. We then apply it to single-flavor quantum chromodynamics in 1+1D axial gauge for which the three qubits directly represent the occupancy of quarks in the three colors. We show that two atoms are sufficient to simulate both vacuum persistence oscillations and string breaking. We consider resource requirements and connections to error detection/correction. Our work is a step towards resource-efficient digital simulation of nuclear matter and opens new opportunities for versatile qubit encoding in neutral atom quantum processors.

This study presents a comprehensive experimental and theoretical characterisation of Stokes polarimetry in potassium (K) vapour on the D1 line. Measurements were performed in the weak-probe regime, investigating the influence of neon buffer gas in the presence of an applied magnetic field in the Faraday geometry. While previous Stokes polarimetry studies in alkali-metal vapours have been conducted, the specific effects of buffer gas-induced broadening and shifts on the observed Stokes parameters remained largely underexplored. Here, experimental measurements of absolute absorption and dispersion were compared with a theoretical model for the electric susceptibility of the vapour, calculated using the established software package $ElecSus$. This work marks the first application of $ElecSus$ to model buffer gas polarimetry of the potassium D1 line, with validation performed against experimental spectra for magnetic fields up to 1.2 kG. Our findings provide new insight into how the presence of buffer gas influences the observed Stokes parameters, thereby enhancing the predictive capabilities of theoretical frameworks for atom-light interactions in buffer-gas environments.