We carried out calculations of the energies and magnetic dipole hyperfine-structure constants of the low-lying states of ${}^{233}\mathrm{U}^{+}$ and ${}^{233}\mathrm{U}$ using two different approaches. With six valence electrons and a very heavy core, uranium represents a major challenge for precision atomic theory even using large-scale computational resources. The first approach combines configuration interaction (CI) with a method allowing us to include core-valence correlations to all orders of the perturbation theory over residual Coulomb interaction. The second approach is a pure CI method which allows the use of different initial approximations. We present a detailed analysis of all calculated properties and discuss the advantages and disadvantages of each of these methods. We report a preliminary value of the U nuclear magnetic moment and outline the need for further experiments.

We report the measurement of hyperfine splitting in the $7d$ ${}^{2}D_{3/2}$ state of ${}^{133}\mathrm{Cs}$ using high-resolution Doppler-free two-photon spectroscopy in a Cs vapor cell. We determine the hyperfine coupling constants $A=7.3509\left(9\right)$ MHz and $B=-0.041\left(8\right)$ MHz, which represent an order of magnitude improvement in the precision. We also obtain bounds on the magnitude of the nuclear magnetic octupole coupling constant $C$. Additionally, we measure the ac Stark shift of the $6s{}^2\mathrm{S}_{1/2}\to 7d$ ${}^{2}D_{3/2}$ transition at 767.8 nm to be $-49\pm 5\mathrm{Hz}/\left(\mathrm{W}/\mathrm{c}{\mathrm{m}}^2\right)$, in agreement with theoretical calculations. We further report the measurement of collisional shift (−32.6 ± 2.0 kHz/mTorr) and pressure broadening for the individual hyperfine levels of the $6s{}^2\mathrm{S}_{1/2}\to 7d$ ${}^{2}D_{3/2}$ transition. These measurements provide valuable inputs for analysis of systematic effects in optical frequency standards based on the cesium $6s{}^2\mathrm{S}_{1/2}\to 7d$ ${}^{2}D_{3/2}$ two-photon transition.

The nonadditive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bifunctional of electron densities ${\rho }_{\mathrm{B}}$ and ${\rho }_{\mathrm{tot}}={\rho }_{\mathrm{A}}+{\rho }_{\mathrm{B}}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of ${\rho }_{\mathrm{B}}$ and ${\rho }_{\mathrm{tot}}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, ${\mathrm{HeLi}}^{+}$, and ${\mathrm{H}}_2$, using analytical inversion to obtain a numerically exact $v^{\mathrm{NAD}}$ for the local density approximation. We examine features of $v^{\mathrm{NAD}}$ which can be used for development and testing of approximations to $v^{\mathrm{NAD}}[{\rho }_{\mathrm{B}},{\rho }_{\mathrm{tot}}]$ and kinetic-energy functionals.

We formulate a measure that quantifies chirality in single electron ionization triggered in atoms, which are achiral systems. We do so in the context of Ar driven by a different type of optical fields that consists of two noncollinear laser beams giving rise to chirality that varies in space across the focus of the beams. Our computations account for realistic experimental conditions. To define this measure of chirality, we first find the sign of the electron final momentum scalar triple product ${\mathbf{p}}_x·({\mathbf{p}}_y\times {\mathbf{p}}_z)$ and multiply it with the probability for an electron to ionize with certain values of the momentum components. Then, we integrate over all values of $p_x$, $p_y$, $p_z$. We show this to be a robust measure of chirality in electron ionization triggered by chiral electric fields.

A class of linear, spiral phenomena is discovered in the photoelectron momentum distribution when studying photoionization of $S$-state atoms by a pair of linearly chirped, oppositely circularly polarized attosecond pulses eventually delayed in time by $\tau$. This controllable effect, dubbed. reversible electron spirals because of its energy-dependent sense of rotation, is identified and can be isolated in the absence of time delay for the case of opposite chirp rates. The astrophysical concept of spiral arm pitch angle is borrowed to gain a better insight into the energy dependence of the reversible spiral rotation, to determine the attochirp as well as the binding energy characteristic of an atomic target. Our results indicate potential applications in attochirpmetry and polarimetry.

Within the framework of stochastic electrodynamics we derive the noise spectrum of a laser beam reflected from a suspended mirror. The electromagnetic field follows Maxwell's equations and is described by a deterministic part that accounts for the laser field and a stochastic part that accounts for thermal and zero-point background fluctuations. Likewise, the mirror motion satisfies Newton's equation of motion and is composed of deterministic and stochastic parts, similar to a Langevin equation. We consider a photodetector that records the power of the field reflected from the mirror interfering with a frequency-shifted reference beam (heterodyne interferometry). We theoretically show that the power spectral density of the photodetector signal is composed of four parts: (i) a deterministic term with beat notes, (ii) shot noise, (iii) the actual heterodyne signal of the mirror motion, and (iv) a cross term resulting from the correlation between measurement noise (shot noise) and backaction noise (radiation pressure shot noise). The latter gives rise to the Raman sideband asymmetry observed with ultracold atoms, cavity optomechanics, and with levitated nanoparticles. Our classical theory fully reproduces experimental observations and agrees with the results obtained by a quantum theoretical treatment.

In quantum photonics, threshold detectors, distinguishing between vacuum and one or more photons, such as superconducting nanowires and avalanche photodiodes, are routinely used to measure Fock and Gaussian states of light. Despite being the standard measurement scheme, there is no general closed form expression for measurement probabilities with threshold detectors, unless accepting coarse approximations or combinatorially scaling summations. Here, we present new matrix functions to fill this gap. We develop the Bristolian and the loop Torontonian functions for threshold detection of Fock and displaced Gaussian states, respectively, and connect them to each other and to existing matrix functions. By providing a unified picture of bosonic statistics for most quantum states of light, we provide novel tools for the design and analysis of photonic quantum technologies.

In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the Förster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.

Topological order, reflected in long-range patterns of entanglement, is quantified by the topological entanglement entropy $\gamma$. We show that for gapped quantum spin liquids it is possible to extract $\gamma$ using two-spin local correlators. We demonstrate our method for the gapped ${\mathbb{Z}}_2$ Kitaev spin liquid on a honeycomb lattice with anisotropic interactions. We show that the $\gamma =ln2$ for ${\mathbb{Z}}_2$ topological order can be simply extracted from local two-spin correlators across two different bonds that involve only Majorana fermions, with an accuracy comparable to or higher than the Kitaev-Preskill construction. This implies that even though the ground state can be factorized into the product of Majorana and gauge sectors, the different superselection sectors of ${\mathbb{Z}}_2$ gauge theory determined by global Wilson loop operators can be reflected locally in the Majorana sector.

Quantum random access codes (QRACs) provide a basic tool for demonstrating the advantages of quantum resources and protocols, which have a wide range of applications in quantum information processing tasks. However, the investigation and application of high-dimensional $\left(d\right)$ multi-input $\left(n\right)n^{\left(d\right)}\to 1$ QRACs are still lacking. Here, we present a general method to find the maximum success probability of $n^{\left(d\right)}\to 1$ QRACs. In particular, we give the analytical solution for maximum success probability of $3^{\left(d\right)}\to 1$ QRACs when measurement bases are mutually unbiased bases (MUBs). Based on the analytical solution, we show the relationship between MUBs and $n^{\left(d\right)}\to 1$ QRACs. First, we provide a systematic method of searching for the operational inequivalence of MUBs (OI-MUBs) when the dimension $d$ is a prime power. Second, we theoretically prove that, surprisingly, the commonly used Galois MUBs are not the optimal measurement bases to obtain the maximum success probability of $n^{\left(d\right)}\to 1$ QRACs, which indicates a breakthrough according to the traditional conjecture regarding the optimal measurement bases. Furthermore, based on high-fidelity high-dimensional quantum states of orbital angular momentum, we experimentally achieve two-input and three-input QRACs up to dimension 11. We experimentally confirm the OI-MUBs when $d=5$. Our results open alternative avenues for investigating the foundational properties of quantum mechanics and quantum network coding.

The notion of capacity of entanglement is the quantum information theoretic counterpart of the heat capacity which is defined as the second cumulant of the entanglement spectrum. Given any bipartite pure state, we can define the capacity of entanglement as the variance of the modular Hamiltonian in the reduced state of any of the subsystems. Here, we study the dynamics of this quantity under a nonlocal Hamiltonian. Specifically, we address the following question: Given an arbitrary nonlocal Hamiltonian, what is the capacity of entanglement that the system can possess? As a useful application, we show that the quantum speed limit for creating the entanglement is not only governed by the fluctuation in the nonlocal Hamiltonian, but also depends inversely on the time average of the square root of the capacity of entanglement. Furthermore, we discuss this quantity for a general self-inverse Hamiltonian and provide a bound on the rate of capacity of entanglement. Towards the end, we generalize the capacity of entanglement for bipartite mixed states based on the relative entropy of entanglement and show that the above definition reduces to the capacity of entanglement for pure bipartite states. Our results can have several applications in diverse areas of physics.

Single- and double-electron-capture processes occurring in ${\mathrm{Ar}}^{8+}$ and He collisions are investigated in a broad energy domain ranging from 0.1 to 100 keV/u. Total and partial cross sections are calculated using a two-active-electron semiclassical asymptotic-state close-coupling approach. For single-electron-capture cross sections the present results show the best overall agreement with available experimental data for both total and partial cross sections, and possible reasons for observed discrepancies are discussed. Furthermore, we extend the understanding of the electron-capture processes on that system to impact energies above 20 keV/u for which no data exist. The cross sections for double-electron-capture processes are also reported and show severe discrepancies with the rare available experimental data.

The Thomas–Reiche–Kuhn sum rule is used to form an effective potential that is added to the time-dependent configuration-interaction singles (TDCIS) equations of motion in velocity gauge. The purpose of the effective potential is to include virtual coupling from singles to doubles, which is required for size-consistent velocity-gauge TDCIS results. The proposed method is compared to length-gauge TDCIS results for laser-assisted photoionization. Finally, a dynamical interference effect controlled by two-color fields is predicted for atomic targets.

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by Biagioni et al. [G. Biagioni, N. Antolini, A. Alaña, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground-state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) one-dimensional behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signaling the onset of a dimensional crossover.

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to $\text{SU}\left(2\right)$ rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in $\text{SU}\left(4\right)$, thereby creating the opportunity for dynamics not possible in typical $\text{SU}\left(2\right)$ one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.

In this work we design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description, i.e., a description based on representative points in classical phase spaces. This is obtained by relating quantum states to representative points via generalized coherent states (GCSs) and designing a positive-operator-valued measure (POVM) for GCS discrimination. Conditions upon this discrimination are defined such that the POVM results convey enough information to meet our needs for reliability and precision, as gauged by two parameters $\epsilon$, of our arbitrary choice, and $\delta$, set by the experimental apparatus, respectively. The procedure implies a definition of what is meant by the “size” of the system, in terms of the number $N$ of elementary constituents that provide the global algebra leading to the phase space for the emergent classical-like description. The above conditions on GCS discrimination can be thus turned into $N>N_{\mathrm{t}}(\epsilon ,\delta )$, where $N_{\mathrm{t}}(\epsilon ,\delta )$ is the threshold size mentioned in the title. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly discussed. Results for pseudospin and bosonic systems are also given.

High-quality randomness, certified to be unpredictable by eavesdroppers, is key to secure information processing. Quantum mechanics enables randomness certification with minimal trust in the devices used, by exploiting quantum nonlocality. However, such full device independence is challenging to implement. We present a scheme for quantum randomness certification based on quantum steering. The protocol is one-sided device independent, providing high security, but requires only states and measurements that are simple to realize on quantum optics platforms—squeezed vacuum states and homodyne detection. This ease of implementation is demonstrated experimentally and implies that gigahertz random bit rates should be attainable with current technology. Furthermore, our scheme is immune to the detection loophole and represents the closest to full device independence that can be achieved using purely Gaussian states and measurements.