We test the Moskowitz-Lombardi rule, originally formulated for mercury, which gives a simple relation between the magnetic moment of an atomic nucleus and the effect of its radial distribution on the hyperfine structure: the magnetic hyperfine anomaly or Bohr-Weisskopf (BW) effect. While the relation for the differential effect between isotopes may be completely determined experimentally, the value for the additive constant that is needed to give the BW effect for a single isotope has remained unverified. In this work, we determine the BW effect in H-like, singly ionized, and neutral mercury isotopes from experimental muonic-${}^{199}\mathrm{Hg}$ data together with differential anomalies and our atomic calculations. We check this result by directly extracting the BW effect from the measured hyperfine constant for ${}^{199}\mathrm{Hg}^{+}$ using state-of-the-art atomic many-body calculations. From this we deduce an empirical value for the additive constant in the Moskowitz-Lombardi rule, which differs significantly from the values advocated previously. This result allows for increased precision in calculations of the hyperfine structure and improved tests of atomic and nuclear theory.

Rydberg dressing traditionally refers to a technique where interactions between cold atoms are imprinted through the far off-resonant continuous-wave excitation of high-lying Rydberg states. Dipolar interactions between these electronic states are then translated into effective interactions among ground-state atoms. Motivated by recent experiments, we investigate two dressing protocols, in which Rydberg atoms are resonantly excited in a stroboscopic fashion. The first one is nonadiabatic, meaning Rydberg states are excited by short pulses. In this case, mechanical forces among Rydberg atoms result in electron-motion coupling, which generates effective multibody interactions. In the second, adiabatic protocol, Rydberg states are excited by smoothly varying laser pulses. We show that also, in this protocol, substantial multibody interactions emerge.

We study the probability distribution of the first return time to the initial state of a quantum many-body system subject to global projective measurements at stroboscopic times. We show that this distribution can be mapped to a continuation of the canonical partition function of a classical spin chain with noninteracting domains at equilibrium, which is entirely characterized by the Loschmidt amplitude of the quantum many-body system. This allows us to conclude that this probability may decay either algebraically or exponentially at long times, depending on whether the spin chain displays a ferromagnetic or a paramagnetic phase. We illustrate this idea on the example of the return time of $N$ adjacent fermions in a tight-binding model, revealing a rich phase behavior, which can be tuned by scaling the probing time as a function of $N$. The analysis presented here provides an overarching understanding of many-body quantum first detection problems in terms of equilibrium thermodynamic phases. Our theoretical predictions are in excellent agreement with exact numerical computations.

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian-basis-set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a one-electron atom, our results show excellent agreement with those obtained using the exact Dirac-Coulomb wave functions. The developed method can be of interest for high-precision studies of heavy few-electron molecular systems, where the rigorous computation of QED corrections is currently a formidable task.

The 8.4-eV transition in the ${}^{229}\mathrm{Th}$ nucleus is the basis for a high-precision nuclear clock with exceptional sensitivity to new physics effects. We have identified several cases in the ${\mathrm{Th}}^{+}$ ion where electronic excitations closely resonate with the nuclear excitation, with the smallest energy difference being $\mathrm{\Delta }=-0.09{\mathrm{cm}}^{-1}$. We investigate the electronic bridge process, in which nuclear excitation is induced via electronic transitions, and demonstrate that a proper selection of laser frequencies can lead to a dramatic enhancement of this effect. Additionally, we show that the interaction with electrons significantly shortens the lifetime of the nuclear excited state.

The driven-dissipative nonlinear photon systems provide a promising platform to model the nonequilibrium quantum phase transitions. However, the critical property of such a phase transition has remained elusive. With the scaling theory, we accurately measure the critical point and critical exponents of the second-order quantum phase transition in a bosonic mode with a Kerr nonlinearity. The results show that the dissipative phase transition exhibits a weak universality class, in which the universality classes of the close and open quantum Rabi models in the previous studies are both included. Further, one may understand the spatial dimension $d=1$ and the correlation length from the photon occupation probability distribution. When coupled to a quantum-dot electronic circuit, such quantum criticality can be detected by a simple transport signature. As an application, the photocurrent in an unbiased quantum dot system can be significantly enhanced near the phase transition.

We demonstrate that the Wasserstein distance $W_1$ corresponding to optical tomograms of nonclassical states faithfully captures changes that arise due to photon addition to or subtraction from these states. $W_1$ is a true measure of distance in the quantum state space and is sensitive to the underlying interference structures that arise in the tomogram after changes in the photon number. Our procedure is universally applicable to the cat and squeezed states, the former displaying the characteristic negativity in its Wigner function, while the latter does not do so. We explicate this in the case of the squeezed vacuum and even coherent states and show that photon addition (or subtraction) is mirrored in the shift in the intensity of specific regions in the tomogram. Further, we examine the dependence of $W_1$ on the squeezing parameter and its sensitivity to different quadratures.

In understanding strongly correlated quantum systems, quantifying the non-Gaussian nature of interparticle correlations is invaluable. We show that, for a uniform quantum gas, there exists a natural connection between non-Gaussian correlations and the generation of momentum-space entanglement. Furthermore, this entanglement can be directly measured in an experiment using time-of-flight techniques. To create a prototype of our method, we numerically study entanglement generation in a degenerate Bose gas following a quench to the unitary regime, where Gaussian and non-Gaussian correlations are generated sequentially in time.

We have determined the atomic mass of ${}^3\mathrm{He}$ to 12 parts per trillion relative precision from a measurement of the cyclotron frequency ratio of ${}^3\mathrm{He}^{+}$ and ${}^{12}\mathrm{C}^{4+}$ in a Penning trap. From the obtained mass of the ${}^3\mathrm{He}^{+}$ ion, the mass of the neutral atom can be calculated without loss of precision: $m\left({}^3\mathrm{He}\right)=3.016029322011\left(35\right)$ u. This result provides independent, high-precision data for the last missing link between the masses in the regime of light ions, thereby resolving discrepancies in the reported masses of light atomic nuclei from various experiments.

We investigate whether one can detect the presence of a quantum resource in some operational task or equivalently whether every quantum resource provides an advantage over its free counterpart in some black box scenarios where one does not have much information about the devices. For any dimension $d$, we find that for any resource theory with less than $d^2$ number of linearly independent free states or free operations, there exist correlations that can detect the presence of a quantum resource. For this purpose, we introduce the framework for detecting quantum resources semidevice independently by considering the prepare-and-measure scenario with the restriction on the dimension of the quantum channel connecting the preparation box with the measurement box. We then explicitly construct witnesses to observe the presence of various quantum resources. We expect these results will open avenues for detecting and finding uses of quantum resources in general operational tasks.

We show that the complete photoemission dynamics in situations of electron-ion entanglement can be retrieved from photoelectron spectral measurements without information on the ion. To this end, we develop an energy-time analysis of the photoelectron's reduced density matrix based on first principles. We test and assess our approach with numerical simulations on a low-dimensional model molecule in interaction with broadband composite pulses concealing the vibrational resolution. Our method is directly applicable to recent experimental schemes measuring the photoelectron reduced density matrices in atomic and molecular photoemission. Therefore, it opens a new window on the dynamics of decoherence and entanglement at the attosecond timescale.

We study the collapse of an attractive Bose-Einstein condensate, where an unstable system evolves towards a singularity, by numerically solving the underlying cubic-quintic nonlinear Schrödinger equation. We find good agreement between our simulations and the atom-loss measurements with a ${}^{39}\mathrm{K}$ condensate. Our simulations reveal an interplay of weak collapse and the propensity of the system to form a hotspot and we uncover scaling laws that govern this behavior. We also identify promising signatures of the theoretically predicted, but so far experimentally elusive, elastic three-body interactions.

Dynamically localized states in quantum many-body systems are fundamentally important in understanding quantum thermalization and have applications in quantum information processing. Here we explore many-body dynamical localization (MBDL) without disorders in a nonintegrable quantum $\mathit{XY}$ spin chain under periodical and quadratic kicks. We obtain the localization phase regimes with the MBDL and delocalized states and show dynamical observables to extract the phase regipmes. For proper kick strengths in the MBDL phase, we reveal a local dynamical decoupling effect for persistent Rabi oscillation of certain spins. Furthermore, we propose the MBDL-protected quantum information at high temperatures and present an analysis of the dynamical decoupling to obtain the required system parameters for quantum storage. Compared to other nonthermalized states, the disorder-free MBDL states require much fewer repetitions and resources, providing a promising way to protect and store quantum information robust against thermal noises.

We study the direct experimental verification of continuous-variable (CV) energy-time entanglement, a crucial resource for long-distance quantum communication. Despite its potential advantages, including higher information capacity and robustness against noise, verifying energy-time CV entanglement under practical conditions has remained challenging. We find that nonlocal dispersion cancellation (NDC) provides an effective means to probe energy-time CV entanglement, successfully emulating photon propagation through a 379-km optical fiber at telecom wavelengths. By implementing NDC, we experimentally demonstrate that pairs of energy-time-entangled photons experience opposite dispersions, leaving the two-photon wave packet unbroadened, despite significant local dispersion acting individually on each photon. Our results show a violation of the separability criterion [Phys. Rev. A 82, 052120 (2010)] by 32 standard deviations, confirming energy-time CV entanglement independently of entanglement in other degrees of freedom. This work establishes a practical method for robustly verifying CV energy-time entanglement, facilitating advances in quantum information processing and secure long-distance quantum communication.

Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and thus agree with the true mean in expectation. In this Letter, we consider a biased scheme, intentionally introducing a bias in the expectation value by rescaling the conventional classical-shadow estimators to reduce the error in the finite-sample regime. The approach is straightforward to implement and requires no quantum resources. We analytically prove average-case as well as worst- and best-case scenarios, and rigorously prove that it is, in principle, always worth biasing the estimators. We illustrate our approach in a quantum simulation task of a 12-qubit spin-ring problem and demonstrate how estimating expected values of nonlocal perturbations can be significantly more efficient using our biased scheme.

In this Letter, we study quantum circuit Born machines (QCBMs) in the context of photonic quantum computing. QCBMs are a popular choice of quantum generative machine learning models, and we present a QCBM designed for linear optics. We show that a recently developed error mitigation technique called recycling mitigation greatly improves the training of QCBMs in realistic scenarios with photon loss, which is the primary source of noise in photonic systems. We demonstrate this through numerical simulations and through an experiment on a quantum photonic integrated processor. We expect our work to pave the way towards more demonstrations of error mitigation techniques tailored to photonic devices which can enhance the performance of a quantum algorithm.

A quantum control protocol is proposed for the creation of NOON states with $N$ ultracold bosonic atoms on two modes, corresponding to the coherent superposition $|N,0\rangle +|0,N\rangle$. This state can be prepared by using a third mode where all bosons are initially placed and which is symmetrically coupled to the other two modes. Tuning the energy of this third mode across the energy level of the other modes allows the adiabatic creation of the NOON state. While this process normally takes too much time to be of practical use, due to the smallness of the involved spectral gap, it can be drastically boosted through counterdiabatic driving which allows for efficient gap engineering. We demonstrate that this process can be implemented in terms of static parameter adaptations that are experimentally feasible with ultracold quantum gases. Gain factors in the required protocol speed are obtained that increase exponentially with the number of involved atoms and thus counterbalance the exponentially slow collective tunneling process underlying this adiabatic transition. Besides optimizing the protocol speed, our NOON state preparation scheme achieves excellent fidelities that are competitive for practical applications.

We introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

We present a theoretical study on the harnessing and redistribution of the imaginary Poynting momentum (IPM) by introducing a radial degree of freedom in polarization. For specific radial indices, we find that the azimuthal optical force exerted by the IPM on nanoparticles varies with the light wavelength, particle radius, and the initial phase of the vector optical field. This finding demonstrates the controllability of the azimuthal IPM density and its mechanical effects on nanoparticles, providing insights into the manipulation of optical forces. Importantly, the light-driven motion is not dependent on spin or orbital angular momentum, or the use of inhomogeneous particles. Our results offer an alternative method for optical micromanipulation, thereby enhancing the potential for applications in physical and biochemical systems.