For superheavy elements with atomic numbers $120\le Z\le 170$, the concept of the ground-state configuration is being reexamined. To this end, relativistic calculations of the electronic structure of the low-lying levels are carried out by means of the Dirac-Fock and configuration-interaction methods. The magnetic and retardation parts of the Breit interaction as well as the QED effects are taken into account. The influence of the relativistic, QED, and electron-electron correlation effects on the determination of the ground state is analyzed.

We study theoretically the nonequilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system and characterize both their normal and anomalous momentum distributions. We apply this formalism to the interaction quench of a 2D Bose gas and study the ensuing dynamics of its quantum structure factor and coherence function, both recently measured experimentally. Our results indicate that, in two dimensions, a description in terms of independent quasiparticles becomes quickly inaccurate and should be systematically questioned when dealing with nonequilibrium scenarios.

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cramér-Rao bound. Our results may contribute to the development of practical quantum sensing.

The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary operation $U\left(N\right)$ by a sequence of single-qubit and two-qubit unitary gates from a universal set. Although this certainly facilitates the experimentalists as they only need to prepare several different kinds of universal gates, the number of gates required to implement an arbitrary desired unitary operation is usually large. Hence, the efficiency in terms of the circuit depth or running time is not guaranteed. Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation $U\left(N\right)$ without the need to decompose it into a sequence of gates of smaller sizes. Our model is essentially a quantum neural network based on DTQW. Firstly, it is universal as we show that any unitary operation $U\left(N\right)$ can be realized via an appropriate choice of coin operators. Secondly, our DTQW-based neural network can be updated efficiently via a learning algorithm, i.e., a modified stochastic gradient descent algorithm adapted to our network. By training this network, one can promisingly find approximations to arbitrary desired unitary operations. With an additional measurement on the output, the DTQW-based neural network can also implement general positive-operator-valued measure (POVM) measurements. We show its capacity in implementing arbitrary two-outcome POVMs via numeric simulation. We further demonstrate that the network can be simplified and can overcome device noises during the training so that it becomes more friendly for laboratory implementations. Our work shows the capability of the DTQW-based neural network in quantum computation and its potential in laboratory implementations.

Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with nonvanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.

The many-body-theory approach to positronium (Ps) interactions with atoms developed by the authors [Phys. Rev. Lett. 120, 183402 (2018)] is applied to the noble-gas atoms He, Ne, Ar, Kr, and Xe. In this method, the Ps-atom interaction is described by the sum of the electron-atom and positron-atom correlation potentials (self-energies) and the screening of the electron-positron Coulomb interaction by the atomic electrons. Phase shifts and cross sections for elastic scattering are presented, along with values of the pickoff annihilation parameter ${}^1{Z}_{\text{eff}}$, accounting for short-range electron-positron correlations via vertex enhancement factors. Comparisons are made with available experimental data for elastic and momentum-transfer cross sections and ${}^1{Z}_{\text{eff}}$. Values of ${}^1{Z}_{\text{eff}}$ for He and Ne are found to be in near-perfect agreement with experiment; for Ar, Kr, and Xe, they are within 20% of measured values.

The rubidium $5S\text{−}5D$ Doppler-free two-photon transition has been observed in a thermal vapor cell by detecting the infrared radiation emitted during the decay from the $5D$ excited level to the $5P$ intermediate level. Different to the usual detection scheme based on blue light emission this approach does not suffer from reabsorption and still works at high densities. This not only allows for a dramatically enhanced detectable emission rate but also for investigating collisional effects such as collisional broadening and collisional energy transfer. Furthermore, we observe a yet unknown temperature dependence of the resonance linewidth for transitions into the states of the $5D_{\text{5/2}}$ level. Consequences for the design of an optical Rb-frequency standard are discussed.

Nonlocal interaction between ultracold atoms trapped in optical lattices can give rise to interesting quantum many-body phenomena. However, its realization usually demands unconventional techniques, for example, the artificial gauge fields or higher-orbit Feshbach resonances, and is not highly controllable. Here, we propose a valid and feasible scheme for realizing a tunable finite-range interaction for spinless fermions immersed into the bath of bosons. The strength of the effective interaction for the fermionic subsystem is artificially tunable by manipulating bosons, ranging from the repulsive to the attractive regime. In addition, the interaction distance is locked to the hopping of bosons, making the finite-range interaction perfectly clean for the fermionic subsystem. Specifically, we find that, by introducing an additional staggered hopping of bosons, the proposal is readily applied to search the Majorana corner modes in such a spinless system, without the implementation of complex artificial gauge fields, which is totally distinct from existing results reported in spinful systems. Therefore, this scheme provides a potential platform for exploring the unconventional topological superfluids and other nontrivial phases induced by long-range interactions in ultracold atoms.

Abruptly autofocusing vortex beams were proposed for a variety of applications such as optical manipulation, but their quantitative characterization of their trapping capability remains largely unexplored. In this paper, we propose a type of autofocusing vortex beams named multi-Airy vortex beams (MAVBs) and investigate their autofocusing and trapping characteristics theoretically and experimentally. It is found that the autofocusing performance and trapping ability of MAVBs can be enhanced by adjusting the relevant parameters and increasing the number of superposed Airy within a certain range. Although the trapping force and trapping stiffness of MAVBs decrease as the topological charge increases, we found that MAVBs have advantages in capturing and manipulating large-sized particles in our experiments. In the process of manipulating multiple particles for rotation, the larger the topological charge, the more particles can be rotated simultaneously by MAVBs. Moreover, the speed and even the direction of rotation can be easily adjusted by controlling the degree of dispersion between particles. Our work provides a guide to quantitatively exploring the optical trapping capabilities of autofocusing vortex beams, which may lead to different photonic tools for optical trapping and manipulation.

We introduce a computational Maxwell-Bloch framework for investigating out-of-equilibrium optical emitters in open systems. To do so, we compute the pulse-induced dynamics of each emitter from fundamental light-matter interactions and self-consistently calculate their radiative coupling, including phase inhomogeneity from propagation effects. This semiclassical framework is applied to open quantum dots systems with different densities and dipolar coupling. We observe signatures of superradiant behavior, such as directionality and faster decay, as well as subradiant emission. We compare and discuss the computed light emission obtained with our method and a master equation approach. Our framework enables quantitative investigations of large optical ensembles in the time domain and could be used to design new systems with enhanced superradiant and subradiant properties.

Quantum reservoir processing offers an option to perform quantum tomography of input objects by postprocessing quantities, obtained from local measurements, from a quantum reservoir network that has interacted with the former. We develop a method to assess a tomographic completeness criterion for arbitrary quantum reservoir architectures. Furthermore, we propose a figure of merit that quantifies their robustness against imperfections. Measured quantities from the reservoir nodes correspond to effective observables acting on the input objects, and we provide a way to retrieve them. Finally, we present examples of quantum tomography for demonstration. Our general method offers guidance in optimizing implementations of quantum reservoir processing.

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scales exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography, enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

The ($1+1$)-dimensional ($1+1\text{D}$) O(3) nonlinear $\sigma$-model is a model system for future quantum lattice simulations of other asymptotically free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use of two-dimensional layouts presently available on cold-atom quantum simulators. A different definition of the renormalized coupling is introduced, which is applicable to systems with open boundary conditions and can be measured using analog quantum simulators. Monte Carlo and tensor network calculations are performed to determine the quantum resources required to reproduce perturbative short-distance observables. In particular, we show that a rectangular array of 48 Rydberg atoms with existing quantum hardware capabilities should be able to adiabatically prepare low-energy states of the perturbatively matched theory. These states can then be used to simulate nonperturbative observables in the continuum limit that lie beyond the reach of classical computers.

The theoretical approach developed here treats uniformly the direct and indirect mechanisms of dissociative recombination (DR) in a diatomic ion. The present theory is based on electron-scattering calculations performed at several internuclear distances in the molecule. It is easy to implement because there is no need to separately evaluate couplings and the bound dissociative states of the neutral molecule. The theory can be applied to molecular ions with or without electronic resonances at low energies. The approach is applied to compute the DR cross section in electron-${\mathrm{CH}}^{+}$ collisions. The computed cross section agrees generally well with recent state-resolved data from a cryogenic storage experiment, which validates the approach.

We extend the theory of nonthermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field from a nonperturbative two-particle irreducible effective action, which resums a series of closed loop chains akin to a large-$N$ expansion at next-to-leading order. The resulting kinetic equation is analyzed for possible scaling solutions in space and time that are characterized by a set of universal scaling exponents and encode self-similar transport to low momenta. Assuming the momentum occupancy distribution to exhibit a scaling form we can determine the exponents by identifying the dominating contributions to the scattering integral and power counting. If the field exhibits strong variations across many wells of the cosine potential, the scattering integral is dominated by the scattering of many quasiparticles such that the momentum of each single participating mode is only weakly constrained. Remarkably, in this case, in contrast to wave turbulent cascades, which correspond to local transport in momentum space, our results suggest that kinetic scattering here is dominated by rather nonlocal processes corresponding to a spatial containment in position space. The corresponding universal correlation functions in momentum and position space corroborate this conclusion. Numerical simulations performed in accompanying work yield scaling properties close to the ones predicted here.

We study multiphoton blockade effects in a single-mode cavity interacting with two three-level atoms in $\mathrm{\Lambda }$ configuration having position-dependent atom-field coupling. We consider the effects of dipole-dipole interaction (DDI) between the three-level atoms and show how the presence of DDI strongly influences the multiphoton blockade. For symmetric coupling of the atoms with the field, the DDI induces an asymmetry in the emission spectra as a function of pump field detuning. At positive detuning, the single-photon blockade gets stronger as a function of DDI strength, leading to photon antibunching. However, it becomes weaker at negative detuning and can also completely vanish. We show that this vanishing single-photon blockade is associated with a strong two-photon blockade, leading to two-photon bunching. Therefore, by just tuning the frequency of the pump field, we can achieve two very distinct features. We also study the effects of DDI when the atoms are asymmetrically coupled with the field and show that the proposed system exhibits two-photon bunching. We believe our results are important for the experimental realization of such systems where DDI may be present.