The procedure for the calculation of the self-energy-corrected wave function of the bound electron in the field of the nucleus is discussed. We present the related formulas and discuss the numerical difficulties and the methods used to overcome them. The results of the calculation are presented for a wide range of ions. Possible applications of the numerically obtained wave functions are discussed.

We investigate the thermal properties of interacting spin-orbit-coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state nonperturbatively in a range of spin-orbit couplings and chemical potentials. Our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudocondensates. These have been observed to be destroyed by the spin-orbit interactions.

Considering the ground state of a quantum spin model as the initial state of the quantum battery, we show that both ordered and disordered interaction strengths play a crucial role in increasing the extraction of power from it. In particular, we demonstrate that exchange interactions in the $xy$ plane and in the $z$ direction, leading to the $XYZ$ spin chain, along with the local charging field in the $x$ direction substantially enhance the efficiency of the battery compared to the model without interactions. Moreover, such an advantage in power obtained due to interactions is almost independent of the system size. We find that the behavior of the power, although measured during dynamics, can faithfully mimic the equilibrium quantum phase transitions present in the model. We observe that with the proper tuning of system parameters, an initial state prepared at finite temperature can generate higher power in the battery than that obtained with zero temperature. Finally, we report that defects or impurities, instead of reducing the performance, can create a larger amount of quenched averaged power in the battery in comparison with the situation when the initial state is produced from the spin chain without disorder, thereby showing the disorder-induced order in dynamics.

We address the dynamics of continuous-time quantum walk (CTQW) on planar two-dimensional (2D) lattice graphs, i.e., those forming a regular tessellation of the Euclidean plane (triangular, square, and honeycomb lattice graphs). We first consider the free particle: On square and triangular lattice graphs we observe the well-known ballistic behavior, whereas on the honeycomb lattice graph we obtain a sub-ballistic one, although still faster than the classical diffusive one. We impute this difference to the different amount of coherence generated by the evolution and, in turn, to the fact that, in 2D, the square and the triangular lattices are Bravais lattices, whereas the honeycomb one is non-Bravais. From the physical point of view, this means that CTQWs are not universally characterized by the ballistic spreading. We then address the dynamics in the presence of a perpendicular uniform magnetic field and study the effects of the field by two approaches: (i) introducing the Peierls phase factors, according to which the tunneling matrix element of the free particle becomes complex or (ii) spatially discretizing the Hamiltonian of a spinless charged particle in the presence of a magnetic field. Either way, the dynamics of an initially localized walker is characterized by a lower spread compared to the free particle case; larger fields correlate to more localized stays of the walker. Remarkably, upon analyzing the dynamics by spatial discretization of the Hamiltonian (vector potential in the symmetric gauge), we obtain that the variance of the space coordinate is characterized by pseudo-oscillations, a reminiscence of the harmonic oscillator behind the Hamiltonian in the continuum, whose energy levels are the well-known Landau levels.

We present a bipartite two-level system coupled to electromagnetic quantum vacuum fluctuations through a general dipolar coupling. We derive the master equation in the framework of an open quantum system, assuming an environment composed of (i) solely vacuum fluctuations and (ii) the vacuum fluctuations and a conducting plate located at a fixed distance from the bipartite system. For both cases considered, we study the dynamics of the bipartite system and the temporal evolution of the concurrence of an initial entangled bipartite state. We further analyze the generation of entanglement due to the vacuum structure. Finally, we study the different induced contributions to the correction of the unitary geometric phase of a bipartite quantum state so as to explore the possibility of future experimental setups by exploring the influence of boundaries conditions in vacuum.

Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We classify each error syndrome to the decoder which is more likely to decode it correctly using machine learning techniques. We apply our framework to an ensemble of minimum-weight perfect matching (MWPM) and hard-decision re-normalization-group decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudothreshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.

We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the controlling ancillary qubit. Such a Hadamard-test-like primitive is iterated so as to achieve the spectral projection, and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state of a final Hamiltonian, and we simulate this for quantum many-body spin chains.

We propose a practical high-dimensional quantum key distribution protocol based on mutually partially unbiased bases utilizing transverse modes of light. In contrast to conventional protocols using mutually unbiased bases, our protocol uses Laguerre-Gaussian and Hermite-Gaussian modes of the same mode order as two mutually partially unbiased bases for encoding, which leads to a scheme free from mode-dependent diffraction in long-distance channels. Since only linear and passive optical elements are needed, our experimental implementation significantly simplifies qudit generation and state measurement. Since this protocol differs from conventional protocols using mutually unbiased bases, we provide a security analysis of our protocol.

We construct a classical cryptographic analog of multipartite entanglement which can be verified solely from separable marginals. That is a set of marginal classical probability distributions carrying no secret correlations, which are compatible only with a joint distribution containing secret correlations. This demonstrates that the emergent correlation properties do not exist only in the quantum world. Viewed from a different perspective, our result reveals another possible application of the quantum marginal problems in that they can help us to design and solve interesting classical marginal problems.

The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean-field method that extends the previously proposed excited constrained-density-functional theory (XCDFT) from single Slater determinants to ensemble one-body reduced density matrices for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal density functional theory (DFT) calculation while at the same time it is capable of approaching states with multireference character. We benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal time-dependent DFT.

We report on experimental elastic differential and integral cross sections for electron scattering from bismuth. The energy range of those measurements is 10–100 eV, while the scattered electron angular range in the differential cross section data is ${10}^{\circ }–{150}^{\circ }$. We also supplement our experimental results with theoretical data from our optical potential approach, in this case applying two different sets of scattering potentials to the problem. Good overall qualitative accord is typically observed between our measured and calculated results, particularly when allowance is made for the dimer contribution in the experimental atomic beam.

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2{L}_j$; $L\le 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X{}^1\mathrm{\Sigma }^{+}$; $v=0, J=0$). We compute the associated $C_6$ dispersion coefficients of atom-molecule pairs involving ${}^{133}\mathrm{Cs}$ and ${}^{85}\mathrm{Rb}$ atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O\left(n^7\right)$ over the range of principal quantum numbers $40\le n\le 150$. For all atom-molecule pairs considered, Rydberg states $n{}^{2}S_j$ and $n{}^{2}P_j$ result in attractive $1/R^6$ potentials. In contrast, $n{}^{2}D_j$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as $n^{-5}$ for $n>40$. For intermediate values of $n\lesssim 40$, both repulsive and attractive interaction energies of the order of 10–$1000\mu \mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported $C_6$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\Delta }{C}_6/C_6$ estimated to be no greater than 1% on average.

We present a theoretical study of $K$-shell photodetachment of ${\mathrm{C}}_2{}^{-}$ and ${\mathrm{C}}_3{}^{-}$ ions. The calculations were carried out using the complex Kohn variational method. Our study addresses the recent observation that what appears as a single, narrow shape resonance close to threshold in the $K$-shell photodetachment of ${\mathrm{C}}^{-}$ splits into several peaks in the longer ${\mathrm{C}}_n{}^{-}$ carbon anion chains, with the number of peaks increasing with increasing $n$ values. We argue that the number of expected peaks is related to the number of symmetry-equivalent carbon atoms.

We present a theory of time-resolved photoionization in the presence of a vortex beam. In a pump-probe setup, an extreme ultraviolet or an x-ray pump pulse triggers ionization, which is probed by a synchronized infrared pulse with nonzero orbital angular momentum. We show how this property of the probe pulse affects the electron dynamics upon ionization, in a way that is independent of the initial and final angular momentum states of the ionizing system.

We consider elastic scattering of atoms from elongated clouds taking into account an effective, finite duration of the collision due to the expansion of the condensates. We also include the quasicondensate nature of the degenerate quantum gas, due to a finite temperature of the system. We evaluate the pair-correlation function measured experimentally in Kheruntsyan et al. [Phys. Rev. Lett. 108, 260401 (2012)] and show that the finite duration of the collision is an important factor determining the properties of the correlations. Our analytic calculations are in agreement with the measurements. The analytical model we provide, useful for identifying physical processes that influence the correlations, is relevant for experiments with nonclassical pairs of atoms.

Correspondence imaging can achieve positive-negative ghost images by just conditional averaging of partial patterns, without treating bucket intensities as weights. To explain its imaging mechanism, we develop a probability theory assuming the targets are of grayscale and the thermal reference speckles obey an arbitrary independent and identical distribution. By both simulation and experiments, we find that the recovered values in each region of the same original gray value conditionally obey a Gaussian distribution. A cross-point–to–standard-deviation ratio is used as the figure of merit to prove that the patterns with respect to larger bucket values generate a positive image with a higher quality and vice versa for a negative one. This work complements the theory of ghost imaging.

Induced transparency and attenuation effects are observed in the throughput of a single whispering-gallery microresonator due to mode coupling between two coresonant orthogonally polarized whispering-gallery modes of very different quality factors. Intracavity cross-polarization coupling, occurring when either the transverse electric (TE) mode or the transverse magnetic (TM) mode is driven, results in coupled-mode induced transparency or coupled-mode induced attenuation. Coresonance between the TE and TM modes is obtained by strain tuning, and the cross-polarization coupling is produced by polarization rotation due to optical spin-orbit interaction in a slightly asymmetric resonator. The observed behavior enables slow light and fast light, i.e., the delay or advancement of an incident resonant pulse. Experimental results representative of several different types of behavior are presented here. Induced transparency is seen to be accompanied by pulse delay, whereas induced attenuation can involve pulse advancement or delay. The results are analyzed and explained by analytical modeling and by comparison to the output of a more detailed numerical model describing these effects. Delays of up to 170 ns and advancements of up to 14 ns are found. The observed range of cross-polarization coupling strengths (probability of polarization change per round trip), namely, ${10}^{-10}–{10}^{-7}$, is in agreement with theory.

The Rydberg blockade mechanism is now routinely considered for entangling qubits encoded in clock states of neutral atoms. Challenges towards implementing entangling gates with high fidelity include errors due to thermal motion of atoms, laser amplitude inhomogeneities, and imperfect Rydberg blockade. We show that adiabatic rapid passage by Rydberg dressing provides a mechanism for implementing two-qubit entangling gates by accumulating phases that are robust to these imperfections. We find that the typical error in implementing a two-qubit gate, such as the controlled phase gate, is dominated by errors in the single-atom light shift, and that this can be easily corrected using adiabatic dressing interleaved with a simple spin echo sequence. This results in a two-qubit Mølmer-Sørensen gate. A gate fidelity $\sim 0.995$ is achievable with modest experimental parameters and a path to higher fidelities is possible for Rydberg states in atoms with a stronger blockade, longer lifetimes, and larger Rabi frequencies.

Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.

A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we present a practical solution to this: We derive a Bayesian multi-parameter quantum bound, construct the optimal measurement when our bound can be saturated for a single shot, and consider experiments involving a repeated sequence of these measurements. Our method properly accounts for the number of measurements and the degree of prior information, and we illustrate our ideas with a qubit sensing network and a model for phase imaging, clarifying the nonasymptotic role of local and global schemes. Crucially, our technique is a powerful way of implementing quantum protocols in a wide range of practical scenarios that tools such as the Helstrom and Holevo Cramér-Rao bounds cannot normally access.