Bragg projection ptychography (BPP) is a coherent diffraction imaging technique capable of mapping the spatial distribution of the Bragg structure factor in nanostructured thin films. Here, we show that, because these images are projections, the structural sensitivity of the resulting images depends on the film thickness and the aspect ratio and orientation of the features of interest and that image interpretation depends on these factors. We model changes in contrast in the BPP reconstructions of simulated ${\mathrm{PbTiO}}_3$ ferroelectric thin films with meandering ${180}^{\circ }$ stripe domains as a function of film thickness, discuss their origin, and comment on the implication of these factors on the design of BPP experiments of general nanostructured films.

We investigate the gas-pressure dependence of macroscopic harmonic spectra generated in a high-ionization medium using intense 800-nm laser pulses. The harmonics obtained at the optimal pressure show good spatial coherence with small divergence (less than 2 mrad) in the far field. By analyzing the evolution of the laser's electric field as it propagates, we find that dynamic phase matching conditions are fulfilled in the second half of the gas cell and that harmonic yields do not depend on the position of the gas cell with respect to the focusing position. We also demonstrate that harmonic yields at the optimal pressure can be further enhanced by increasing input laser energy or by adding a few percent of second or third harmonic to the fundamental.

The problem of estimating an unknown phase $\phi$ using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. We introduce a simple model in which the phase-imprinting operation on the probes is realized by a unitary transformation with a randomly sampled generator. We determine the optimal phase sensitivity in a sequential estimation protocol and derive a general (tight-fitting) lower bound. The sensitivity grows quadratically with the number of applications $N$ of the phase-imprinting operation, then attains a maximum at some $N_{\text{opt}}$, and eventually decays to zero. We provide an estimate of $N_{\text{opt}}$ in terms of accessible geometric properties of the noise and illustrate its usefulness as a guideline for optimizing the estimation protocol. The use of passive ancillas and of entangled probes in parallel to improve the phase sensitivity is also considered. We find that multiprobe entanglement may offer no practical advantage over single-probe coherence if the interrogation at the output is restricted to measuring local observables.

Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.

We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of such correlations, and show that they are not monotonous under local operations and classical communication. Nevertheless, we demonstrate their usefulness in entanglement detection with a single random observable per party. Finally we study convex-roof extension of the correlations and provide a closed-form necessary and sufficient condition for entanglement in rank-2 mixed states and a witness in general.

We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy, and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Matsubara frequencies. It is shown that the Casimir entropy for two graphene sheets goes to zero when the temperature vanishes, i.e., the third law of thermodynamics (the Nernst heat theorem) is satisfied. At low temperature, the magnitude of the thermal correction to the Casimir pressure between two graphene sheets is shown to vary inversely proportional to the separation. The Nernst heat theorem for graphene is discussed in the context of problems occurring in Casimir physics for both metallic and dielectric plates.

Atomic spectral lines from different isotopes display a small shift in energy, commonly referred to as the line isotope shift. One of the components of the isotope shift is the field shift, which depends on the extent and the shape of the nuclear charge density distribution. The purpose of this work is to investigate how sensitive field shifts are with respect to variations in the nuclear size and shape and what information of nuclear charge distributions can be extracted from measurements. Nuclear properties are obtained from nuclear density functional theory calculations based on the Skyrme-Hartree-Fock-Bogoliubov approach. These results are combined with multiconfiguration Dirac-Hartree-Fock methods to obtain realistic field shifts and it is seen that phenomena such as nuclear deformation and variations in the diffuseness of nuclear charge distributions give measurable contributions to the isotope shifts. Using a different approach, we demonstrate the possibility to extract information concerning the nuclear charge densities from the observed field shifts. We deduce that combining methods used in atomic and nuclear structure theory gives an improved description of field shifts and that extracting additional nuclear information from measured isotope shifts is possible in the near future with improved experimental methods.

We predict ionization potentials of superheavy elements No, Lr, and Rf and their ions using a relativistic hybrid method that combines configuration interaction (CI) with the linearized coupled-cluster approach. Extensive study of the completeness of the four-electron CI calculations for Hf and Rf was carried out. As a test of theoretical accuracy, we also calculated ionization potential of Yb, Lu, Hf, and their ions, which are homologues of the superheavy elements of this study.

Wentzel-Kramers-Brillouin (WKB) methodology is used to undertake a systematic analysis of shape resonances in exoergic reactive collisions at low energies $E$, and examples investigated are $\mathrm{Li}+{\mathrm{H}}^{+}, \mathrm{He}\left(2{}^{3}S\right)+\mathrm{H}$, and $\mathrm{He}\left(2{}^{3}S\right)+\mathrm{Mu}$ (muonium). In so doing, the resonance positions should be measured by the tunneling parameter $\alpha$ and not by $E$. The resonance peak height $P_{\mathrm{res}}$ of the reaction probability and the resonance width times the vibrational period of the quasibound resonance state can be given by simple closed-form expressions with two variables, $\alpha$ and $P_0$, the latter of which is a reaction probability given at collision energies much above a centrifugal barrier top and is determined by only short-range interactions. The resonance promotes the reaction maximally (i.e., $P_{\mathrm{res}}=1$) when the resonance satisfies $\alpha ={\alpha }_0={\left(2\pi \right)}^{-1}ln[(1-P_0)/P_0]$, in other words, when the transmission coefficient of tunneling through the centrifugal barrier happens to be equal to $P_0$ at the resonance energy. If ${\alpha }_0\gtrsim 1$, the reaction system is rich in tunneling resonances. If ${\alpha }_0\lesssim 0$, the prominent resonances are mostly an over-barrier type. The resonances occurring at $\alpha \gg {\alpha }_0$ are of no significance in the reaction.

A numerical method based on Zabaydullin and Dubau's work [O. Zabaydullin and J. Dubau, J. Phys. B: At. Mol. Opt. Phys. 45, 115002 (2012)] has been developed to calculate the Cauchy principal value integral in scattering matrices and obtain photorecombination (PR) cross sections of low-lying resonances according to Davies and Seaton's theory [J. Phys. B 2, 757 (1969)], in which radiation damping is included. The Dirac $R$-matrix method is employed to secure the dipole matrix. Using this method, PR cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are acquired, and compared with available experimental measurements and other close-coupling theoretical results. It is shown that our damped cross sections reproduce the experimental data and are in agreement with other theoretical results. Meanwhile, radiation damping can reduce the PR cross section for the $1s2p^2{}^{2}P$ resonance (corresponding to two levels ${\left[{\left(1s2p_{1/2}\right)}_{1}2p_{3/2}\right]}_{1/2}$ and ${\left[1s{\left(2p_{3/2}^2\right)}_2\right]}_{3/2}$ by three orders of magnitude. The unresolved and underestimated resonances $1s2p^2{}^{4}P, 1s2s2p{}^{4}P$, and $1s2p^2{}^{2}P$ in the undamped Breit-Pauli $R$-matrix calculations [H. L. Zhang et al., J. Phys. B: At. Mol. Opt. Phys. 32, 1459 (1999)] are corrected. Besides, dielectronic recombination cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are also presented for comparison using the relativistic configuration-interaction (RCI) method implemented in flexible atomic code (fac), which show radiation damping has pronounced influences on $1s2p^2{}^{2}P$ due to much larger radiative rates compared with autoionization rates. Furthermore, radiative and autoionization rates for the intermediate states ${\left[{\left(1s2p_{1/2}\right)}_{1}2p_{3/2}\right]}_{1/2}$ and ${\left[1s{\left(2p_{3/2}^2\right)}_2\right]}_{3/2}$ of the He-like ions with $6\le Z\le 83$ are calculated using fac, scaling laws of which are checked. Autoionization rates comply with the $Z_{\mathrm{eff}}^0$ scaling law for $Z\ge 32$, which is caused by relativistic effects.

Characteristic features of Wigner photoemission time delay from endohedral anions A@${\mathrm{C}}_{60}{}^q$ along with their dependence on the anion charge $q$ are unraveled. Specifically, significant enhancement of the time delay in the innermost dipole photoionization channels near threshold is found, owing to the presence of the Coulomb confined resonances (CRs). Moreover, it is shown that interchannel coupling of the inner-shell Coulomb CRs with outer-shell photoionization channels results in resonantly enhanced time delay in the release of the outer-shell photoelectron well above, several hundreds eV, the outer-shell thresholds. It is also demonstrated that, and explained why, photoionization cross sections of the innermost subshells as well as outer subshells (near the inner-subshell threshold) depends only very weakly on the anion charge $q$, but the dependence of the corresponding time delays on $q$ can be significant. Furthermore, Coulomb CRs are found to emerge in the innermost quadrupole photoionization channels as well, thereby causing considerable time delay in the quadrupole photoemission. These findings are illustrated in calculations of the photoionization of inner and outer subshells of the endohedral anions Ne@${\text{C}}_{60}{}^{-1}$ and Ne@${\mathrm{C}}_{60}{}^{-5}$ that were chosen as case studies.

We derive the analytical formula of the ratio of the ionization rates of degenerate valence ${\pi }_{\pm }$ orbitals of prealigned linear molecules in strong circularly polarized (CP) laser fields. Interestingly, our theory shows that the ionization ratio for molecular orbitals with opposite azimuthal quantum numbers $\pm \left|m\right|$ (e.g., ${\pi }_{\pm }$) is identical to that for atomic orbitals with the same $\pm \left|m\right|$ (e.g., $p_{\pm }$). In general, the electron counter-rotating to the CP laser field tunnels more easily, not only for atoms but also for linear molecules. Our theoretical predictions are then verified by numerically solving the three-dimensional time-dependent Schrödinger equation for the ionization of the prealigned nitric oxide (NO) molecule in strong CP laser fields. Due to the spin-orbital coupling in the electronic ground state of NO and the sensitivity of ionization to the sense of electron rotation, the ionization of NO in CP fields can produce spin-polarized photoelectrons with high controllability of spin polarization up to $100\%$.

Artificial spin-orbit coupling in optical lattices can be engineered to tune band structure into extreme regimes where the single-particle band flattens leaving only interparticle interactions to define many-body states of matter. Lin et al. [F. Lin, C. Zhang, and V. W. Scarola, Phys. Rev. Lett. 112, 110404 (2014)] showed that under such conditions interactions lead to a Wigner crystal of fermionic atoms under approximate conditions: no bandwidth or band mixing. The excitations were shown to possess emergent kinetics with fractionalized charge derived entirely from interactions. In this work we use numerical exact diagonalization to study a more realistic model with nonzero bandwidth and band mixing. We map out the stability phase diagram of the Wigner crystal. We find that emergent properties of the Wigner crystal excitations remain stable for realistic experimental parameters. Our results validate the approximations made by Lin et al. and define parameter regimes where strong interaction effects generate emergent kinetics in optical lattices.

Binary mixtures of Bose-Einstein condensates (BECs) trapped in deep optical lattices and subjected to equal contributions of Rashba and Dresselhaus spin-orbit coupling (SOC) are investigated in the presence of a periodic time modulation of the Zeeman field. SOC tunability is explicitly demonstrated by adopting a mean-field tight-binding model for the BEC mixture and by performing an averaging approach in the strong modulation limit. In this case, the system can be reduced to an unmodulated vector discrete nonlinear Schrödinger equation with a rescaled SOC tuning parameter $\alpha$, which depends only on the ratio between amplitude and frequency of the applied Zeeman field. We consider the attractive interaction case and focus on the effect of the SOC tuning on the localized ground states. The dependence of the spectrum of the linear system on $\alpha$ has been analytically characterized. In particular, we show that extremal curves (ground and highest excited states) of the linear spectrum are continuous piecewise functions (together with their derivatives) of $\alpha$, which consist of a finite number of decreasing band lobes joined by constant lines. This structure also remains in the presence of inter- and intra-species interactions, the nonlinearity mainly introducing a number of localized states in the band gaps. The stability of ground states in the presence of the modulating field has been demonstrated by real-time evolutions of the original (unaveraged) system. Localization properties of the ground state induced by the SOC tuning, and a parameter design for possible experimental observation, have also been discussed.

Multimode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavorable scaling of required resources for many-particle problems and therefore a simplified criterion based on a threshold value for the least occupied mode function is often used. Here we show how the separable quantum motion of the center of mass can be used to sensitively detect unconverged numerical multiparticle dynamics in harmonic potentials. Based on an experimentally relevant example of attractively interacting bosons in one dimension, we demonstrate that the simplified convergence criterion fails to assure qualitatively correct results. Furthermore, the numerical evidence for the creation of two-hump fragmented bright soliton-like states presented by A. I. Streltsov et al. [Phys. Rev. Lett. 100, 130401 (2008)] is shown to be inconsistent with exact results. Implications for understanding dynamical fragmentation in attractive boson systems are briefly discussed.

We propose and analyze two-well Bose-Hubbard models with pumping and losses, finding that these models, with damping and loss able to be added independently to each well, offer a flexibility not found in optical coupled cavity systems. With one well pumped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. Both the systems we analyze remain far from equilibrium, preserving good coherence between the wells in the steady state. We find a degree of quadrature squeezing and mode entanglement in these systems. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.

Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes, and ribbons. As such, it has found myriads of applications in astrophysics, fluid dynamics, atmospheric sciences, and biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of centerline vorticity can be downright impossible to apply in complex and turbulent scenarios. We present a definition of helicity which overcomes these problems and which gives the expected result in the large-scale limit. With it, we show that certain reconnection events can excite Kelvin waves and other complex motions of the centerline vorticity, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum fluids. This process also results in the depletion of helicity in a fully turbulent quantum flow, in a way reminiscent of the decay of helicity in classical fluids.

According to the famous Kibble-Zurek mechanism (KZM), the universality of spontaneous defect generation in continuous phase transitions (CPTs) can be understood by the critical slowing down. In most CPTs of atomic Bose-Einstein condensates (BECs), the universality of spontaneous defect generations has been explained by the divergent relaxation time associated with the nontrivial gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge fields, their spontaneous superfluidity breakdown results from the divergent correlation length associated with the zero Landau critical velocity. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown obeys the KZM. The Kibble-Zurek scalings are derived from the Landau critical velocity which determines the correlation length. Furthermore, the critical exponents are numerically extracted from the critical spatiotemporal dynamics of the bifurcation delay and the spontaneous vortex generation. Our study provides a general way to explore and understand the spontaneous superfluidity breakdown in CPTs from a single-well dispersion to a double-well one, such as BECs in synthetic gauge fields, spin-orbit-coupled BECs, and BECs in shaken optical lattices.

We studied the atomic momentum distribution of a superposition of Bloch states in the lowest band of an optical lattice after the action of the standing-wave pulse. By designing the imposing pulse on this superposed state, an atomic momentum pattern appears with a narrow interval between the adjacent peaks that can be far less than double recoil momentum. The patterns with narrower interval come from the effect of the designed pulse on the superposition of many Bloch states with quasimomenta throughout the first Brillouin zone. Our experimental result of narrow interval peaks is consistent with the theoretical simulation. The patterns of multiple modes with different quasimomenta may be helpful for precise measurement and atomic manipulation.

We theoretically study the linear transmission of linearly polarized light pulses in an ensemble of cold atoms submitted to a static magnetic field parallel to the direction of propagation. The carrier frequency of the incident pulses coincides with a resonance frequency of the atoms. The transmitted light, the electric field of which is transversal, is examined in the polarizations parallel and perpendicular to that of the incident pulses. We give explicit analytic expressions for the transfer functions of the system for both polarizations and for the corresponding group delays. We demonstrate that slow light can be observed in a polarization, whereas fast light is simultaneously observed in the perpendicular polarization. Moreover, we point out that, due to the polarization postselection, the system is not necessarily minimum phase shift. Slow light can then be obtained in situations where an irrelevant application of the Kramers-Kronig relations could lead one to expect fast light. When the incident light is step modulated, we finally show that, in suitable conditions, the system enables one to separate optical precursor and main field.