A singular-value thresholding (SVT) operation is a fundamental core module of many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. A quantum SVT (QSVT) algorithm was proposed in Phys. Rev. A. 96, 032301 (2017) to solve an image-classification problem. This algorithm runs in $O\left[{log}_2\left(pq\right)\right]$, an exponential speed improvement over the classical algorithm, which runs in $O\left[\text{poly}\left(pq\right)\right]$. In this paper, we design a scalable quantum circuit for a QSVT. The quantum circuit is designed with $O\left[{log}_2\left(pq/\varepsilon \right)\right]$ qubits and $O\left[\text{poly}{log}_2\left(1/\varepsilon \right)\right]$ quantum gates in terms of error $O\left(\varepsilon \right)$. We also show that a high-probability and high-fidelity output can be obtained in one iteration of the quantum circuit. The quantum circuit for a QSVT implies a tempting possibility for experimental realization on a quantum computer. Finally, we propose a small-scale quantum circuit for a QSVT. We numerically simulate and demonstrate the performance of this circuit, verifying its capability to solve the intended SVT.

We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-$\frac{1}{2}$ $XY$ Hamiltonians, we give an analytic formula for the out-of-time-ordered correlator of a local observable and show that it can be efficiently evaluated by a classical computer even when the explicit Heisenberg time evolution cannot. Because this quantity bounds the average error incurred by truncating the evolution to a spatially limited region, we demonstrate dynamical localization as a means for classically simulating quantum computation and give examples of localized phases under certain spatiotemporal disordered Hamiltonians.

We report on the radiative decay of double $K$-shell vacancy states produced in solid Ca, V, Fe, and Cu targets by impact with about 10 MeV/amu C and Ne ions. The resulting $K$ hypersatellite x-ray emission spectra were measured by means of high-energy-resolution spectroscopy using a von Hamos bent crystal spectrometer. The experiment was carried out at the Philips variable energy cyclotron of the Paul Scherrer Institute. From the fits of the x-ray spectra the energies, line widths, and relative intensities of the hypersatellite x-ray lines could be determined. The fitted intensities were corrected to account for the energy-dependent solid angle of the spectrometer, effective source size, target self-absorption, crystal reflectivity, and detector efficiency. The single-to-double $K$-shell ionization cross-section ratios were deduced from the corrected relative intensities of the hypersatellites and compared to theoretical predictions from the semiclassical approximation model using hydrogenlike and Dirac-Hartree-Fock wave functions and from classical trajectory Monte Carlo calculations.

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.

Passive optical interferometry with single photons injected into some input ports and vacuum into others is enriched by admitting polarization, thereby replacing the scalar electromagnetic description by a vector theory, with the recent triad phase being a celebrated example of this richness. On the other hand, incorporating polarization into interferometry is known to be equivalent to scalar theory if the number of channels is doubled. We show that passive multiphoton $m$-channel interferometry described by $\mathrm{SU}\left(m\right)$ transformations is replaced by $\mathrm{SU}\left(2m\right)$ interferometry if polarization is included and thus that the multiphoton coincidence landscape, whose domain corresponds to various relative delays between photon arrival times, is fully explained by the now-standard approach of using immanants to compute coincidence sampling probabilities. Consequently, we show that the triad phase is manifested simply as SU(6) interferometry with three input photons, with one photon in each of three different input ports. Our analysis incorporates passive polarization multichannel interferometry into the existing scalar-field approach to computing multiphoton coincidence probabilities in interferometry and demystifies the triad phase.

The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion approach as well as the stochastic decoupling scheme. We demonstrated that the HEOMs obtained by these two different stochastic dynamical methods are identical. Moreover, we present some numerical examples to verify the feasibility of our formalism.

We introduce a one-dimensional non-Hermitian four-band tight-binding lattice system. We find stable topological edge states protected by particle-hole and parity-time symmetries. We show that a topological phase appears in the system. We discuss that the system can also be used as a topological laser if the gain and loss positions in a unit cell are judiciously arranged.

We present a scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other proposals, our scheme requires the same amount of classical communication and entangled resources as conventional teleportation, does not reveal any reference frame information, and is robust against changes in reference frame alignment while the protocol is under way. The mathematical foundation of our scheme is a unitary error basis which is permuted up to a phase by the conjugation action of the group. We completely classify such unitary error bases for qubits, exhibit constructions in higher dimension, and provide a method for proving nonexistence in some cases.

We generalize the definition of strong positive partial transpose (SPPT) to the multipartite system. The tripartite case was first considered by Yu and Zhao [Int. J. Theor. Phys. 54, 292 (2014)]. In this extension, unfortunately, desired properties such as the PPT of SPPT states and the separability of super and pure SPPT states are not preserved. In contrast, this paper provides an alternative generalization to multipartite cases with these properties preserved. We also provide sufficient conditions for the separability of SPPT states.

We study process of dielectronic recombination with He-like uranium initially being in one of the metastable states $[{\left(1s2s\right)}_0$ and ${\left(1s2p_{1/2}\right)}_0]$. We consider resonant regions of the incident electron energy corresponding to participation of triply excited states of Li-like uranium. The total and differential cross sections for dielectronic recombination as well as the energies and widths of the autoionizing states are calculated accurately within the QED theory. The cross section of the considered process is comparable in order of magnitude with the cross section of dielectronic recombination with H-like or He-like uranium initially being in the ground states. We investigated the contribution of the Breit interaction to the cross section; in particular, we found that the Breit interaction may both significantly increase and decrease the cross section.

We introduce a description of Ramsey spectra under atomic interactions as a sum of decomposed components with differing dependence on interaction parameters. This description enables intuitive understanding of the loss of contrast and asymmetry of Ramsey spectra. We derive a quantitative relationship between the asymmetry and atomic interaction parameters, which enables their characterization without changing atom density. The model is confirmed through experiments with a Yb optical lattice clock.

We experimentally and numerically investigate thermalization processes of a trapped ${}^{87}\mathrm{Rb}$ Bose gas, initially prepared in a nonequilibrium state through partial Bragg diffraction of a Bose-Einstein condensate (BEC). The system evolves in a Gaussian potential, where we observe the destruction of the BEC due to collisions and subsequent growth of a new condensed fraction in an oscillating reference frame. Furthermore, we occasionally observe the presence of defects, which we identify as gray solitons. We simulate the evolution of our system using the truncated Wigner method and compare the outcomes with our experimental results.

A generalized Mermin-Ho relation for a spin-1 Bose-Einstein condensate is derived, which is applicable to vortices regardless of the symmetry and spin polarization of the order parameter. The obtained relation implies an su(3) mass-current circulation and two classes of vortices corresponding to two different su(2) subalgebras.

Experimental advances in synthesizing spin-orbit couplings in cold atomic Bose gases promise to create single-particle dispersion laws featuring energy minima that are degenerate on a ring or a sphere in momentum space. We show that for arbitrary space dimensionality the ground-state properties of a dilute system of spin-orbit-coupled Bose particles with such dispersion and short-range repulsive interactions are universal: the chemical potential exhibits a quadratic dependence on the particle density as found in a one-dimensional free Fermi gas.

We analyze a single-atom cavity QED model to isolate the dynamic mechanism of stochastic switching between regions of state space associated with mean-field attractors of absorptive bistability. We present evidence from simulations that such switching is correlated with variations in the timings of atomic spontaneous emission events, and we interpret this finding in terms of the dynamics of the coupled intracavity field and atomic dipole. Somewhat surprisingly, both upward and downward (in intracavity photon number) switching transitions may be induced by rapid succession of several atomic emissions. Based on our results we propose an implementation of bidirectional “toggle” control for a single-atom optical latch.

Optical nonlinearities at the single-photon level are key features to build efficient photon-photon gates and to implement quantum networks. Such optical nonlinearities can be obtained using an ideal two-level system such as a single atom coupled to an optical cavity. While efficient, such atom-photon interface however presents a fixed bandwidth, determined by the spontaneous emission time and thus the spectral width of the cavity-enhanced two-level transition, preventing an efficient transmission to bandwidth-mismatched atomic systems in a single quantum network. In the present work, we propose a tunable atom-photon interface making use of the direct dipole-dipole coupling of two slightly different atomic systems. We show that, when weakly coupled to a cavity mode and directly coupled through dipole-dipole interaction, the subradiant mode of two slightly detuned atomic systems is optically addressable and presents a widely tunable bandwidth and single-photon nonlinearity.

We extend the usual multipolar theory of linear Rayleigh and Raman scattering to include the second-order correction. These terms promise a wealth of information about the shape of a scatterer and yet are insensitive to the scatterer's chirality. Our extended theory might prove especially useful for analyzing samples in which the scatterers have nontrivial shapes but no chiral preference overall, as the zeroth-order theory offers little information about shape and the first-order correction is often quenched for such samples. A basic estimate suggests that our extended theory can be applied to a scatterer as large as $k_{0}d\sim 1/10$ with less than $\sim 0.1\%$ error resulting from the neglect of the third- and higher-order corrections. Our results are entirely analytical.

We discuss the Bloch-Messiah decomposition for the broadband squeezed light generated by type-I parametric down-conversion with a monochromatic pump. Using an exact solution for this process, we evaluate the squeezing parameters and the corresponding squeezing eigenmodes. Next we consider the Magnus expansion of the quantum-mechanical evolution operator for this process and obtain its first three approximation orders. Using these approximated solutions, we evaluate the corresponding approximations for the Bloch-Messiah decomposition. Our results allow us to conclude that the first-order approximation of the Magnus expansion is sufficient for description of the broadband squeezed light for squeezing values below 12.5 dB. For higher degrees of squeezing we show fast convergence of the Magnus series, providing a good approximation for the exact solution already in the third order. We propose a quantitative criterion for this ultrahigh-gain regime of parametric down-conversion when the higher-order terms of the Magnus expansion, known in the literature as the operator-ordering effects, become necessary.

We study the temporal dynamics of photoexcited carriers in distributed Bragg reflector based semiconductor micropillars at room temperature. Their influence on the process of coherent phonon generation and detection is analyzed by means of pump-probe microscopy. The dependence of the measured mechanical signatures on laser-cavity detuning is explained through a model that accounts for the varying light-cavity coupling existent during the ultrashort times that pump and probe pulses dwell within the structure. To do so, we first explain the optical mode dynamics with an electron-hole diffusion model that accounts for the escape of carriers from the probed area, as well as their recombination in the bulk and on the free surfaces. We thus show that the latter is the most influential factor for pillars below $\sim 10\mu \mathrm{m}$, where 3D confinement of the optical and mechanical fields becomes relevant.

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in postselection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using an experiment in levitated optomechanical systems as an example.