In this work, we propose a scheme of quantum secure ghost imaging (QSGI), which combines temporal quantum ghost imaging and security test based on quantum entanglement. Utilizing the quantum feature of entangled photon pairs, the eavesdropping in the imaging process can be detected, with a certain degree of protection on the object information. The proposed scheme is demonstrated by experiment, in which photon pairs are generated by a quantum light source based on a silicon waveguide. Two-dimensional patterns are imaged line by line over 50 km optical fibers and the security test is realized by two-photon interference for energy-time entanglement. QSGI could be applied in scenarios of secure imaging and surveillance, and may inspire new ideas on specific quantum communication tasks.

We address the impact of spin-orbit coupling on the existence and properties of topological edge states of cold neutral atoms and Bose-Einstein condensates loaded in honeycomb Zeeman lattices—lattices where the spinor components are placed in potentials having opposite signs. We find that the type of spin-orbit-coupling mechanism has profound effect on the emergence of topological edge states. We also reveal that edge states persist when interatomic interactions are present and that they become metastable in Bose-Einstein condensates.

We derive the explicit solution of the problem of time-optimal control by a common magnetic field for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin maximum principle and a symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of $1\%$ and a 70–$80\%$ decrease in the experiment duration as compared to existing methods. This analytical solution and experimental demonstration of time-optimal control in such a system provides a route to achieve time-optimal control in more general quantum systems.

We have experimentally evaluated the nonclassical relation between measurement errors in a joint measurement of two noncommuting polarizations by using entangled photon pairs as a probe. The joint measurement was realized by filtering polarization directions that are sensitive to both of the two target polarizations, and the same filtering procedures were applied independently to the two photons of an entangled pair. Since the statistically independent measurement errors of two identical measurements performed on entangled pairs will reduce an overall visibility of the correlation by the square of the local visibilities, the squared visibilities of the local measurements can be obtained directly from the measurement data. We apply this method to determine the visibility of the correlation between the products of the two noncommuting polarizations, a characteristic of the measurement errors that cannot be obtained locally since there is no self-adjoint operator that describes this product of measurement outcomes as a single-photon observable. The experimental results clearly show that the square of the product visibility is negative, indicating the nonclassical nature of the statistical relation between the measurement errors of noncommuting polarizations.

A general time-dependent quantum system can be driven fast from its initial ground state to its final ground state without generating transitions by adding a steering term to the Hamiltonian. We show how this technique can be modified to improve on the standard quantum adiabatic algorithm by making a single-particle and cluster approximation to the steering term. The method is applied to a one-dimensional Ising model in a random field. For the limit of strong disorder, the correction terms significantly enhance the probability for the whole system to remain in the ground state for the proposed nonstoquastic annealing protocol. We demonstrate that even when transitions occur for stronger interaction between qubits, the most probable quantum state is one of the lower-energy states of the final Hamiltonian. Since the method can be applied to any model, and more sophisticated approximations to the steering term are possible, the alternative technique opens up an avenue for the improvement of the quantum adiabatic algorithm.

We consider a system of two bosonic modes each subject to the dynamics induced by a thermal Markovian environment and we identify instantaneous, local symplectic controls that minimize the loss of entanglement in the Gaussian regime. By minimizing the decrease of the logarithmic negativity at every instant in time, it will be shown that a nontrivial, finite amount of local squeezing helps to counter the effect of decoherence during the evolution. We also determine optimal control routines in the more restrictive scenario where the control operations are applied on only one of the two modes. We find that applying an instantaneous control only at the beginning of the dynamics, i.e., preparing an appropriate initial state, is the optimal strategy for states with symmetric correlations and when the dynamics is the same on both modes. More generally, even in asymmetric cases, the delayed decay of entanglement resulting from the optimal preparation of the initial state with no further action turns out to be always very close to the optimized control where multiple operations are applied during the evolution. Our study extends directly to “monosymmetric” systems of any number of modes, i.e., to systems that are invariant under any local permutation of the modes within any one partition, as they are locally equivalent to two-mode systems.

We study electron momentum vortices in single-photon double ionization of ${\mathrm{H}}_2$ by time-delayed, counter-rotating, elliptically polarized attosecond pulses propagating along $\widehat{\mathbf{k}}$ either parallel or perpendicular to the molecular axis $\mathbf{R}$. For $\widehat{\mathbf{k}}\parallel \mathbf{R}$, kinematical vortices occur similar to those found for He. For $\widehat{\mathbf{k}}\perp \mathbf{R}$, we find dynamical vortex structures originating from an ellipticity-dependent interplay of ${}^1\mathrm{\Sigma }_u^{+}$ and ${}^1\mathrm{\Pi }_u^{+}$ continuum amplitudes. We propose a complete experiment to determine the magnitudes and relative phase of these amplitudes by varying pulse ellipticities and time delays.

We describe a Zeeman slowing method reported in [New J. Phys. 20, 042001 (2018)] and compare it to conventional radiative beam-slowing schemes. The scheme is designed to work on a type-II level structure, making it particularly attractive for radiative beam slowing of molecules. Working on the $D_1$ line of atomic ${}^{39}\mathrm{K}$, we demonstrate efficient slowing of an atomic beam from $400\mathrm{m}{\mathrm{s}}^{-1}$ down to $35\mathrm{m}{\mathrm{s}}^{-1}$ with a final flux of $3.3\times {10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. We give experimental details and compare our results to other established radiative slowing schemes in atomic and molecular physics. We find type-II Zeeman slowing to outperform white-light slowing commonly used in molecular beam slowing and to be comparably as efficient as traditional type-I Zeeman slowing being the standard beam-slowing technique in atomic physics.

We study the dynamics of an Airy wave packet moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wave packet experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wave packet's motion is described by relativistic equations of motion, which surprisingly arise naturally from evolution under the standard nonrelativistic Schrödinger equation. The presence of the lattice potential allows the wave packet's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wave packet's motion is photonlike, this form of control allows it to mimic both standard and negative refraction. Airy wave packets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.

Understanding the interplay between magnetism and superconductivity is one of the central issues in high-temperature superconductors. The recent experimental implementation of cold gases with highly tunable anisotropic interaction, especially in magnetic dipolar atoms or polar molecules, opens up a new thrust on exploring this interesting phenomenon. Here we report a mechanism to drive the interplay between magnetism and superfluidity through engineering the spatially anisotropic interaction via considering loading pseudospin-1/2 dipolar Fermi atoms in bilayer optical lattices. Surprisingly, we find that the weak interlayer interaction can lead to the coexistence of superfluidity and antiferromagnetism at low temperatures for the half filling case. It is distinguished from the usual scheme by doping an antiferromagnetic Mott insulating parent to access high-$T_c$ superconductivity, where at half filling there is no coexistence of superconductivity and magnetism at low temperatures due to the absence of the superconductivity. Furthermore, the interlayer superfluid possesses an unexpected nodal structure, which is reminiscent of the nodal high-$T_c$ superconductivity but differs in origin.

Supersonic helium beams are used in a wide range of applications, for example, surface scattering experiments and, most recently, microscopy. The high ionization potential of neutral helium atoms makes it difficult to build efficient detectors. Therefore, it is important to develop beam sources with a high center-line intensity. Several approaches for predicting the center-line intensity exist, with the so-called quitting surface model incorporating the largest amount of physical dependences in a single analytical equation. However, until now only a limited amount of experimental data has been available. Here we present a comprehensive study where we compare the quitting surface model with an extensive set of experimental data. In the quitting surface model the source is described as a spherical surface from where the particles leave in a molecular flow determined by Maxwell-Boltzmann statistics. We use numerical solutions of the Boltzmann equation to determine the properties of the expansion. The center-line intensity is then calculated using an analytical integral. This integral can be reduced to two cases, one which assumes a continuously expanding beam until the skimmer aperture and another which assumes a quitting surface placed before the aperture. We compare the two cases to experimental data with a nozzle diameter of 10 $\mu \mathrm{m}$, skimmer diameters ranging from 4 to 390 $\mu \mathrm{m}$, a source pressure range from 2 to 190 bars, and nozzle-skimmer distances between 17.3 and 5.3 mm. To further support the two analytical approaches, we also perform equivalent ray-tracing simulations. We conclude that the quitting surface model predicts the center-line intensity of helium beams well for skimmers with a diameter larger than $120\mu \mathrm{m}$ when using a continuously expanding beam until the skimmer aperture. For the case of smaller skimmers the trend is correct, but the absolute agreement is not as good. We propose several explanations for this and test the ones that can be implemented analytically.

We investigate the ground-state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex-antivortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field-theory approach.

An exact solitary wave solution is presented for the nonlinear Schrödinger equation governing the propagation of pulses in optical fibers including the effects of second-, third-, and fourth-order dispersions. The stability of this solitonlike solution with a ${\mathrm{sech}}^2$ shape is proven. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these solitonlike optical pulses propagating in a fiber with higher-order dispersion is that their parameters satisfy efficient scaling relations. The main term of the perturbation theory describing ultrashort localized pulses is also presented when absorption or gain is included in the nonlinear Schrödinger equation. We anticipate that this type of stable localized pulses could find practical applications in communications, slow-light devices, and ultrafast lasers.

The inelastic scattering and conversion process between photons and phonons by laser-driven quantum dots is analyzed for a honeycomb array of optomechanical cells. Using Floquet theory for an effective two-level system, we solve the related time-dependent scattering problem, beyond the standard rotating-wave approximation approach, for a plane Dirac-photon wave hitting a cylindrical oscillating barrier that couples the radiation field to the vibrational degrees of freedom. We demonstrate different scattering regimes and discuss the formation of polaritonic quasiparticles. We show that sideband-scattering becomes important when the energies of the sidebands are located in the vicinity of avoided crossings of the quasienergy bands. The interference of Floquet states belonging to different sidebands causes a mixing of long-wavelength (quantum) and short-wavelength (quasiclassical) behavior, making it possible to use the oscillating quantum dot as a kind of transistor for light and sound. We comment under which conditions the setup can be utilized to observe zitterbewegung.

Random-matrix eigenvalues have a well-known interpretation as a gas of like-charge particles. We make use of this to introduce a model of vortex dynamics by defining a time-dependent wave function as the characteristic polynomial of a random matrix with a parameterized deformation, the zeros of which form a gas of interacting vortices in the phase. By the introduction of a quaternionic structure, these systems are generalized to include antivortices and nonvortical topological defects: phase maxima, phase minima, and phase saddles. The commutative group structure for complexes (which undergo topologically allowed reactions) generates a hierarchy. Several special cases, including defect-line bubbles and knots, are discussed from both an analytical and computational perspective. Finally, we return to the quaternion structures to provide an interpretation of two-vortex fundamental processes as states in a quaternionic space, where annihilation corresponds to scattering out of real space, and identify a time-energy uncertainty principle.

We analyze a method for the creation, storage, and retrieval of optomechanical Schrödinger cat states, in which there is a quantum superposition of two distinct macroscopic states of a mechanical oscillator. In the quantum memory protocol, an optical cat state is first prepared in an optical cavity, then transferred to the mechanical mode, where it is stored and later retrieved using control fields. We carry out numerical simulations for the quantum memory protocol for optomechanical cat states using the positive-P phase space representation. This has a compact, positive representation for a cat state, thus allowing a probabilistic simulation of this highly nonclassical quantum system. It is essential to use importance sampling to carry out the simulation effectively. To verify the effectiveness of the cat-state quantum memory, we consider several cat-state signatures and show how they can be computed. We also investigate the effects of decoherence on a cat state by solving the standard master equation for a simplified model analytically, allowing us to compare with the numerical results. Focusing on the negativity of the Wigner function as a signature of the cat state, we evaluate analytically an upper bound on the time taken for the negativity to vanish, for a given temperature of the environment of the mechanical oscillator. We show consistency with the numerical methods. These provide exact solutions, allowing a full treatment of decoherence in an experiment that involves creating, storing, and retrieving mechanical cat states using temporally mode-matched input and output pulses. Our analysis treats the internal optical and mechanical modes of an optomechanical oscillator, and the complete set of input and output field modes which become entangled with the internal modes. The model includes decoherence due to thermal effects in the mechanical reservoirs, as well as optical and mechanical losses.

In a previous work [Andrade et al., Phys. Rep. 647, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local quantum effects are taken into account through the reflection and transmission scattering amplitudes. To deal with general graphs, two simplifying procedures were developed: regrouping of paths into families of paths and the separation of a large graph into subgraphs. However, for less symmetrical graphs with complicated topologies as, for instance, random graphs, it can become cumbersome to choose the subgraphs and the families of paths. In this work, an even more general procedure to construct the energy domain GF for a quantum graph based on its adjacency matrix is presented. This new construction allows us to obtain the secular determinant, unraveling a unitary equivalence between the scattering Schrödinger approach and the Green's function approach. It also enables us to write a trace formula based on the Green's function approach. The present construction has the advantage that it can be applied directly for any graph, going from regular to random topologies.

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e., using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2\to 1$ random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments.

Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is the fraction of target items in the database. In this paper, we find out that the Grover algorithm can actually apply to the case where one can identify the range that $\lambda$ belongs to from a given series of disjoint ranges. However, Grover's algorithm still cannot maintain high success probability when there exist multiple target items. For this problem, we proposed a complementary-multiphase quantum search algorithm in which multiple phases complement each other so that the overall high success probability can be maintained. Compared to the existing algorithms, in the case defined above, our algorithm achieves the following three goals simultaneously: (1) the success probability can be no less than any given value between 0 and 1, (2) the algorithm is applicable to the entire range of $\lambda$, and (3) the number of iterations is almost the same as that of Grover's algorithm. Especially compared to the optimal fixed-point algorithm [Phys. Rev. Lett. 113, 210501 (2014)], our algorithm uses fewer iterations to achieve a success probability greater than 82.71%, e.g., when the minimum success probability is required to be 99.25%, the number of iterations can be reduced by 50%.

The standard quantum annealing algorithm tries to approach the ground state of a classical system by slowly decreasing the hopping rates of a quantum random walk in the configuration space of the problem, where the on-site energies are provided by the classical energy function. In a quantum reinforcement algorithm, the annealing works instead by increasing gradually the strength of the on-site energies according to the probability of finding the walker on each site of the configuration space. Here, by using the path-integral Monte Carlo simulations of the quantum algorithms, we show that annealing via reinforcement can significantly enhance the success probability of the quantum walker. More precisely, we implement a local version of the quantum reinforcement algorithm, where the system wave function is replaced by an approximate wave function using the local expectation values of the system. We use this algorithm to find solutions to a prototypical constraint satisfaction problem (XORSAT) close to the satisfiability to unsatisfiability phase transition. The study is limited to small problem sizes (a few hundreds of variables), nevertheless, the numerical results suggest that quantum reinforcement may provide a useful strategy to deal with other computationally hard problems and larger problem sizes even as a classical optimization algorithm.