We demonstrate nonlinear coupling in a discrete optical system. This is achieved in waveguide arrays with quadratic nonlinearity, where the symmetries of the nonlinearly interacting waveguide modes are used to suppress the usually dominating nonlinear effects within individual waveguides. We derive a mathematical model to describe the nonlinear coupling in such waveguide arrays and show experimentally the profound effects of this nonlinear coupling mechanism on second-harmonic generation.

We explore the effects of nonlinear mechanisms, i.e., carrier density pulsation, carrier heating, and spectral hole burning on mode multistability in microring lasers (MRLs) both theoretically and numerically. Expressions for achieving mode multistable operation are derived and analyzed. We find that nonlinear mechanisms play an important role in mode multistability. We verify the theoretical results by numerical simulations, and find that spectral hole burning is more effective than carrier density pulsation and carrier heating in increasing the number of multistable modes in MRLs. The results also show that a decrease in the ring radius will result in a reduction in the number of multistable modes.

We demonstrate the appearance of unexpected reflection resonances in corrugated dielectric waveguides. These are due to the curvature of the boundary. The effect is as strong as the ordinary Bragg resonances, and reduces the transmission through our waveguide by 20%. It is thus of high relevance for the design of optimized waveguiding structures. We validate our analytical predictions based on coupled-mode theory by a comparison to numerical simulations.

In a recent work of ours [Phys. Rev. Lett. 112, 073601 (2014)], we generalized the Power-Zineau-Woolley gauge to describe the electrodynamics of atoms in an arbitrary confined geometry. Here we complement the theory by proposing a tractable form of the polarization field to represent atomic material with well-defined intra-atomic potential. The direct electrostatic dipole-dipole interaction between the atoms is canceled. This theory yields a suitable framework to determine limitations on the light-matter coupling in quantum optical models with discernible atoms. We find that the superradiant criticality is at the border of covalent molecule formation and crystallization.

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with a fixed number parity yet not necessarily a fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert space $\mathcal{H}$ is defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases of $\mathcal{H}$ is a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined by J. Schliemann et al. [Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement. It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that in the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy is evaluated analytically, extending the results in previous reference to general states.

The angular coefficients ${\psi }_{k,p}(\alpha ,\theta )$ of the Fock expansion characterizing the $S\text{-state}$ wave function of the two-electron atomic system are calculated in hyperspherical angular coordinates $\alpha$ and $\theta$. To solve the problem the Fock recurrence relations separated into the independent individual equations associated with definite power $j$ of the nucleus charge $Z$ are applied. The “pure” $j$ components of the angular Fock coefficients, orthogonal to the hyperspherical harmonics $Y_{kl}$, are found for even values of $k$. To this end, the specific coupling equation is proposed and applied. Effective techniques for solving the individual equations with the simplest nonseparable and separable right-hand sides are proposed. Some mistakes or misprints made earlier in representations of ${\psi }_{2,0}$, are noted and corrected. All $j$ components of ${\psi }_{4,1}$ and the majority of components and subcomponents of ${\psi }_{3,0}$ are calculated and presented. All calculations are carried out with the help of Wolfram Mathematica.

A number of optical frequency standards have been evaluated with fractional uncertainties between ${10}^{-17}$ and ${10}^{-18}$. Reduction of the statistical uncertainty of a clock comparison to this level is challenging, requiring the best possible stability to avoid excessively long averaging times. We report recent improvements of our ${}^{88}\mathrm{Sr}{}^{+}$ single-ion standard that have reduced its 1-s Allan deviation from $1\times {10}^{-14}$ to $3\times {10}^{-15}$, yielding an order of magnitude decrease in averaging time for a given statistical uncertainty level. Among the improvements made are the implementation of a clear-out laser that transfers the ion from the metastable state to the ground state at each cycle, followed by a state preparation step that transfers the ion to the ground-state magnetic sublevel of the probed transition. With these changes, the ion clock transition interacts with the probe laser at every interrogation cycle. The stability of our optical standard is essentially limited by the quantum projection noise for pulse lengths up to $\approx 100$ ms.

We consider a time-dependent trap externally manipulated in such a way that one of its bound states is brought up towards the continuum threshold and then down again. We evaluate the probability $P^{\mathrm{stay}}$ of a particle, initially in a bound state of the trap, continuing in it at the end of the passage. We use the Sturmian representation, whereby the problem is reduced to evaluating the reflecting coefficient of an absorbing potential. In the slow-passage limit, $P^{\mathrm{stay}}$ goes to 1 for a state turning before reaching the continuum threshold and vanishes if the bound state crosses into the continuum. For a slowly moving state, just “touching” the threshold $P^{\mathrm{stay}}$ tends to a universal value of about $38\%$, for a broad class of potentials. In the rapid-passage limit, $P^{\mathrm{stay}}$ depends on the choice of the potential. Various types of trapping potentials are considered, with an analytical solution obtained in the special case of a zero-range well.

This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose generalizations of the standard GRAPE algorithm suited to this constraint. We test the validity and the efficiency of this approach for the inversion of an inhomogeneous ensemble of spin systems with different offset frequencies. It is shown that a remarkable efficiency can be achieved even for a very limited number of discrete values. Some applications in nuclear magnetic resonance are discussed.

We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.

We report on the observation of multiphoton interband absorption processes for quantum gases in shaken light crystals. Periodic inertial forcing, induced by a spatial motion of the lattice potential, drives multiphoton interband excitations of up to the ninth order. The occurrence of such excitation features is systematically investigated with respect to the potential depth and the driving amplitude. Ab initio calculations of resonance positions as well as numerical evaluation of their strengths exhibit good agreement with experimental data. In addition our findings could make it possible to reach novel phases of quantum matter by tailoring appropriate driving schemes.

Preparation of a nonclassically correlated state is the first step of any quantum-enhanced interferometric protocol. An efficient method is the one-axis twisting, which entangles a collection of initially uncorrelated particles by means of two-body interactions. Here we investigate the limits of the quantum improvement which can be reached with this method in realistic experimental conditions. We demonstrate that the usefulness of this entangling mechanism is a result of fine structures introduced into the quantum state. The scale at which these structures vary allows us to identify the minimal requirements for the precision of the complete interferometric sequence. Our results—especially the explanation of the underlying principle of the entangling method—may help to develop ultraprecise interferometers.

We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on the number states of the oscillator, which, together with displacement operations, can achieve universal control of the oscillator. Based on our proof of universal control, we provide a straightforward recipe to perform arbitrary unitary operations on the oscillator. With the capability of universal control, we can significantly reduce the number of operations to prepare the number state $\left|n\right.〉$ from $O\left(n\right)$ to $O\left(\sqrt{n}\right)$. This universal control scheme of the oscillator enables us to efficiently manipulate the quantum information stored in the oscillator, which can be implemented using superconducting circuits.

We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on accurate many-body numerical calculations as well as on a quasiparticle microscopic theory. For sufficiently fast decaying long-range potentials, we find that the quantum speed limit set by the long-range Lieb-Robinson bounds is never attained and a purely ballistic behavior is found. For slowly decaying potentials, a radically different scenario is observed. In the bosonic case, a remarkable local spreading of correlations is still observed, despite the existence of infinitely fast traveling excitations in the system. This is in marked contrast to the spin case, where locality is broken. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in the bosonic model.

Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.

We study and extend the semidefinite programming (SDP) hierarchies introduced in Navascués and Vértesi [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of the statistical correlations arising from finite-dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device-independent and semi-device-independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive a number of dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes.

von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are, however, static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can be overcome by “wrapping” the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup specific. We shall here develop a unified framework for designing optimized measurements. Our approach is twofold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which—taken individually—have a low quantum efficiency can be arranged into circuits where, collectively, the limitations of inefficiency are compensated for.

We characterize both entanglement and quantum coherence in a molecular system by connecting the linear entropy of electronic-nuclear entanglement with Wigner-Yanase skew information measuring vibronic coherence and local quantum uncertainty on electronic energy. Linear entropy of entanglement and quantifiers of quantum coherence are derived for a molecular system described in a bipartite Hilbert space $\mathcal{H}={\mathcal{H}}_{el}⨂{\mathcal{H}}_{vib}$ of finite dimension $N_{el}\times N_v$, and relations between them are established. For the specific case of the electronic-vibrational entanglement, we find the linear entropy of entanglement as having a more complex informational content than the von Neumann entropy. By keeping the information carried by the vibronic coherences in a molecule, linear entropy seizes vibrational motion in the electronic potentials as entanglement dynamics. We analyze entanglement oscillations in an isolated molecule, and show examples for the control of entanglement dynamics in a molecule through the creation of coherent vibrational wave packets in several electronic potentials by using chirped laser pulses.

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of the magnetic flux through the unit cell to the flux quantum as a control parameter. For a given flux ratio, we obtain faster spreading for a small number of steps and the walker tends to be highly localized around the origin. Moreover, the spreading of the walk can be suppressed and decreased within a limited time interval for specific rational values of flux ratio. When the flux ratio is an irrational number, even for a large number of steps, the spreading exhibits diffusive behavior rather than the well-known ballistic one as in the classical random walk and there is a significant probability of finding the walker at the origin. We also analyze the coin-position entanglement and show that the asymptotic behavior vanishes when the flux ratio is different from zero and the coin-position entanglement become nearly maximal in a periodic manner in a long time range.