The optimal properties for single photons may vary drastically between different quantum technologies. Along with central frequency conversion, control over photonic temporal waveforms will be paramount to the effective coupling of different quantum systems and efficient distribution of quantum information. Through the application of pulse shaping and the nonlinear optical process of sum-frequency generation, we examine a framework for manipulation of single-photon waveforms. We use a nonperturbative treatment to determine the parameter regime in which both high-efficiency and high-fidelity conversion may be achieved for Gaussian waveforms and study the effect such conversion techniques have on energy-time entanglement. Additionally, we prove that aberrations due to time ordering are negligible when the phase matching is nonrestrictive over the input bandwidths. Our calculations show that ideal quantum optical waveform conversion and quantum time lensing may be fully realized using these techniques.

In this paper, we study the optimal simulation of the three-qubit unitary using two-qubit gates. First, we completely characterize the two-qubit gate cost of simulating the Deutsch gate (controlled-controlled gate) by generalizing our result on the two-qubit cost of the Toffoli gate. The function of any Deutsch gate is simply a three-qubit controlled-unitary gate and can be intuitively explained as follows: The gate outputs the states of the two control qubits directly, and applies the given one-qubit unitary $u$ on the target qubit only if both the states of the control qubits are $|1\rangle$. Previously, it was only known that five two-qubit gates are sufficient for implementing such a gate [Sleator and Weinfurter, Phys. Rev. Lett. 74, 4087 (1995)]. We show that if the determinant of $u$ is 1, four two-qubit gates are optimal. Otherwise, five two-qubit gates are required. For the Fredkin gate (the controlled-swap gate), we prove that five two-qubit gates are necessary and sufficient, which settles the open problem introduced in Smolin and DiVincenzo [Phys. Rev. A 53, 2855 (1996)].

In this work we investigate the different states of a system of spin-1 bosons in two potential wells connected by tunneling, with spin-dependent interaction. The model utilizes the well-known Bose-Hubbard Hamiltonian, adding a local interaction term that depends on the modulus of the total spin in a well, favoring a high- or low-spin state for different signs of the coupling constant. We employ the concept of fidelity to detect critical values of parameters for which the ground state undergoes significant changes. The nature of the states is investigated through evaluation of average occupation numbers in the wells and of spin correlations. A more detailed analysis is done for a two-particle system, but a discussion of the three-particle case and some results for larger numbers are also presented.

Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has good scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.

The Berry curvature is a geometrical property of an energy band which can act as a momentum-space magnetic field in the effective Hamiltonian of a wide range of systems. We apply the effective Hamiltonian to a spin-$\frac{1}{2}$ particle in two dimensions with spin-orbit coupling, a Zeeman field, and an additional harmonic trap. Depending on the parameter regime, we show how this system can be described in momentum space as either a Fock-Darwin Hamiltonian or a one-dimensional ring pierced by a magnetic flux. With this perspective, we interpret important single-particle properties, and identify analog magnetic phenomena in momentum space. Finally, we discuss the extension of this work to higher-spin systems, as well as experimental applications in ultracold atomic gases and photonic systems.

Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.

Various schemes have been proposed to overcome the drawback of the decoherence on quantum-enhanced parameter estimation. Here we suggest an alternative method, quantum feedback, to enhance the parameter precision of optimal quantum estimation of a dissipative qubit by investigating its dynamics of quantum Fisher information. We find that compared with the case without feedback, the quantum Fisher information of the dissipative qubit in the case of feedback has a large maximum value in time evolution and a smaller decay rate in the long time.

We investigate plasmonic mode propagation in nonlinear binary plasmonic waveguide arrays composed of two kinds of metal slabs alternately embedded in nonlinear dielectric materials, and numerically obtain soliton solutions with different symmetries. In particular, we find discrete gap solitons with strong transverse confinements reaching the scale of 10 nm. The equations to describe the mode propagations indicate that the system also provides a plasmonic platform to simulate aspects of quantum dynamics.

Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time- $\left(\mathcal{PT}\text{−}\right)$ symmetric waveguides, their linear spectrum is partially complex; thus light exponentially grows or decays upon propagation, and this growth or decay is not altered by nonlinearity. However, several classes of non-$\mathcal{PT}$-symmetric waveguides are also identified to possess all-real linear spectrum. For $\mathcal{PT}$-symmetric waveguides, phase transition is predicted analytically. In the nonlinear regime longitudinally periodic and transversely quasilocalized modes are found for $\mathcal{PT}$-symmetric waveguides both above and below phase transition. These nonlinear modes are stable under evolution and can develop from initially weak initial conditions.

A common experimental strategy for demonstrating nonclassical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have “jitter,” coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-realistic system to show apparent violation, the so-called “coincidence loophole.” Here, we introduce a family of Bell inequalities based on signed, directed distances between the parties' sequences of recorded time tags. Given that the time tags are recorded for synchronized, fixed observation periods and that the settings choices are random and independent of the source, violation of these inequalities unambiguously shows nonclassical correlations violating local realism. Distance-based Bell inequalities are generally useful for two-party configurations where the effective size of the measurement outcome space is large or infinite. We show how to systematically modify the underlying Bell functions to improve the signal-to-noise ratio and to quantify the significance of the violation.

We present a detailed theoretical characterization of the two fundamental collective resonances underlying the xenon giant dipole resonance (GDR). This is achieved consistently by two complementary methods implemented within the framework of the configuration-interaction singles (CIS) theory. The first method accesses the resonance states by diagonalizing the many-electron Hamiltonian using the smooth exterior complex scaling technique. The second method involves a different application of the Gabor analysis to wave-packet dynamics. We identify one resonance at an excitation energy of 74 eV with a lifetime of 27 as and the second at $107\text{eV}$ with a lifetime of $11\text{as}$. Our work provides a deeper understanding of the nature of the resonances associated with the GDR: a group of close-lying intrachannel resonances splits into two far-separated resonances through interchannel couplings involving the $4d$ electrons. The CIS approach allows a transparent interpretation of the two resonances as new collective modes. Due to the strong entanglement between the excited electron and the ionic core, the resonance wave functions are not dominated by any single particle-hole state. This gives rise to plasma-like collective oscillations of the $4d$ shell as a whole.

We consider the ground-state properties of the two-component spin-orbit-coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the noninteracting case, the ground state supports giant vortices carrying large angular momenta without rotating the trap. The vorticity is highly tunable by varying the amplitudes and orientations of the magnetic field. Interactions drive the system from a giant-vortex state to various configurations of vortex lattice states along a ring. Vortices exhibit ellipse-shaped envelopes with the major and minor axes determined by the spin-orbit coupling and healing lengths, respectively. Phase diagrams of vortex lattice configurations are constructed and their stabilities are analyzed.

We present comparatively simple two-dimensional and three-dimensional checkerboardlike optical lattices possessing nontrivial topological properties accompanied by topological surface states. By simple tuning of the parameters, these lattices can have a topological insulating phase, a topological semimetallic phase, or a trivial insulating phase. This allows the study of different topological phase transitions within a single cold-atom system. In the topologically nontrivial phases, flat bands appear at the surfaces of the system. These surface states possess short localization lengths such that they are observable even in systems with small lattice dimensions.

We examine a spinor Bose gas confined by an elongated trap. Since a spin-independent energy is much higher than a spin-dependent energy in alkali species, the system exhibits different properties by changing a radial confinement. We show that if a spin-dependent coupling is positive, a spin-liquid condensate, which breaks the charge $\text{U}\left(1\right)$ symmetry but preserves the spin rotational symmetry, can be realized in an intermediate confinement regime. Properties of the spin-liquid condensate are visible if a temperature is lower than a spin gap to characterize the spin-disorder property. If a temperature is higher than the gap but lower than a spin-dependent coupling energy, on the other hand, a regime in which a spin sector is described by a semiclassical wave emerges. A characterization in each regime by means of correlation functions and topological solitons is also discussed.

We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the Fokas-Lenells equation, the defocusing vector nonlinear Schrödinger equation, and the long-wave–short-wave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.

We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of states with different total number of particles, particle entanglement is necessary but not sufficient to overcome the shot noise limit. The highest possible phase estimation sensitivity, the Heisenberg limit, is established under general unbiased properties of the estimator. If coherences can be created, manipulated, and detected, the Heisenberg limit can only be set in the central limit, with a sufficiently large repetition of interferometric measurements.

We apply the time-dependent decoherence-free subspace theory to a Markovian open quantum system in order to present a proposal for a quantum-state engineering program. By quantifying the purity of the quantum state, we verify that the quantum-state engineering process designed via our method is completely unitary within any total engineering time. Even though the controls on the open quantum system are not perfect, the asymptotic purity is still robust. Owing to its ability to completely resist decoherence and the lack of restraint in terms of the total engineering time, our proposal is suitable for multitask quantum-state engineering program. Therefore, this proposal is not only useful for achieving the quantum-state engineering program experimentally, it also helps us build both a quantum simulation and quantum information equipment in reality.

Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. Variational methods can yield highly accurate energies, but may be less accurate for other operators of interest. A pseudospectral method yields very accurate expectations values for the two-electron ion with nuclear charge at and close to the critical value which yields zero ionization energy. As an illustration, the ground-state density is calculated and an extremely accurate parametrization is given. Other components in Kohn-Sham density functional theory are also calculated, and the efficacy of approximations is discussed.

We present absolute measurements of radiative and Auger decay rates of $K-\text{shell}$ vacancies in highly charged iron ions. The ions were resonantly excited with monochromatic x rays from the PETRA III synchrotron source. By measuring x-ray fluorescence and Auger decay simultaneously, absolute transition rates could be determined independently of most experimental parameters. The results confirm theoretical calculations, which are essential to model the photoexcited plasmas in x-ray binary stars and active galactic nuclei.

A scheme of designing laser pulses for controlling discrete quantum states has been proposed, relying on the recently developed highly accurate Maxwell-Schrödinger hybrid simulation. A single electron confined in a quasi-one-dimensional nanoscale potential well has been used as an illustrative example and a control pulse transferring completely the probability density from the ground state to the first excited state has been designed by the present Maxwell-Schrödinger hybrid scheme and by the conventional one that solves the time-dependent Schrödinger equation only without accounting for feedback from the electron system to the external electromagnetic field. The resultant pulses obtained by these two methods can be different largely owing to the modification of the laser field by the locally strong radiation from the excited electron. The present study demonstrates that light control pulses designed by the conventional method may need to be rectified for practical implementation in experiments.