We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O\left(\sqrt{N}\right)$ Grover bounded-error algorithm for the original problem, we seek the results for the exact algorithms, i.e., those that succeed with certainty. Under the standard oracle model ${\sum }_j{\left(-1\right)}^{{\delta }_{\tau j}}|j⟩⟨j|$, we demonstrate a tight lower bound $\frac{2}{3}N+o\left(N\right)$ of the number of queries for any parallel scheme with unentangled input states. With the assistance of entanglement, we obtain a general lower bound $\frac{1}{2}\left(N-\sqrt{N}\right)$. We provide concrete examples to illustrate our results. In particular, we show that the case of $N=6$ can be solved exactly with only two queries by using a bipartite entangled input state. Our results indicate that in the standard oracle model the complexity of the exact quantum search with one unique solution can be strictly less than that of the calculation of the OR function.

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped $A$ phase with Abelian anyon excitations to a gapless $B$ phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\xi =2{\text{sinh}}^{-1}\left[\sqrt{2J_z-1}/\left(1-J_z\right)\right]$, which diverges around the critical point $J_z={\left(1/2\right)}^{+}$.

We consider the realization of a quantum Fredkin gate with only linear optics and single photons. First we construct a heralded Fredkin gate using four heralded controlled-NOT (CNOT) gates. Then we simplify this method to a post-selected one utilizing only two CNOT gates. We also give a possible realization of this method which is feasible with current experimental technology. Another post-selected scheme requires time entanglement of the input photons but needs no ancillary photons.

We present a density-functional scheme for calculating the orbital-dependent exchange-correlation potential using the virial theorem as a sum rule. In order to check the validity of this scheme, atomic-structure calculations only with the exchange potential are performed. The accuracy of this scheme is shown to be comparable to that of the optimized effective potential (OEP) method, while the computational workload is extremely reduced compared to the OEP method.

We study stationary states of a two-dimensional (2D) Bose-Einstein condensate with both attractive and repulsive nonlinearities in a combination of a double-square-well potential in one direction and a perpendicular optical lattice. We look for dual-core solitons in this configuration, focusing on their symmetry-breaking bifurcations. For attractive interactions, without the lattice, a similar analysis was performed [M. Matuszewski et al., Phys. Rev. A 75, 063621 (2007)], where subcritical bifurcation transforming antisymmetric gap solitons into asymmetric ones was found. Here we focus on the effect of an optical lattice and the so created gap solitons. We discover that a phase transition occurs when the lattice depth increases and the additional dimension becomes strongly suppressed. The bifurcation type changes from subcritical (typical for a 2D system, with hysteresis) to supercritical (typical for a one-dimensional system). An additional advantage of the lattice is that gap solitons exist even for repulsive interactions. In this case we also discover bifurcation of a supercritical type. The analysis is based on a variational approximation, which is surprisingly well verified by numerical results.

We carry out a detailed examination of the ground-state properties of a few-boson system in a one-dimensional hard-wall potential with a $\delta$ split in the center. In the Tonks-Girardeau limit with infinite repulsion between particles, we use the Bose-Fermi mapping to construct the exact $N$-particle ground-state wave function, which allows us to study the correlation properties accurately. For the general case with finite interparticle interaction, the exact diagonalization method is exploited to study the ground-state density distribution, occupation number distribution, and momentum distribution for variable interaction strengths and barrier heights. The secondary peaks in the momentum distribution reveal the interference between particles on the two sides of the split, which is more prominent for large barrier strength and small interaction strength.

In current Bose-Einstein condensate experiments, the shot-to-shot variation of the atom number fluctuates up to 10%. In here, we present a procedure to suppress such fluctuations by using a nonlinear $p-\pi -\overline{p}$ matter wave interferometer for a Bose-Einstein condensate with two internal states and a high beam-splitter asymmetry $\left(p\ne 0.5\right)$. We analyze the situation for an inhomogeneous trap within the Gross-Pitaevskii mean-field theory, as well as a quantum mechanical Josephson model, which addresses complementary aspects of the problem and agrees well otherwise.

A scheme for controlling light speed from slower-than-$c$ to faster-than-$c$ in an atomic system is presented in this paper. The scheme is based on far detuning Raman effect. Two far detuning coupling fields with small frequency difference will produce two absorptive peaks for the probe field in a $\Lambda$ structure, and an optical pump between the two ground states can change the absorptive peaks into enhanced peaks, which makes the normal dispersion between the two peaks change into anomalous dispersion, so the probe field can change from slow light to superluminal propagation.

We investigate the effect of electromagnetically induced transparency inside a laser cavity. By changing the intensity of an external drive field, we can control the absorption to the laser field. A semiclassical analysis shows that the system undergoes a switch between first-order and second-order phase transitions. Around the tricritical point there could be a second-order phase transition followed by a first-order phase transition.

We report on an ab initio investigation of light-matter interactions in a spherical Mie laser. We derive a three-dimensional vector set of Maxwell-Bloch (MB) equations and solve them by the finite-difference time-domain (FDTD) method. Parallel MB-FDTD simulations are employed to study the nonlinear behavior of these nanosized lasers with a varying geometry and different material parameters. The retrieved electromagnetic resonances are consistent with those expected from Mie theory. The lasing regime is characterized by a rich physical scenario, including mode competition and dynamical frequency pulling effects. Application of these dynamics could favor the realization of nonlinearly controlled highly tunable nanolaser devices.

Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.

For a system composed of nine qubits, we show that natural interactions among the qubits induce the time evolution that can be regarded, at discrete times, as the Rabi oscillation of a logical qubit. Neither fine tuning of the parameters nor switching of the interactions is necessary. Although the straightforward application of quantum error correction fails, we propose a protocol by which the logical Rabi oscillation is protected against all single-qubit errors. The present method thus opens a simple and realistic way of protecting the unitary time evolution against noise.

We calculated the inelastic electron impact excitation cross sections of ${\text{He}}^{+}$ by electrons for a model helium atom to examine the onset of the signature of quantum chaotic scattering in this simple system. We find Ericson fluctuations (EF) in the calculated inelastic scattering cross sections only when the impact energies lie within about 0.21 eV below the double ionization threshold. We also discuss the stringent requirements and the proper methods for analyzing the inelastic scattering cross sections in order to observe EF experimentally.

The classical ensemble method is applied to study ionization processes of a one-dimensional model lithium atom interacting with an intense laser pulse. The motion of electrons is described by the classical Hamiltonian canonical system of equations. The ratio of double-to-single ionization with the increasing laser intensity is calculated and explained in terms of the energy distribution of electrons. The triple ionization of lithium is also investigated and the primary triple ionization path is found. Our results show a clear transition from nonsequential to sequential double ionization as the intensity increases, which is in agreement with the quantum calculation.

We studied the optical manipulation of spin coherence in rubidium atoms by using polarization spectroscopy with the pump-probe technique. Two types of optically induced spin echoes, namely on- and off-resonant manipulations, whose creation mechanism are the optical pumping effect and the light shift effect, respectively, are studied theoretically and experimentally. A theory of optically induced spin echoes that can be applied to both types of spin echoes is considered by using the density matrix, and a general expression for the refocusing efficiency of the control pulse is presented. The effect of the off-resonant manipulation was examined by using light pulses of two frequencies provided by two lasers. Vector models for the two types of spin echoes are presented, and the observed dependences of the frequency and the duration of the control pulse on the spin-echo intensity are suitably explained by the theoretically derived refocusing efficiency. The off-resonant manipulation gives the possibility of arbitrary-angle spin rotation around an arbitrary axis.

We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam’s initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.

By cyclic adiabatic change of two control parameters of an optical trap one can induce a circulating current of condensed bosons. The amount of particles that are transported per period depends on the “radius” of the cycle, and this dependence can be utilized in order to probe the interatomic interactions. For strong repulsive interaction the current can be regarded as arising from a sequence of Landau-Zener crossings. For weaker interaction one observes either gradual or coherent mega crossings, while for attractive interaction the particles are glued together and behave like a classical ball. For the analysis we use the Kubo approach to quantum pumping with the associated Dirac monopoles picture of parameter space.

We construct families of optical semidiscrete composite solitons (SDCSs), with one or two independent propagation constants, supported by a planar slab waveguide, cross-phase-modulation coupled to a periodic array of stripes. Both structures feature the cubic nonlinearity and support intrinsic modes with mutually orthogonal polarizations. We report three species of SDCSs, odd, even, and twisted ones, the first type being stable. Transverse motion of phase-tilted solitons, with potential applications to beam steering, is considered also.

We have experimentally studied the reflection of a weak probe beam from a dense atomic potassium vapor in the presence of a strong laser field tuned to the atomic resonance transition. We have observed an Autler-Townes doublet under hitherto unexplored conditions, namely, that the Rabi frequency induced by the strong laser field is much smaller than the self-broadened width of the resonance transition of the unexcited vapor. We attribute our observation to a reduction of the atomic decoherence by the strong drive field. We present a theoretical model of nonlinear processes in a dense atomic gas to explain the observed results.

We study the possibility of creating spatial patterns having subwavelength size by using the so-called dark states formed by the interaction between atoms and optical fields. These optical fields have a specified spatial distribution. Our experiments in Rb vapor display spatial patterns that are smaller than the length determined by the diffraction limit of the optical system used in the experiment. This approach may have applications to interference lithography and might be used in coherent Raman spectroscopy to create patterns with subwavelength spatial resolution.