Recently, the problem of discriminating multipartite unitary operations by local operations and classical communication (LOCC) has attracted significant attention. The latest work in the literature on this problem showed that two multipartite unitary operations can always be perfectly distinguished by LOCC when a finite number of runs are allowable. However, in these schemes, local entanglement (an entangled state held by one party) was required, which seems to imply that local entanglement is necessary for perfect discrimination between unitary operations by LOCC. In this paper, we show that a perfect discrimination between two unitary operations acting on a two-qudit system can always be achieved without exploiting any entanglement. As a result, we conclude that local entanglement is not necessary for perfect discrimination between unitary operations acting on a two-qudit system by LOCC. Our result, in general, is based on the assumption made by X. F. Zhou, Y. S. Zhang, and G. C. Guo [Phys. Rev. Lett. 99, 170401 (2007)] that for any unitary operation $U$, we can obtain its reverse transformation $U^{†}$ by exchanging the input and output ports of the whole setup. Thus, we further consider whether we can avoid using this assumption, and we find that for unitary operations acting on two qubits, our result can be obtained without using this assumption. However, in higher dimension how to do that seems to be unclear.

We propose a scheme to generate polarization entanglement from spatially correlated photon pairs. We experimentally realized a scheme by means of a spatial correlation effect in a spontaneous parametric down-conversion and a modified Michelson interferometer. The scheme we propose in this paper can be interpreted as a conversion process from spatial correlation to polarization entanglement.

Collision cross sections are calculated for the three systems ${\text{O}}_2\text{-He}$, ${\text{Na}}_2\text{-Na}$ and ${\text{K}}_2\text{-K}$ at cold and ultracold temperatures. We discuss their relevance for cold molecule formation by buffer-gas cooling and by other cooling methods where collisions between molecules and atoms are important, e.g photoassociation. The molecule is treated as a rigid rotator in the electronic and vibrational ground state. We have calculated ab initio the potential energy surfaces for the three systems with special emphasis on the long range potential which is very important at low energies. With relevance to buffer gas cooling, we have also studied the thermalization process between ${\text{O}}_2$ molecules and He atoms as determined by the calculated cross sections.

We have developed a general method to perform optical pumping by a pulsed laser with the aid of an optical cavity (cavity-assisted optical pumping). Optical pumping is achieved by repetitive interaction of a single laser pulse with a target material in the cavity. This method is demonstrated for manganese ions, ${\text{Mn}}^{+}$, stored in a linear radio-frequency ion trap; about ${10}^8$ ions are spin polarized by a 5-ns laser pulse via ${{}^{7}P}_J\leftarrow {{}^{7}S}_3$ ($J=3$ or 4) transition in the ultraviolet region. The linewidth of the pulsed light source is broad enough to transfer the populations of lower hyperfine levels to the highest one $\left(F=11/2\right)$ in the ${{}^{7}S}_3$ ground state; the nuclear spin is polarized as well.

Short-range interactions between strongly nonlocal spatial solitons were investigated and found to depend periodically on the soliton phase difference. Two solitons in close proximity can be intertrapped via the strong nonlocality, and propagate together as a whole. The trajectory of the propagation is a straight line with a slope controlled by the phase difference. Experimental results carried out in nematic liquid crystals agree quantitatively with the prediction. The modification of the Snyder-Mitchell model is also discussed. Our study suggests that the phenomenon in which optical beams can be steered by controlling the phase difference could be used in all-optical information processing.

In this investigation recurrence spectra of potassium are acquired using 405 and $980\mathrm{nm}$ laser diodes. Atoms were excited to Rydberg-Stark states $(n\approx 70)$ resonantly via the $5p_{3∕2}$ state and recurrence spectra were obtained near the classical ionization threshold. The data suggest that the outgoing distribution of electrons is more symmetric in potassium than in hydrogen or sodium and that phase shifts incurred by the electron wave function as it passes through the atomic core cause regular destructive interference within the recurrence spectra.

We derive Bell inequalities for graph states by generalizing the approach proposed by Ardehali [Phys. Rev. A 46, 5375 (1992)] for Greenberger-Horne-Zeilinger (GHZ) states. Using this method, we demonstrate that Bell inequalities with nonstabilizer observables are often superior to the optimal GHZ-Mermin-type (or stabilizer-type) Bell inequalities.

The quantum adiabatic theorem is a widely applied result in quantum mechanics. However, recently, counterexamples were produced, indicating that the transition probabilities in some systems do not converge as predicted by the adiabatic theorem [K. P. Marzlin and B. C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)]. In this paper, we examine a proof of the adiabatic theorem, paying specific attention to the validity of the assumptions made in the proof. We show that the convergence of the transition probabilities is path dependent when the change in the Hamiltonian is large. Finally, we consider the application of this reformulated form of the adiabatic theorem to the adiabatic evolution paradigm in quantum computation.

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient alternative quantum algorithms for the non-Abelian hidden-subgroup problem. Previous work has identified the optimal single-copy measurement for the hidden-subgroup problem over Abelian groups as well as for the non-Abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single-copy measurement for the hidden-subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single-copy optimal measurements for the hidden-subgroup problem.

We present fully empirical exchange-correlation functionals to be used within reduced-density-matrix-functional theory (RDMFT). These are of the popular $J\text{−}K$ form [involving only Coulomb- $\left(J\right)$ and exchange- $\left(K\right)$ type integrals over the natural orbitals], where the function of the occupation numbers that multiplies the Fock orbital term is written as a Padé approximant. The coefficients of the Padé approximant are optimized for a test set of eight molecules, and then refined for a larger set of $35\text{molecules}$. Two different approaches were tried, either keeping the self-interaction terms, or by removing them explicitly from the functional. The functionals thus obtained involve very few parameters, but are able to outperform other RDMFT functionals, yielding correlation energies that are, on average, even slightly better than second-order Møller-Plesset theory.

We revisit the problem of $\mathrm{H}_2{}^{+}$ in an intense, short laser pulse to investigate the role of nuclear rotation and thus gauge the validity of the more common aligned molecule approximation. For the laser parameters considered, our results show rough qualitative agreement, but not quantitative agreement. In one case, however, the aligned molecule approximation deviates even qualitatively from the more complete calculation by overestimating the importance of vibrational trapping.

We study the interference patterns of a superfluid Fermi gas released from optical lattices below and above Feshbach resonance based on a simple phenomenological approach. We first solve the order-parameter equation valid for the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) to obtain an initial distribution of subcondensates formed in an optical lattice. Then we investigate the coherent evolution of the subcondensates when both harmonic oscillator and optical lattice potentials are switched off. The interference patterns of the superfluid Fermi gas along the BCS-BEC crossover during a nearly ballistic expansion are calculated by means of Feynman propagator method combined with numerical simulations. The result obtained agrees with the recent experimental observation reported by the MIT group [J. K. Chin et al., Nature (London) 443, 961 (2006)].

The phenomenon of random intensity patterns, for waves propagating in the presence of disorder, is well known in optics and in mesoscopic physics. We study this phenomenon for cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.

Using the Lagrangian formalism, with a simple trial function for dissipative optical two-dimensional (2D) soliton beams, we show that there are two disjoint sets of stationary soliton solutions of the complex cubic-quintic Ginzburg-Landau equation, with concave and convex phase profiles, respectively. These correspond to continuously self-focusing and continuously self-defocusing types of 2D solitons. Their characteristics are distinctly different, as the energy for their existence can be generated either at the center or in the outer layers of the soliton beam. These predictions are corroborated with direct numerical simulations of the Ginzburg-Landau equation. Regions of existence in the parameter space of these two types of solutions are found and they are in reasonable agreement with the predictions of the Lagrangian approach. In addition, direct numerical simulations allow us to find more complicated localized solutions around these regions. These solutions lack cylindrical symmetry and/or pulsate in time. Examples of the complex behavior of these beams are presented.

In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced [Gelens et al., Phys. Rev. A 75, 063812 (2007)] generalization of the Lugiato-Lefever model that includes a weakly nonlocal response of an intracavity metamaterial. A rich scenario, in which the localized structures exhibit different types of oscillatory instabilities, tristability, and excitability, including a regime of conditional excitability in which the system is bistable, is presented and discussed. Finally, it is shown that the scenario is organized by a pair of Takens-Bogdanov codimension-2 points.

Application of the adiabatic method and program packages for solving the boundary problem for a discrete and continuous spectrum of a hydrogenlike atom in a homogeneous magnetic field is presented. Based on this the estimation of the photoionization cross section and laser-induced recombination rate is carried out. Effects of resonance transmission and total reflection of oppositely charged particles in a homogeneous magnetic field are demonstrated.

The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and an approximation for the density background is useful to understand vortex motion. We analyze the vortex motion on a variety of background configurations motivated by experiments on trapped Bose-Einstein condensates including linear and quadratic traps. We show that close to the center of the condensate cloud in the Thomas-Fermi regime the vortex is moving predominantly due to the image vortex that is effectively shifted because of the large density depletion of the condensate at the boundary. Close to the boundary the vortex moves mostly due to a large background density gradient across the vortex core. The vortex velocity is a nonlinear combination of these effects and of the global shape of the background density. We find the complete families of the traveling coherent structures in an infinitely long two-dimensional channel and derive an approximation of the velocity of a single vortex moving close to the center of the channel in the Thomas-Fermi regime.

We study adiabatic population transfer between discrete positions. Being closely related to stimulated Raman adiabatic passage in optical systems, this transport is coherent and robust against variations of experimental parameters. Thanks to these properties the scheme is a promising candidate for transport of quantum information in quantum computing. We study the effects of spatially registered noise sources on the quantum transport and in particular model Markovian decoherence via nonlocal coupling to nearby quantum point contacts which serve as information readouts. We find that the rate of decoherence experienced by a spatial superposition initially grows with spatial separation but surprisingly then plateaus. In addition we include non-Markovian effects due to couplings to nearby two-level systems and we find that although the population transport exhibits robustness in the presence of both types of noise sources, the transport of a spatial superposition exhibits severe fragility.

In this paper, we study time-optimal control problems related to a system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take a much longer time as compared to the time required to produce unitary transformations on the first qubit, but a much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup $\text{SU}\left(2\right)\times \text{SU}\left(2\right)\times \text{U}\left(1\right)$, which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum-information processing.