In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger modules, such that the desired unitary matrix expressing the algorithm is directly implemented. We demonstrate this experimentally by taking the two-qubit Grover’s algorithm implemented in NMR quantum computations, whose pseudopure state is generated by cyclic permutations of the state populations. This is the first exact time-optimal solution, to our knowledge, obtained for a self-contained quantum algorithm.

We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.

Total electron scattering cross sections are reported for $\mathrm{Kr}$ and $\mathrm{Xe}$ for $250–4500\mathrm{eV}$ electrons by measurement of the electron-beam intensity attenuation through a gas cell. These cross sections are compared with the previous experimental measurements and the predictions by theoretical and semiempirical models. Discrepancies in experimental cross sections between different experimental groups are explained using the oscillator strengths and inelastic threshold of electron-energy-loss spectra. The correlation between the total electron scattering cross section and the atomic radius is discussed for $\mathrm{Ne}$, $\mathrm{Ar}$, $\mathrm{Kr}$, and $\mathrm{Xe}$ atoms.

Marked characteristics in charge-transfer cross sections between collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ ions with ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ molecules, the so-called isotope effect, are observed in the energy range from $0.18\text{to}1.0\mathrm{keV}∕\mathrm{u}$. The observed cross-section ratios $\sigma ({\mathrm{D}}^{+}+{\mathrm{D}}_2)∕\sigma ({\mathrm{H}}^{+}+{\mathrm{H}}_2)$ of charge transfer in ${\mathrm{D}}^{+}+{\mathrm{D}}_2$ and in ${\mathrm{H}}^{+}+{\mathrm{H}}_2$ collisions are found to be 0.665 at $0.18\mathrm{keV}∕\mathrm{u}$ and gradually increases, finally approaching unity at higher energies. Similar behavior and magnitude within the error bars of the cross-section ratios $\sigma ({\mathrm{H}}^{+}+\mathrm{H}\mathrm{D})∕\sigma ({\mathrm{H}}^{+}+{\mathrm{H}}_2)$ and $\sigma ({\mathrm{D}}^{+}+\mathrm{H}\mathrm{D})∕\sigma ({\mathrm{H}}^{+}+{\mathrm{H}}_2)$ have been observed, although the present calculation predicts a sizable difference for heteronuclear molecules. The cross section differences due to the target isotope effect are pronounced even in the high-eV to low-keV region. On the other hand, charge-transfer cross-section ratios for the same target but different projectile isotopes, e.g., $\sigma ({\mathrm{H}}^{+}+\mathrm{H}\mathrm{D})∕\sigma ({\mathrm{D}}^{+}+\mathrm{H}\mathrm{D})$ and $\sigma ({\mathrm{D}}^{+}+{\mathrm{D}}_2)∕\sigma ({\mathrm{H}}^{+}+{\mathrm{D}}_2)$, are constant near unity, which indicates a minor role of collision-induced vibrations as compared to the target vibrational spacing. It is understood that the isotope effect in the charge transfer of ion-molecule collisions originates from the combination of a small offset in binding and vibrational energies and the different spaces occupied by the wave functions of the target ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ molecules.

We present our recent results on the scattering length of ${}^4\mathrm{He}-{}^4\mathrm{He}_2$ collisions. These investigations are based on the hard-core version of the Faddeev differential equations. As compared to our previous calculations of the same quantity, a much more refined grid is employed, providing an improvement of about 10%. Our results are compared with other ab initio and model calculations.

The probability of the ejection of a neutral atom in a specific quantum state after keV-ion beam sputtering is often interpreted in terms of the interaction between the atomic states of the escaping atom and the electronic states of the solid. In this work, we examined this interplay in the sputtering of iridium as this element has—unlike the elements employed in previous investigations—a complex atomic structure due to strong configuration interactions. Double-resonant two-photon laser ionization is used to probe the sputtered Ir atoms yielding information about the probability for an ejected atom to populate a specific atomic state and its escape velocity. The qualitative features of the corresponding population partition and state-selective velocity distributions show the influence of the excitation energy and the electronic structure of the different atomic states. A comparison is made between the experimental data and predictions from the resonant electron transfer description.

The dynamics of a two-dimensional $\mathrm{H}_2{}^{+}$ molecule interacting with a strong laser pulse beyond the usual approximation of fixed nuclei is presented. The motion of the nuclei is studied by using the classical Newton laws while the electron is described with a full quantal treatment. The axis of the molecule, initially not aligned to the laser field, performs a long-period pendular motion around the laser polarization axis. Vibrational degrees of freedom are seen to be excited. The radiation emitted by the oscillating charges presents variations that are synchronous to the pendular motion. The possibility of monitoring the motion of the molecule through the emitted radiation is discussed.

We study properties of ultracold bosonic atoms in one-, two-, and three-dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose-Hubbard model in parabolic confining potentials. Our results indicate that local properties of the atoms can be accessed by probing the system’s response to local potential perturbations. Furthermore, we show how the formation of Mott insulating regions is reflected in the momentum distribution of the atoms, amenable to experimental detection. We disprove previous claims concerning the relevance of fine structure in the momentum distribution function. Furthermore, we discuss limitations of local density approximations for confined systems, and demonstrate the absence of quantum criticality due to the inhomogenous potential. Instead, we show that quantum critical behavior can be observed in flat confining potentials. Our results indicate that the experimental detection of the Mott transition in moderately sized optical lattices would be significantly eased in flat confinement potentials.

The role of spontaneous emission noise and gain line profile in the dynamics of a multimode semiconductor laser with weak-to-moderate optical feedback is studied. Two models of such a laser are compared. If the gain profile is flat and in the absence of noise, model A predicts that all modal intensities are in phase, and model B predicts antiphase dynamics of the modal intensities. Noise induces out-of-phase solutions in model A and hardly affects model B. Weakly curved gain profile determines the number of lasing modes but otherwise has little effect on the laser dynamics in both models.

A recently proposed purification method, in which Zeno-like measurements of a subsystem can bring about a distillation of another subsystem in interaction with the former, is utilized to yield entangled states between distant systems. It is shown that measurements of a two-level system, locally interacting with two other spatially separated uncoupled subsystems, can distill entangled states from the latter irrespective of the initial states of the two subsystems.

We present a scheme for generating polarization-entangled photons pairs with arbitrary joint spectrum. Specifically, we describe a technique for spontaneous parametric down-conversion in which both the center frequencies and the bandwidths of the down-converted photons may be controlled by appropriate manipulation of the pump pulse. The spectral control offered by this technique permits one to choose the operating wavelengths for each photon of a pair based on optimizations of other system parameters (loss in optical fiber, photon counter performance, etc.). The combination of spectral control, polarization control, and lack of group-velocity matching conditions makes this technique particularly well suited for a distributed quantum information processing architecture in which integrated optical circuits are connected by spans of optical fiber.

We present an experimental and computational study of the ion and fusion neutron yields from explosions of deuterium clusters irradiated with 100-TW laser pulses. We find that the cluster explosion energy and resultant fusion yield are sensitive to the laser pulse rise time as determined by the pulse duration for a fixed envelope shape. Our experimental observations are consistent with the results of particle simulations of the laser-cluster interaction which show that the explosion energies of the clusters are determined by a single parameter: the ratio of the cluster ionization time to its intrinsic expansion time. This competition of time scales sets a fundamental constraint on the ion emission and resultant neutron yield performance of these targets as a function of laser-pulse duration.

A quantitative, analytic model of evaporative cooling covering both the small- $(<4)$ and large- $(>4)$ $\eta$ regimes is presented. $\eta$ is the dimensionless parameter defined as the trap depth divided by the temperature of the trapped sample. Although some of the same general properties present at large $\eta$ are also present at small $\eta$, there are significant quantitative differences. These differences must be taken into account in order to accurately extract from the trapping data quantitative measurements of, for example, collisional atomic cross sections.

Using the variational approximation and direct simulations in real and imaginary time, we find stable two-dimensional (2D) and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction $\left(z\right)$ and periodic in the others (however, the quasi-1D potentials cannot stabilize 3D solitons). The family of solitons includes single- and multiple-peaked ones. The results apply to Bose-Einstein condensates (BEC’s) in optical lattices (OL’s) and to spatial or spatiotemporal solitons in layered optical media. This is the first prediction of mobile 2D and 3D solitons in BEC’s, as they keep mobility along $z$. Head-on collisions of in-phase solitons lead to their fusion into a collapsing pulse. Slow collisions between two multiple-peaked solitons whose main peaks are separated by an intermediate channel end up with their fusion into one single-peaked soliton in the middle channel, $\simeq 1∕3$ of the original number of atoms being shed off. Stable localized states in the self-repulsive GPE with the low-dimensional OL combined with a parabolic trap are found too. Two such pulses in one channel perform recurrent elastic collisions, periodically featuring sharp interference patterns in the strong-overlap state.

Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression $T_c=T_c^0\{1+c_{1}a{n}^{1∕3}+[c_2^{\prime }\ln \left(a{n}^{1∕3}\right)+c_2^{″}]a^2{n}^{2∕3}+\mathrm{O}\left(a^{3}n\right)\}$, where $T_c^0$ is the critical temperature for an ideal gas, $a$ is the $s$-wave scattering length, and $n$ is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient $c_1$ between their results and the (apparently) other reliable results in the literature. Our results show that $\{(T_c-T_c^0)∕T_c^0\}∕\left(a{n}^{1∕3}\right)$ depends strongly on the interaction strength $a{n}^{1∕3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain $c_1=1.32\pm 0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\varphi }^4$ field theory and variational perturbation theory.

We perform a time-dependent analysis of four-wave mixing (FWM) in a double-$\Lambda$ system in an ultraslow-propagation regime and obtain the analytical expressions of pulsed probe laser, FWM-generated pulse, phase shifts and absorption coefficients, group velocities, and FWM efficiency. With these analytical expressions, we show that an efficiently generated FWM field can acquire the same ultraslow group velocity $(V_g∕c\sim {10}^{-4}–{10}^{-5})$ and pulse shape of a probe pump and that the maximum FWM efficiency is greater than 25%, which is orders of magnitude larger than previous FWM schemes in the ultraslow-propagation regime.

We propose a new set of observables for experiments on entangled particles of arbitrarily large spin that produce significant Clauser-Horne-Shimony-Holt inequality violations for fixed analyzer settings over a wider range of spins than was previously possible. These observables are better suited for experiments where analyzer orientations must be chosen before the spin of the entangled particles is known, such as experiments using polarization entangled downconverted photons.

Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and nondistillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely biseparable. Our results are not only restricted to this class of quantum states, since they rest upon very general properties of mixed states and unextendible product bases for any possible number of parties. Robustness against noise of the relevant properties of these states implies the significance of their possible experimental realization, therefore being of physical—and not exclusively mathematical—interest.

We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.

We study the $S$ matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending the Schrödinger evolution to complex time, one can obtain an exact answer for some of the transition amplitudes. Similar to the Landau-Zener case, our result covers both the adiabatic (slow evolution) and the diabatic (fast evolution) regimes. The form of the exact transition amplitude coincides with that obtained in a sequential pairwise level crossing approximation, in accord with the conjecture of Brundobler and Elser [J. Phys. A 26, 1211 (1993)].