The determination of the parity of a string of $N$ binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least $N∕2$ oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor $2^k$, with $k∊\{1,2,\dots ,{\log }_2(N∕2)\}$, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.

We consider collective decoherence for the quantum Shor algorithm. A quantum computer which interacts with its environment is modeled by a spin-$1∕2$ chain interacting with harmonic oscillators at a given temperature. We calculate the nondiagonal matrix elements of the density matrix which are important for implementation of the quantum Shor algorithm, and study the decay rate and the Lamb phase shift for these elements. It is shown that the probability of superdecoherence in the quantum Shor algorithm is extremely small. The conditions for preserving quantum entanglement are formulated.

A modified experimental apparatus with improved angular resolution and stability has been used to measure the total electron scattering cross sections for $\mathrm{S}{\mathrm{F}}_6$ and $\mathrm{S}{\mathrm{F}}_5\mathrm{C}{\mathrm{F}}_3$ in the energy range of $100–5000\mathrm{eV}$. A detailed analysis of the experimental error sources is provided. The experimental results are compared with integral elastic and inelastic cross sections calculated using the independent atom model approximation and a modified single-center additivity rule for electron energies ranging from $1\text{to}\mathrm{10,000}\mathrm{eV}$. The accuracy of these approximations method is discussed through a comparison with the experimental results. Previous cross-sectional data for $\mathrm{S}{\mathrm{F}}_6$ are compared with the present theoretical and experimental results. For $\mathrm{S}{\mathrm{F}}_5\mathrm{C}{\mathrm{F}}_3$, we present the first electron scattering cross-sectional data for the $100–\mathrm{10,000}\mathrm{eV}$ energy range, as well as the first empirical determination of the molecular polarizability.

We discuss the BCS-BEC crossover for one-dimensional spin-$1∕2$ fermions at zero temperature using the boson-fermion resonance model in one dimension. We show that in the limit of a broad resonance, this model is equivalent to an exactly solvable single-channel model, the so-called modified Gaudin-Yang model. We argue that the one-dimensional crossover may be realized either via the combination of a Feshbach resonance and a confinement-induced resonance or using direct photoassociation in a two-component Fermi gas with effectively one-dimensional dynamics. In both cases, the system may be driven from a BCS-like state through a molecular Tonks-Girardeau gas close to resonance to a weakly interacting Bose gas of dimers.

We propose an entanglement swapping scheme in cavity QED. In the scheme, the previously used joint measurement is not needed. The entanglement swapping in our proposal is a non-post-selection one, i.e., after the swapping is done, the swapped entanglement is still there.

We evaluate triply differential cross sections (TDCSs) for the photo-double-ionization (PDI) of He-like ions, and equal electron energy sharing, by using the SC3 model for the three-body final state. These cross sections are fitted with the usual dipolar Gaussian form which is found able to describe the theoretical TDCS, and could be applied for the interpretation of experimental data even at intermediate photon energies. We determine the dependence of the correlation factor on the excess energy $\left(E_f\right)$ and target nuclear charge $\left(Z\right)$. We find that its width has an $E_f^{1∕4}$ dependence near the atomic double-ionization threshold but departs from this law and attains a plateau as the excess energy increases. We compare our results with the predictions of classical and semiclassical Wannier approaches.

A simple treatment is presented to analyze the modulational instability of two-component Bose-Einstein condensates, described within the Gross-Pitaevskii approximation, in a quasi-one-dimensional geometry. An explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed analytically.

We propose a simple experimental scheme of preparing a four-photon entangled state, which is a useful resource for two-qubit quantum operations, e.g., the controlled-NOT gate. The scheme can successfully postselect the events of the desired four-photon entangled state in the coincidence basis and can be constructed with four photons from parametric down conversion, linear optical devices, and conventional photon detectors, all of which are available in current technology. We also show an experimental scheme for a controlled-NOT gate based on teleportation with the prepared four-photon state.

It is possible to tune the scattering length for the collision of ultracold ground-state alkaline-earth-metal atoms using an optical Feshbach resonance. This is achieved with a laser far detuned from an excited molecular level near the frequency of the atomic intercombination transition. Simple resonant-scattering theory, illustrated by the example of , allows an estimate of the magnitude of the effect. Unlike alkali metal species, large changes of the scattering length are possible while atom loss remains small, because of the very narrow linewidth of the molecular photoassociation transition. This raises prospects for control of atomic interactions for a system without magnetically tunable Feshbach resonance levels.

We study a continuous-variable (CV) teleportation protocol based on a shared entangled state produced by the quantum-nondemolition (QND) interaction of two vacuum states. The scheme utilizes the QND interaction or an unbalanced beam splitter in the Bell measurement. It is shown that in the nonunity gain regime the signal transfer coefficient can be enhanced while the conditional variance product remains preserved by applying appropriate local squeezing operation on sender’s part of the shared entangled state. In the unity gain regime, it is demonstrated that the fidelity of teleportation can be increased with the help of the local squeezing operations on parts of the shared entangled state that effectively convert our scheme to the standard CV teleportation scheme. Further, it is proved analytically that such a choice of the local symplectic operations minimizes the noise by which the mean number of photons in the input state is increased during the teleportation. Finally, our analysis reveals that the local symplectic operation on sender’s side can be integrated into the Bell measurement if the interaction constant of the interaction in the Bell measurement can be adjusted properly.

Dynamics based on quantum trajectories with approximate quantum potential is generalized to nonadiabatic systems and its semiclassical properties are discussed. The formulation uses the mixed polar-coordinate space representation of a wave function. The polar part describes the overall time evolution of the wave-function components semiclassically using the single-surface approximate quantum potential. The coordinate part represents a complex“population” amplitude, which in case of localized coupling can be solved for quantum mechanically in an efficient manner. In the high-energy regime this is accomplished by using a small basis determined by the coupling between surfaces. An illustration is given for a typical curve-crossing problem. The energy-resolved probabilities obtained from the time evolution of two wave packets for a wide range of energies are in excellent agreement with exact results for energies above the threshold of the diabatic reaction, including the case of total nonadiabatic transition.

We study a diatomic homonuclear molecule incident upon a potential barrier. We allow transitions between binding energy states of the molecule during the process of tunneling and consider both single and double barriers. By applying an elegant method to solve this system we show that transmission resonances do occur in both cases and that expressions for the locations of the resonances can be found. Moreover, we find that the addition of binding energy levels tends to decrease the probability of tunneling. We also show that by relaxing rigor and treating the length of the molecule as though it is fixed we can obtain exact analytical expressions for the transmission probability that capture important features of the full solution.

We investigate the question as to whether Michelson-type interferometry is possible if the role of the beam splitter is played by a spontaneous process. This question arises from an inspection of trajectories of atoms bouncing inelastically from an evanescent-wave (EW) mirror. Each final velocity can be reached via two possible paths, with a spontaneous Raman transition occurring during either the ingoing or the outgoing part of the trajectory. At first sight, one might expect that the spontaneous character of the Raman transfer would destroy the coherence and thus the interference. We investigated this problem by numerically solving the Schrödinger equation and applying a Monte Carlo wave-function approach. We find interference fringes in velocity space, even when random photon recoils are taken into account.

A Bose-Einstein “double-slit” interferometer has been recently realized experimentally by Y. Shin et al., Phys. Rev. Lett. 92 050405 (2004). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevskii equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong degradation of the interference pattern observed experimentally. The role of quantum fluctuations is discussed.

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.

We examine in detail an alternative method of retrieving the information written into an atomic ensemble of three-level atoms using electromagnetically induced transparency. We find that the behavior of the retrieved pulse is strongly influenced by the relative atom-light coupling strengths of the two relevant transitions. When the individual atom-light coupling strength for the retrieval beam is the stronger of the two transitions, regeneration of the stored pulse is possible. Otherwise, we show the retrieval process can lead to creation of solitonlike pulses.

The measurement-modified decay rate is calculated in two distinct formalisms, i.e., the conventional formalism and the dynamical formalism. The relation between the two formalisms is clarified, by recasting the decay rates obtained by the two formalisms into a unified form. It is shown that the dynamical formalism reproduces the conventional results only under the condition that the apparatus detects the decayed states with an identical response time.