We demonstrate numerically the efficient generation of vortices in Bose-Einstein condensates (BECs) by using a “phase imprinting” method. The method consists of passing a far-off-resonant laser pulse through an absorption plate with an azimuthally dependent absorption coefficient, imaging the laser beam onto a BEC, and thus creating the corresponding nondissipative Stark-shift potential and condensate phase shift. In our calculations we take into account experimental imperfections. We also propose an interference method to detect vortices by coherently pushing part of the condensate using optically induced Bragg scattering.

We demonstrate that a Bose-Einstein condensate that interacts with a standing wave in a cavity shows the same Bragg oscillations as a single atom. This may serve as a basis for the construction of a beam splitter for condensates. The setup is compared with the beam splitter for condensates based on a standing laser wave.

Random chaotic relaxation oscillation burst generations have been observed in laser-diode-pumped microchip multimode lasers coupled to a single-mode optical fiber. Dynamical characterizations have been carried out by the singular value decomposition method and the joint time-frequency analysis, and the observed instability has been identified to be a random switching between stable and chaotic operation.

Rarely occurring single-photon electronic transitions in the Raman-driven quantized motion of a trapped ion are considered. Using a quantum trajectory approach it is demonstrated that these transitions, which are usually ignored, may cause significant quantum decoherence effects. In addition, we find an asymmetric evolution in the Wigner function due to induced transitions of a nonsymmetric type.

The state of a signal-idler photon pair of spontaneous parametric down-conversion is a typical nonlocal entangled pure state with zero entropy. The precise correlation of the subsystems is completely described by the state. However, it is an experimental choice to study only one subsystem and to ignore the other. What can we learn about the measured subsystem? Results of this kind of measurements look peculiar. The experiment confirms that the two subsystems are both in mixed states with entropy greater than zero. One can only obtain statistical knowledge of the subsystems in this kind of measurement.

An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase-space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an operational positive operator-valued measure in phase space is introduced and investigated. In such an operational formalism a quantum-mechanical time operator is constructed and analyzed. A phase-space time and energy uncertainty relation is derived.

We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical linear-quadratic-Gaussian control theory with residual feedback.

We find an analogy between turbulence and the dynamics of the continuous spontaneous localization model (CSL) of the wave function. The use of a standard white noise in the localization process gives Richardson’s $t^3$ law for the turbulent diffusion, while the introduction of an affine noise in the CSL allows us to obtain the intermittency corrections to this law.

A method is presented for reconstructing the quantum state of vibrational wave packets in diatomic molecules by a heterodyne experiment. After the preparation of a wave packet, a femtosecond laser pulse interferes with the induced polarization and the resulting signal is frequency filtered and measured by a photodetector. The conditions are analyzed under which the resulting time- and frequency-resolved photocurrent contains the information needed to recover the quantum state of the prepared wave packet. It is shown that the vibrational wave function in the excited electronic state can be measured directly without the need of involved numerical reconstruction. Simulations of the proposed experiment are performed for sodium dimers.

The inconsistency between quantum mechanics and Einstein-Podolsky-Rosen assumptions about locality and reality cannot be avoided by restricting attention to correlations. This is demonstrated by reworking the logical scheme that was developed to show inconsistency without inequalities for two particles, adapting it to correlations in two pairs of particles, so the Einstein-Podolsky-Rosen arguments can be made entirely in terms of correlations. A simple example is given.

We define a class of Lorentz-invariant Bohmian quantum models for N entangled but noninteracting Dirac particles. Lorentz invariance is achieved for these models through the incorporation of an additional dynamical space-time structure provided by a foliation of space time. These models can be regarded as the extension of Bohm’s model for N Dirac particles, corresponding to the foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to more general foliations. As with Bohm’s model, there exists for these models an equivariant measure on the leaves of the foliation. This makes possible a simple statistical analysis of position correlations analogous to the equilibrium analysis for (the nonrelativistic) Bohmian mechanics.

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of $k$ parties hold some partial input data to some fixed $k$-variable function $f.\mathrm{}$ The communication complexity of $f$ is the minimum number of classical bits required to be broadcasted for every party to know the value of $f$ on their inputs. We construct a function $G$ such that for the one-round communication model and three parties, $G$ can be computed with $n+1\mathrm{}$ bits of communication when the parties share prior entanglement. We then show that without entangled particles, the one-round communication complexity of $G$ is $\mathrm{}(3/2)n+1.\mathrm{}$ Next we generalize this function to a function $F.\mathrm{}$ We show that if the parties share prior quantum entanglement, then the communication complexity of $F$ is exactly $k.\mathrm{}$ We also show that, if no entangled particles are provided, then the communication complexity of $F$ is roughly $k{\log }_{2}k.\mathrm{}$ These two results prove communication complexity separations better than a constant number of bits.

Grover’s algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First-order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked states. These equations are solved exactly. New expressions are derived for the optimal time of measurement and the maximal probability of success. They are found to depend on the averages and variances of the initial amplitude distributions of the marked and unmarked states, but not on higher moments. Our results imply that Grover’s algorithm is robust against modest noise in the amplitude initialization procedure.

I show that for any number of oracle lookups up to about $\pi /4\mathrm{}\sqrt{N},$ Grover’s quantum searching algorithm gives the maximal possible probability of finding the desired element. I explain why this is also true for quantum algorithms which use measurements during the computation. I also show that unfortunately quantum searching cannot be parallelized better than by assigning different parts of the search space to independent quantum computers.

The teleportation of the signal beam of a parametric amplifier is considered, and its entanglement with the idler beam before and after the teleportation process is computed. A criterion based on homodyne measurements is proposed to discount purely classical effects, and it is suggested that the preservation of the Einstein-Podolsky-Rosen correlations during teleportation may be verified experimentally.

We show how to teleport a running-wave superposition of zero- and one-photon field states through the projection-synthesis technique. The fidelity of the scheme is computed taking into account the noise introduced by dissipation and the efficiency of the detectors. These error sources have been introduced through a single general relationship between input and output operators.

We study the mapping that occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system that, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two two-dimensional Hilbert spaces. We exhibit quantum circuits that can reproduce the results of any two-qubit copying machine of this type. A simple stochastic generalization (using a classical random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.

Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit (qubit) conditional on the state of the remaining qubits in the system. We show that such selective gates, termed $(\mathrm{controlled}{)}^n-\mathrm{NOT}$ gates, or ${\mathrm{c}}^n-\mathrm{NOT}$ gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of ${\mathrm{c}}^n-\mathrm{NOT}$ gates for any number of control spins. In this work, a catalog of ${\mathrm{c}}^n-\mathrm{NOT}$ gates for systems of as many as 16 spins is provided along with an experimental implementation of a ${\mathrm{c}}^3-\mathrm{N}\mathrm{O}\mathrm{T}$ gate on a four spin system, ${}^{13}\mathrm{C}$ alanine.

The results of ab initio calculations of electric-dipole amplitudes, lifetimes, and polarizabilities for several low-lying levels of ytterbium are reported. The effective Hamiltonian for two valence electrons $H_{\mathrm{eff}}$ was constructed by means of the many-body perturbation theory and solutions of the two-electron equation $H_{\mathrm{eff}}{\Phi }_n{=E}_n{\Phi }_n$ were found.

A generalized Franck-Condon (GFC) principle for resonant x-ray Raman scattering and for resonant photoemission in particular is derived and numerically investigated. The GFC amplitudes differ from ordinary FC amplitudes by the presence of photon and photoelectron phase factors which describe the coupling—or interference—of the x-ray photons or Auger electrons with the nuclear motion. With the GFC amplitudes, a Kramers-Heisenberg relation is obtained for vibronic transitions that corrects the so-called lifetime-vibrational interference formula. For resonant photoemission in the soft-x-ray region involving typical bound potential surfaces, the generalization gives a contribution to the FC factors that can amount to 20%. For core excitation above the dissociation threshold, the GFC principle relates to Doppler effects on the ejected photoelectron both for the so-called “molecular” and “atomic” bands. The role of the GFC principle in direct photoionization is briefly discussed.