The maximally connected state (MCS) which was first introduced by Briegel and Raussendorf [Phys. Rev. Lett. 86, 910 (2001)] has many interesting properties in quantum information theory. Many important states that we are focusing on currently are included in this special set of states. To decide whether a state is a MCS or not is the main problem concerned in this paper. In this paper, (1) we give a general criterion for MCS; (2) when the ranks of all of the two-qubit reduced density matrices are two, we give a convenient criterion.

In this paper we employ a circulating ring of trapped atoms, that we have named the atomotron, to study cold collisions. The atomotron is obtained from a conventional magneto-optical trap when the two pairs of normally retroreflecting Gaussian laser beams in the $x\text{−}y$ plane are slightly offset. Circulating stable atomic orbits then form a racetrack geometry in this plane. The circulating atom flux behaves similarly to an atomic beam with an average tangential velocity much greater than the transverse components, and is therefore suitable for one-dimensional atomic collision studies. Using the atomotron, we have investigated the polarization dependence of ultracold photoassociation collisions between Rb atoms circulating in the racetrack. The ability to investigate collisions in ultracold circulating atomic rings reveals alignment and orientation properties that are averaged away in ordinary three-dimensional magneto-optical trap collision processes.

The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving (PNC) amplitude in cesium and francium is evaluated to all orders in $\alpha Z$ using a local form of the Dirac-Fock potential. The calculations are performed in both length and velocity gauges for the absorbed photon and the total binding QED correction is found to be $-0.27\left(3\right)\%$ for Cs and $-0.28\left(5\right)\%$ for Fr. Moreover, a high-precision calculation of the electron-correlation and Breit-interaction effects on the $7s\text{−}8s$ PNC amplitude in francium using a large-scale configuration-interaction Dirac-Fock method is performed. The obtained results are employed to improve the theoretical predictions for the PNC transition amplitude in Cs and Fr. Using an average value from two most accurate measurements of the vector transition polarizability, the weak charge of ${}^{133}\mathrm{Cs}$ is derived to amount to $Q_W=-72.65{\left(29\right)}_{\exp }{\left(36\right)}_{\mathrm{theor}}$. This value deviates by $1.1\sigma$ from the prediction of the standard model. The values of the $7s\text{−}8s$ PNC amplitude in ${}^{223}\mathrm{Fr}$ and ${}^{210}\mathrm{Fr}$ are obtained to be $-15.49\left(15\right)$ and $-14.16\left(14\right)$, respectively, in units of $i\times {10}^{-11}(-Q_W)∕N\mathrm{a.u.}$

It has been shown that finding generic Bell-state diagonal-entanglement witnesses for $d_1\otimes d_2\otimes \cdots \otimes d_n$ systems reduces to linear programming if the feasible region is a polygon by itself, and it can be solved approximately via linear programming if the feasible region is encircled by a polygon. Since solving linear programming for the generic case is difficult, multiqubit, $2\otimes N$ and $3\otimes 3$ systems for the special case of generic Bell-state diagonal-entanglement witnesses for some particular choice of parameters have been considered. We obtain the optimal nondecomposable entanglement witness for a $3\otimes 3$ system for some particular choice of parameters. By proving the optimality of the well-known reduction map and combining it with the optimal and nondecomposable $3\otimes 3$ Bell-state diagonal-entanglement witnesses (named critical entanglement witnesses) the family of optimal and nondecomposable $3\otimes 3$ Bell-state diagonal-entanglement witnesses has also been obtained. Using the approximately critical entanglement witnesses, some $3\otimes 3$ bound entangled states are so detected. So the well-known Choi map as a particular case of the positive map in connection with this witness via Jamiolkowski isomorphism has been considered.

We give full account of our recent report in E. A. Galapon, R. Caballar, and R. Bahague, Phys. Rev. Lett. 93, 180406 (2004), where it is shown that formulating the free quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding a complete set of states that evolve to unitarily arrive at a given point at a definite time. For a spatially confined particle, here it is shown explicitly that the problem admits a solution in the form of an eigenvalue problem of a class of compact and self-adjoint time of arrival operators derived by a quantization of the classical time of arrival. The eigenfunctions of these operators are numerically demonstrated to unitarily arrive at the origin at their respective eigenvalues.

The use of Bayes theorem in quantum mechanics is discussed. It is shown that the quantum Bayes theorem follows from the ordinary quantum measurement theory, when applied to density operators that represent our knowledge of a system. The examples studied involve measurements on multiple copies of the same (unknown) state. The theorem is used to determine the unknown state by successive measurements on several of the copies of the state. An idealized information-theoretic description of propagating CW laser beams is treated in detail. It is shown how photon detections on part of the beams can be used to determine the phase of the rest of the beams. Also discussed, are the limitations on the accuracy of the phase determination that follow from the fact that it is accomplished by the detection of a finite number of photons. Explicit expressions are derived for the conditional probabilities of detecting photons at different locations, given the numbers of photons detected in the past. The quantitative predictions could be used, in principle, to test proposed quantum states of propagating laser beams.

We investigate the effects of fuzzy measurements on spin entanglement for identical particles, both fermions and bosons. We first consider an ideal measurement apparatus and define operators that detect the symmetry of the spatial and spin part of the density matrix as a function of particle distance. Then, moving on to realistic devices that can only detect the position of the particle to within a certain spread, it was surprisingly found that the entanglement between particles increases with the broadening of detection.

The intermediate quantum states of multiple qubits, generated during the operation of Shor’s factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated during the preprocessing stage of the algorithm and remains nearly constant during the quantum Fourier transform stage. The entanglement is found to be correlated with the speedup achieved by the quantum algorithm compared to classical algorithms.

We present a process for the construction of a SWAP gate which does not require a composition of elementary gates from a universal set. We propose to employ direct techniques adapted to the preparation of this specific gate. The mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided.

Reionization of an ion colliding with a solid surface is possible when the atomic level of the ion crosses the Fermi level of the surface. We use a recently reported soluble model to show that a shift of the atomic level above the Fermi level comparable to the surface bandwidth leads to oscillations in the ion survival probability, even when Stueckelberg oscillations are absent. The competing mechanisms responsible for this interesting oscillatory behavior are elucidated and related to a previously unexpected interference between the initially full and empty metallic states.

A demonstration of coherent quantum control for ultrafast precise selection of closely-lying states is reported. A phase-locked pair of femtosecond laser pulses is generated through a pulse shaper to excite the ground-state cesium atom to the $\mathrm{Cs}\left(7D_{3∕2}\right)$ and $\mathrm{Cs}\left(7D_{5∕2}\right)$ states by two-photon absorption. The excited state population is measured by detecting fluorescence from each spin-orbit state. By controlling the phase-difference of the pulse pair, an ultrafast precise selection is accomplished. The contrast ratio of the maximal to minimal selection ratio exceeds ${10}^3$ with the delay less than $400\mathrm{fs}$.

The eigenvalue problem for the dressed bound state of unstable multilevel systems is examined both outside and inside the continuum, based on the $N$-level Friedrichs model, which describes the couplings between the discrete levels and the continuous spectrum. It is shown that a bound-state eigenenergy always exists below each of the discrete levels that lie outside the continuum. Furthermore, by strengthening the couplings gradually, the eigenenergy corresponding to each of the discrete levels inside the continuum finally emerges. On the other hand, the absence of the eigenenergy inside the continuum is proved in weak but finite coupling regimes, provided that each of the form factors that determine the transition between some definite level and the continuum does not vanish at that energy level. An application to the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field is demonstrated.

A liquid-crystal-based, laser-pulse shaper has been used in combination with an adaptive genetic feedback algorithm to investigate closed-loop control of intense laser fragmentation of ${\mathrm{S}}_8$ molecules. We observe that the yield ratios $\mathrm{S}_N{}^{+}:\mathrm{S}_M{}^{+}$, for the production of specific charged fragments $\mathrm{S}_N{}^{+}$ and $\mathrm{S}_M{}^{+}$, can be enhanced by $>300\%$ relative to those observed using transform-limited $150\text{−}\mathrm{fs}$ laser pulses. We have explored the effectiveness of time- and frequency-domain pulse parametrizations while shaping either (i) only the spectral-phase distribution or (ii) the spectral-phase and amplitude distributions of the light. We find that pulse complexity, requiring control beyond simple manipulation of the peak pulse intensity and duration, is critical for optimizing the yield ratios for most species. The “optimum” pulse shapes obtained using different pulse parametrizations show significant differences while yielding similar signal enhancements. In some cases, comparison of the different optimum pulse shapes appears to be a useful method for identifying pulse traits that are, or are not, important for manipulating a particular yield ratio. The importance of specific traits in the optimum pulse shapes is also explored numerically using principal control analysis. We conclude that closed-loop control can be effective for optimizing highly nonlinear strong-field processes. However, in general, intensity variations in a focused laser beam severely limit one’s ability to associate the optimization results with specific dynamical mechanisms that bear primary responsibility for the control.

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67–12.00 fs, and the peak power 25–6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into “bidirectional propagation equations” which are derived directly from Maxwell’s equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schrödinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, both theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.

We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an $800\mathrm{nm}$ laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths.

We present a new set of generators for unitary maps over ${\mathbb{C}}^2$ which differs from the traditional rotation-based generating set in that it uses a single-parameter family of unitaries $J\left(\alpha \right)$. These generators are implementable in the one-way model [Raussendorf and Briegel, Phys. Rev. Lett. 86, 5188 (2001)] using only two qubits, and lead to both parsimonious and robust implementations of general unitaries. As an illustration, we give an implementation of the controlled-$U$ family which uses only 14 qubits, and has a 2-colorable underlying entanglement graph (known to yield robust entangled states).

We have observed the diffraction of a Bose-Einstein condensate of rubidium atoms on a vibrating mirror potential. The matter wave packet bounces back at normal incidence on a blue-detuned evanescent light field after a $3.6\mathrm{mm}$ free fall. The mirror vibrates at a frequency of $500\mathrm{kHz}$ with an amplitude of $3\mathrm{nm}$. The atomic carrier and side bands are directly imaged during their ballistic expansion. The locations and the relative weights of the diffracted atomic wave packets are in very good agreement with the theoretical prediction of Henkel et al. [J. Phys. II 4, 1877 (1994)].

A fully quantum-mechanical theory is presented for the interaction of quantized electromagnetic field with a two-level atom immersed in an isotropic moving causal permeable medium. The time dependence of the atom-field system is obtained in interaction picture. Special attention is paid to the decay rate and the quantum electrodynamics level shift of the atom. Due to the velocity of the medium, the atom experiences an anisotropic characteristic behavior from the background medium. To illuminate this effect, we calculate the torque experienced by a two-level atom.

Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an $\left(N_a\right)$th-order differential equation in time, where $N_a$ is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-$\frac{1}{2}$ meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.