A perturbative approach to quantum-state estimation is formulated. Each perturbation simultaneously affects the eigenvalues and eigenvectors of the density matrix. Fast convergence of the proposed algorithm is illustrated on a simple three-dimensional system observed via the process of stimulated Raman adiabatic passage.

The ${}^{6,7}\mathrm{Li}D$ lines were excited using an electro-optically modulated cw dye laser that intersected an atomic beam. Fluorescence was recorded as the laser was scanned across the resonance. Hence each transition was multiply excited allowing for calibration of the frequency scan. The ${}^{6,7}\mathrm{Li}2P$ fine structures were found to be $10052.964\pm 0.050$ and $10053.119\pm 0.058\mathrm{MHz}$. The $D1$ and $D2$ isotope shifts were determined to be $10534.039\pm 0.070$ and $10534.194\pm 0.104\mathrm{MHz}$. The latter imply values for the ${}^{6,7}\mathrm{Li}$ relative nuclear charge radius that are within $20\times {10}^{-3}\mathrm{fm}$ of each other, which is consistent with the estimated uncertainties.

A theory of channel coupling array is developed for rearrangement reactions in Coulomb three-body systems. Inhomogeneous coupled differential equations for the three Faddeev components are derived and directly solved with the technique of complex rotation in the exterior region. This method is applied to slow antiproton collisions with hydrogen atoms. It is found for a collision energy of $6.8\mathrm{eV}$ that the antiproton is captured dominantly into protonium states with the principal quantum numbers around 40 and that the electron is released with energies around $2\mathrm{eV}$. The electron velocity thereby obtained is much higher than the incident velocity of the antiproton. Time-dependent wave-packet propagation of the Faddeev components is also investigated to illustrate the peculiar dynamics.

We report total cross section measurements for positron scattering from carbon dioxide $\left({\mathrm{CO}}_2\right)$. The energy range of the present measurements is $0.1–20.0\mathrm{eV}$. The present study is undertaken to both try and resolve a discrepancy in the literature between the earlier low-energy works of Hoffman et al. [Phys. Rev. A 25, 1393 (1982)] and Kimura et al. [J. Chem. Phys. 107, 6616 (1997)], and to extend the available data to lower energies. We find generally good agreement with the data of Hoffman et al. over the common experimental energy range. A comparison of the present data with available calculations is also made, as is a comparison with corresponding electron total cross section data.

We consider nonzero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase-separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.

The effect of magnetic-field modulation on a Fermi gas of atoms in the BCS-BEC crossover is studied analytically. Recent experimental findings on the system response to a sinusoidal variation of the field are explained. Specifically, the dissociation processes induced by the modulation in the Bose-Einstein condensate regime are described. The role played by the frequency, amplitude, and application time of the perturbation in the emergence of the observed behavior is clarified. The results uncover also the relevance of the detuning from the Feshbach resonance to the appearance of particular spectral features. The applicability of the field modulation as a spectroscopic tool for probing the crossover is discussed.

We propose a scheme for conditional preparation of two-mode correlated photon number states of the form ${\sum }_{m=0}^N{C}_m\mid m{⟩}_1\mid m{⟩}_2$ by using linear optical elements and photon detectors. These states may find applications in testing Bell inequality based on quadrature using quadrature-phase homodyne measurement and optimize some quantum information processing protocols.

We show that any state that violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty relations provide a straightforward construction of nonlinear entanglement witnesses for the cross norm criterion.

We present a complete analytical formalism of the effect of phase dispersion on the Hong-Ou-Mandel dip with cw pumping, including higher-order terms. We show that the Hong-Ou-Mandel dip is strongly modified by the frequency-dependent phase modulation and even becomes a bump when the phase dispersion is a special step function. We also show that the phase dispersion function can be fully reconstructed via Fourier transformation from the measurement result of the Hong-Ou-Mandel dip when the dispersion function is antisymmetric. An experimental demonstration of the proposed method using a bandpass filter as a test sample is also presented.

We show that general Einstein-Podolsky-Rosen-type (EPR-type) entanglement of continuous variables with arbitrary eigenvalues for bosons can be yielded. For bosons of nonzero resting mass EPR-type entangled state can be achieved by the use of atomic beam splitters in particles of a position eigenstate and $n-1$ momentum eigenstates. For light field in which resting mass of the photon is zero, approximate EPR-type entanglement can be experimentally generated when we apply optical beam splitters to one position-squeezed coherence state and $n-1$ momentum-squeezed coherence states, this approximate version tends to perfect EPR entanglement in the limit of infinite squeezing.

We consider the collision model of Ziman et al. and study the robustness of $N$-qubit Greenberger-Horne-Zeilinger (GHZ), $W$, and linear cluster states. Our results show that $N$-qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of $W$ states could be more robust than that of linear cluster states. We indicate that the collision model of Ziman et al. could provide a physical mechanism for some known results in this area of investigation. More importantly, we show that it could give a clue as to how $N$-partite distillable entanglement would be relatively rare in our macroscopic classical world.

We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double-well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through numerical simulations; the operation time is $\sim 10\mathrm{ms}$ with a performance fidelity above 99.9%. For storage of the state between the operations the qubit state can be transferred efficiently via Raman transitions to two hyperfine states, where its decoherence is strongly inhibited. In addition we discuss the limits imposed by the proximity of the surface to the gate fidelity.

The development of high resolution positron beams has enabled measurements of annihilation rates for molecules as a function of incident positron energy. Vibrational Feshbach resonances in these spectra provide evidence for the existence of positron-molecule bound states. In this paper we present further studies of this phenomenon. Evidence is presented for positronically excited bound states (i.e., in addition to the ground state) in ${\mathrm{C}}_{12}{\mathrm{H}}_{26}$ and ${\mathrm{C}}_{14}{\mathrm{H}}_{30}$. Measurements of the annihilation spectra of the halomethanes, $\mathrm{C}{\mathrm{H}}_3\mathrm{F}$, $\mathrm{C}{\mathrm{H}}_3\mathrm{Cl}$, and $\mathrm{C}{\mathrm{H}}_3\mathrm{Br}$, exhibit strong resonances that vary significantly with the substituted halogen. Annihilation spectra for linear alkanes and ring molecules are compared. Annihilation spectra and infrared absorption spectra are compared for a number of molecules. Finally, annihilation rate measurements are presented for a variety of molecules at energies $⩾0.5\mathrm{eV}$ (i.e., above the vibrational resonances). These provide a measure of the annihilation rates in the absence of vibrational resonances.

We study Bragg spectroscopy of strongly interacting one-dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently introduced extended fermionization model. We find that, due to the system’s inhomogeneity, the excitation spectrum exhibits a multibranched structure, whose origin is related to the presence of superfluid regions with different densities in the atomic distribution. We thus suggest that Bragg spectroscopy in the linear regime can be used as an experimental tool to unveil the shell structure of alternating Mott insulator and superfluid phases characteristic of trapped bosons.

We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm requires just a few incident photons and is thus suitable for very sensitive pictures (similar to the Elitzur-Vaidman problem). Furthermore, for a $2^n\times 2^m$ image, $O(n+m)$ qubits are sufficient. Using the quantum Fourier transform, it is possible to improve the fault tolerance of the quantum algorithm by filtering out small-scale noise in the picture. For example images with $512\times 512$ pixels, we have numerically simulated the unitary operations in order to demonstrate the applicability of the algorithm and to analyze its fault tolerance.

We investigate the enhancement of the intracavity entanglement of a self-phase-locked type-II nondegenerate optical parameter oscillator (SPL NOPO) via homodyne-mediated quantum feedback. It is found that the feedback can effectively enhance the squeezing, entanglement, and purity of the two-mode field in the SPL NOPO. Especially for an ordinary NOPO, our feedback scheme can simulate a standard two-mode squeezed vacuum environment and a pure steady two-mode squeezed vacuum cavity field can be generated, different from the scheme proposed by Mancini [Phys. Rev. A 73, 010304(R) (2006)] in which only a mixed two-mode entangled state is generated.

A classical nonsignaling (or causal) box is an operation on classical bipartite input with classical bipartite output such that no signal can be sent from a party to the other through the use of the box. The quantum counterpart of such boxes, i.e., completely positive trace-preserving maps on bipartite states, though studied in literature, have been investigated less intensively than classical boxes. We present here some results and remarks about such maps. In particular, we analyze: the relations among properties as causality, nonlocality and entanglement; the connection between causal and entanglement breaking maps; the characterization of causal maps in terms of the classification of states with fixed reductions. We also provide proofs of the fact that every nonproduct unitary transformation is not causal, as well as for the equivalence of the so-called semicausality and semilocalizability properties.

We address the information–disturbance tradeoff for state measurements on continuous variable Gaussian systems and suggest minimal schemes for implementations. In our schemes, the symbols from a given alphabet are encoded in a set of Gaussian signals which are coupled to a probe excited in a known state. After the interaction the probe is measured, in order to infer the transmitted state, while the conditional state of the signal is left for the subsequent user. The schemes are minimal, i.e., involve a single additional probe, and allow for the nondemolitive transmission of a continuous real alphabet over a quantum channel. The tradeoff between information gain and state disturbance is quantified by fidelities and, after optimization with respect to the measurement, analyzed in terms of the energy carried by the signal and the probe. We found that transmission fidelity only depends on the energy of the signal and the probe, whereas estimation fidelity also depends on the alphabet size and the measurement gain. Increasing the probe energy does not necessarily lead to a better tradeoff, the most relevant parameter being the ratio between the alphabet size and the signal width, which in turn determine the allocation of the signal energy.

We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of $n$ qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of $k$ qudits. We give a formula for the probability of successful decoding.

Absolute photoionization cross sections for ${\mathrm{Kr}}^{5+}$ were measured in the photon energy range $74–175\mathrm{eV}$ using synchrotron radiation. For comparison, a detailed energy scan of the electron-impact ionization cross section was made in the same energy range and normalized to previously published absolute measurements. The Flexible Atomic Code and Cowan atomic structure code were used to calculate energy levels, excitation energies, and oscillator strengths for $3d\to np$, $3\mathrm{d}\to nf$, and $4s\to np$ autoionizing transitions from the ground and metastable states. Within the experimental uncertainty, oscillator strengths determined from the photoionization measurements are in agreement with both calculations. Excitation-autoionization and resonant excitation-double-autoionization features are evident in the electron-impact ionization cross section.