A geometric interpretation for the $A$ fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the $A$ fidelity are studied by the numerical method. An alternative generalization of the $A$ fidelity, which has the same geometric picture, to an $N$-state quantum system is also discussed.

We demonstrate weak and strong regimes of optical spatial turbulence by considering the nonlinear interaction of three partially coherent spatial beams. The geometry represents a multiple bump-on-tail instability, allowing an interpretation of nonlinear statistical light as a photonic plasma. For weak nonlinearity, we observe instability competition and sequential flattening of the bumps in momentum space, with no observable variations in position-space intensity. For strong nonlinearity, intensity modulations appear and the triple-hump spectrum merges into a single-peaked profile with an algebraic $k^{-2}$ inertial range. This spectrum, with its associated modulations, is a definitive observation of soliton, or Langmuir, turbulence.

$p\text{−}\mathrm{Ar}$ collisions are investigated theoretically and experimentally at impact energies in the keV regime. Total cross sections for double electron capture of $p$ on Ar are calculated by an independent-particle method in the impact energy range $3–100\mathrm{keV}$. We have measured the absolute differential and total cross sections for double electron capture for $1.0–5.0\text{−}\mathrm{keV}$ $p\text{−}\mathrm{Ar}$ collisions. The absolute differential cross section (DCS) for all the collision energies considered shows a decreasing behavior with increasing angle, exhibiting an overall decrease of three orders of magnitude. The integrated DCS is found to be between the range of $0.7\times {10}^{-2}$ and $4.5\times {10}^{-2}{\mathrm{\AA }}^2$, displays an increasing behavior as a function of the incident energy, and merges with previous data at the high-energy side. The theoretical total cross sections reproduce the structures around $5\mathrm{keV}$ and $15\mathrm{keV}$ reported by other available measurements. The analysis of the capture into the $1s^{1}4s^1$ hydrogen-like configuration points in the direction of a common origin for these peaks.

Cavity quantum electrodynamic schemes for quantum gates are amongst the earliest quantum computing proposals. Despite continued progress and the recent demonstration of photon blockade, there are still issues with optimal coupling and gate operation involving high-quality cavities. Here we show that dynamic cavity control allows for scalable cavity-QED based quantum gates using the full cavity bandwidth. This technique allows an order of magnitude increase in operating speed, and two orders reduction in cavity $Q$, over passive systems. Our method exploits Stark shift–based $Q$ switching, and is ideally suited to solid-state integrated optical approaches to quantum computing.

One of the primary goals of information theory is to provide limits on the amount of information one can send through communication channels, and to understand encoding methods that achieve such limits. The discovery of dense coding showed that quantum channels can transmit twice as much classical information than is possible with a classical channel. This optimal rate requires using quantum systems maximally entangled between sender and receiver, and then the sender can encode her messages using unitary operations. The use of nonmaximally entangled systems has been intensively studied in recent years, and it has appeared as though unitary encoding might well be optimal in all cases. Indeed, this optimality of unitary operations has been found to hold under far more general conditions. Nonetheless, we here present numerical evidence supported by analytical arguments that there exist circumstances where more classical information can be encoded using nonunitary, rather than unitary, operations.

We report measured and calculated cross sections for elastic scattering of low-energy electrons by the alcohols $n$-propanol and $n$-butanol in the gas phase. The measurements were carried out using the relative-flow method with an aperture source rather than a conventional tube or capillary-array source, eliminating the need to know molecular diameters. The calculations employed two different implementations of the Schwinger multichannel variational method and included polarization effects. The differential cross sections are dominated by strong forward scattering due to the molecules’ large electric dipole moments, but near $10\mathrm{eV}$, they display structure at intermediate angles that is probably associated with shape resonances, notably a pronounced $f$-wave scattering pattern. Overall agreement between the measured and calculated results is fair. We compare the cross sections of these larger alcohols to those of methanol and ethanol, as well as to those of alkanes.

We present an ab initio study of the ground state of an ideal coupled two-component gas of ultracold atoms in a one-dimensional optical lattice, either bosons or fermions. Due to the internal two-level structure of the atoms, the Brillouin zone is twice as large as imposed by the periodicity of the lattice potential. This is reflected in the Bloch dispersion curves, where the energy bands regularly possess several local minima. As a consequence, when the system parameters are tuned across a resonance condition, a nonzero temperature phase transition occurs, which arises from an interplay between internal and kinetic atomic energies. For fermions, this phase transition is of topological character since the structure of the Fermi surface is changed across the critical value. It is shown that these phenomena are also expected to occur for two- and three-dimensional optical lattices.

We address the dynamics of fundamental and higher-order dark solitons on the intense parabolic background in a planar graded-index waveguide with self-defocusing nonlinearity. It is shown that dark solitons on the parabolic background can propagate stably, and feature the properties similar to dark solitons for standard nonlinear Schrödinger equation. We present an approximate solution for dark soliton on a parabolic background, and discuss its motion trajectory. In addition, the interaction between neighboring dark solitons on parabolic background is investigated.

In this paper, a quantum secure direct communication protocol with $\chi$-type entangled states ${\mid {\chi }^{00}⟩}_{3214}$ is proposed. We analyze the security of this protocol and prove that it is secure in ideal conditions. Then, an alternative way is presented to ensure the security of this protocol in a noisy channel. Moreover, this protocol utilizes quantum superdense coding to achieve a high intrinsic efficiency and source capacity. The practical implementation of this protocol is also discussed.

Both analytical and numerical investigation of the structural features of ultrashort-laser-pulse self-focusing is presented. The analysis is performed under sufficiently general assumptions concerning the medium dispersion. It is demonstrated that the wave-field self-focusing proceeds with overtaking the steepening of the pulse longitudinal profile and shock-wave formation. As a result, a more complex singularity is formed where an unlimited field increase is followed by wave breaking with a broad power-law pulse spectrum.

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement $M$ and preparation $\rho$ the experimenter can determine, given enough time, the probability of a given outcome $a$: $p(a\mid M,\rho )$. How large does the Hilbert space of the quantum system have to be in order to allow us to find density matrices and measurement operators that will reproduce the given probability distribution? In this paper, we prove a simple lower bound for the dimension of the Hilbert space. The main insight is to relate this problem to the construction of quantum random access codes, for which interesting bounds on the Hilbert space dimension already exist. We discuss several applications of our result to hidden-variable or ontological models, to Bell inequalities, and to properties of the smooth min-entropy.

We describe a method for determining the radiative decay properties of a molecule by studying the saturation of laser-induced fluorescence and the associated power broadening of spectral lines. The fluorescence saturates because the molecules decay to states that are not resonant with the laser. The amplitudes and widths of two hyperfine components of a spectral line are measured over a range of laser intensities and the results compared to a model of the laser-molecule interaction. Using this method we measure the lifetime of the $A(v^{\prime }=0)$ state of CaF to be $\tau =19.2\pm 0.7\mathrm{ns}$, and the Franck-Condon factor for the transition to the $X(v=0)$ state to be $Z={0.987}_{-0.019}^{+0.013}$. In addition, our analysis provides a measure of the hyperfine interval in the lowest-lying state of $A(v^{\prime }=0)$, ${\Delta }_e=4.8\pm 1.1\mathrm{MHz}$.

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an $R$-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of $R$-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking into regard the dipole-dipole (DD) and contact interactions. The model is based on the discrete nonlinear Schrödinger equation with an additional nonlocal term accounting for the DD interactions. The existence and stability of fundamental unstaggered solitons are studied for attractive and repulsive signs of both the local and nonlocal interactions. The DD forces strongly affect the shape and stability of on-site and intersite discrete solitons. The corresponding existence and stability regions in the parametric space are summarized in the form of diagrams, which feature a multiple stability exchange between the on-site and intersite families; in the limit of the dominating DD attraction, the on-site solitons are stable, while their intersite counterparts are not. We also demonstrate that the DD interactions reduce the Peierls-Nabarro barrier and enhance the mobility of the discrete solitons.

We study the stability of the paired fermionic $p$-wave superfluid made out of identical atoms all in the same hyperfine state close to a $p$-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a three-dimensional superfluid, in particular, we show that it decays at the same rate as its interaction energy, which may preclude its equilibration before it decays. Then we proceed to study its stability in the case when the superfluid is confined to two dimension (2D) by means of an optical harmonic potential. We find that the relative stability is improved in 2D in the BCS regime, such that the decay rate is now parametrically slower than the appropriate interaction energy scale, leading to the possibility of an equilibrated $p$-wave superfluid in 2D.

We investigate the tunneling properties of a bound pair of Fermi atoms in an optical lattice, comparing with results obtained in an attractive Hubbard model. In the strong-coupling regime of the Hubbard model, it has been predicted that the motion of a bound pair between lattice sites is accompanied by virtual dissociation. To explore the possibility of this interesting phenomenon in an optical lattice, we calculate the molecular wave function in a cosine-shaped periodic potential. We show that the molecular tunneling accompanied by dissociation occurs in the intermediate-coupling regime of the optical-lattice system. In the strong-coupling regime, in contrast to the prediction in the Hubbard model, the bound pair is shown to tunnel through the lattice potential without dissociation. As a result, the magnitude of the molecular band mass $M$ remains finite even in the strong-coupling limit, which is in contrast to the diverging molecular mass in the case of the Hubbard model. Including this finite value of the molecular band mass, we evaluate the superfluid phase transition temperature $T_{\mathrm{c}}$ in the Bose-Einstein-condensate limit of the optical-lattice system, where the Hubbard model gives $T_{\mathrm{c}}=0$ due to the diverging molecular mass.

We investigate the interaction between a single photon and a chain of $N$ equally spaced two-level atoms inside a one-dimensional waveguide. By solving the eigenvectors of the Hamiltonian in the subspace with a single excitation, we address quantum interference effects in two physical processes. First, we analyze the scattering of a single photon when atoms are all initially at their ground states. We discover a set of transmission peaks determined by $N$. These transmission peaks are narrow and sensitive to the relative position between atoms. Second, we examine the spontaneous emission of a photon from an excited atom in the chain in vacuum. The characteristic atomic decay rates are found to be enhanced and reduced by increasing the number of atoms. In particular, the slowest decay rate scales approximately as $N^{-3}$.

Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for noncommuting observables form a subset of these inequalities. In addition, criterion of positivity under partial transposition (PPT) imposes distinct bounds on moments, violations of which signal entanglement. We present bounds on some sets of composite moments, consequent to positive partial transposition of the density operator and report their violation by entangled multiqubit states. In particular, we derive separability bounds on a multiqubit moment matrix (based on PPT constraints on bipartite divisions of the density matrix) and show that three-qubit pure states with nonzero tangle violate these PPT moment constraints. Further, we recover a necessary and sufficient condition of separability in a multiqubit Werner state through PPT bounds on moments.

We study encodings that give the best-known thresholds for the nonzero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that Pauli noise is correctable up to the hashing bound. For a depolarizing channel, this approach allows one to achieve a nonzero capacity for a fidelity (probability of no error) of $f=0.80870$.