The average entanglement of random pure states of an $N\times N$ composite system is analyzed. We compute the average value of the determinant $D$ of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant, we characterize the probability distribution $P\left(D\right)$. Similar results are obtained for the rescaled $N\text{th}$ root of the determinant, called the $G$ concurrence. We show that in the limit $N\to \infty$ this quantity becomes concentrated at a single point $G_{\star }=1∕e$. The position of the concentration point changes if one consider an arbitrary $N\times K$ bipartite system, in the joint limit $N,K\to \infty$, with $K∕N$ fixed.

We analyze application of bright reference pulses to prevent the photon-number-splitting attack in weak-pulse quantum key distribution. Under the analyzed eavesdropping strategy, the optimal parameters of bright reference and signal pulses can ensure a secure transmission distance up to $146\mathrm{km}$. To realize the quantum key distribution scenario with up-present techniques, we present an experimentally feasible scheme to create a large splitting ratio between bright reference and signal pulses, and to switch the bright reference pulses away from signal pulses to avoid the after-pulse disturbance.

The dynamical entanglement of two stretching vibrations of triatomic molecules ${\mathrm{H}}_2\mathrm{O}$ and $\mathrm{S}{\mathrm{O}}_2$ in an algebraic model is studied in terms of the reduced-density linear entropy with initial states that are, respectively, taken to be the product of Fock states and coherent states on each bond. It is shown that the entanglement of initial states with local-mode character is regular while that of states with normal-mode character is irregular. For initial coherent states with a small amplitude, the regularity of the entanglement with a long period appears in $\mathrm{S}{\mathrm{O}}_2$ and “classical” beat phenomena of the entanglement happens in ${\mathrm{H}}_2\mathrm{O}$, where the period of the beat is longer. Those long periods of the entanglement indicate that the entanglement sustains long enough so that quantum information process and quantum computation could be accomplished.

We present a frequency metrology study on the lowest rotational levels of the hydrogen $EF{}^1\Sigma _{\mathit{g}}^{+}\leftarrow X{}^1\Sigma _{\mathit{g}}^{+}(0,0)$ two-photon transition near $202\mathrm{nm}$. For this purpose, the fourth harmonic of an injection-seeded titanium:sapphire pulsed oscillator is employed in a Doppler-free REMPI-detection scheme on a molecular beam of hydrogen. A frequency comb laser is used to perform the absolute frequency calibration on the continuous-wave (CW) laser that injection-seeds the oscillator. Chirp-induced frequency differences between the output of the pulsed oscillator and the seeding light are monitored on-line, while possible systematic shifts related to the AC-Stark and Doppler effects are addressed in detail. The transition frequencies of the $Q\left(0\right)$ to $Q\left(2\right)$ lines in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, and the $Q\left(0\right)$ and $Q\left(1\right)$ lines in HD are determined with an absolute accuracy at the ${10}^{-9}$ level.

We performed two-color resonance ionization spectroscopy to study the highly excited states of hafnium. We obtained the high-resolution spectra of the Rydberg series converging to the first ionization limit. These series of states have not been previously observed. From analyses of the main Rydberg series with Rydberg formula, we derived the ionization potential of hafnium as $55047.9\pm 0.1{\mathrm{cm}}^{-1}$. Comparing the spectra obtained through three different intermediate states, we could assign the $J$ value of all the series in a certain energy region.

We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozières and Schmitt-Rink, we use this definition of ${\rho }_s$ to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap $\Delta$, the chemical potential $\mu$, and ${\rho }_s$ all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density ${\rho }_n\equiv n-{\rho }_s$ naturally separates into a sum of contributions from Fermi BCS quasiparticles $\left({\rho }_n^F\right)$ and Bose collective modes $\left({\rho }_n^B\right)$. The expression for ${\rho }_n^F$ is just Landau’s formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution ${\rho }_n^B$ is more complicated and only reduces to Landau’s formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate are undamped. In a companion paper, we present numerical calculations of ${\rho }_s$ using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.

A three-level EIT (electromagnetically induced transparency) vapor is used to manipulate the transparency and absorption properties of the probe light in a waveguide. The most remarkable feature of the present scheme is such that the optical responses resulting from both electromagnetically induced transparency and large spontaneous emission enhancement are very sensitive to the frequency detunings of the probe light as well as to the small changes of the waveguide dimension. The potential applications of the dimension- and dispersion-sensitive EIT responses are discussed, and the sensitivity limits of some waveguide-based sensors, including electric absorption modulator, optical switch, wavelength sensor, and sensitive magnetometer, are analyzed.

We introduce a positive linear map for a single qubit. This map is a decay only in population of a single-qubit density operator. It is shown that an $n$-fold product of this map may be used for detection of $n$-partite inseparability of an $n$-qubit density operator (i.e., detection of the impossibility of representing a density operator in the form of a convex combination of products of density operators of individual qubits). This product map is also investigated in relation to a variant of the entanglement detection method mentioned by Laskowski and Żukowski.

We have used the distorted-wave Born approximation method to analyze the recently reported $(e,2e)$ experimental results on sodium and potassium atoms in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50 and $60\mathrm{eV}$. Post-collision interaction is included through an angle-dependent effective charge model using two different approximations. Our theoretical results are found to qualitatively reproduce the reported experimental data.

Using a recently developed procedure—multiple wave packet decomposition—here we study the phase time formulation for tunneling or reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties which frequently arise when the stationary phase method is employed for deriving phase (tunneling) time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and an one-dimensional rectangular potential barrier. Summing the amplitudes of the reflected and transmitted waves—using a method we call multiple peak decomposition—is shown to allow reconstruction of the scattered wave packets in a way which allows the stationary phase principle to be recovered.

We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell’s inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an $N$-qubit GHZ state with even $N$ is extremely persistent against dephasing.

Generation and characterization of entanglement are crucial tasks in quantum information processing. A hypothesis testing scheme for entanglement has been formulated. Three designs were proposed to test the entangled photon states created by the spontaneous parametric down conversion. The time allocations between the measurement vectors were designed to consider the anisotropic deviation of the generated photon states from the maximally entangled states. The designs were evaluated in terms of the $p$ value based on the observed data. It has been experimentally demonstrated that the optimal time allocation between the coincidence and anticoincidence measurement vectors improves the entanglement test. A further improvement is also experimentally demonstrated by optimizing the time allocation between the anticoincidence vectors. Analysis on the data obtained in the experiment verified the advantage of the entanglement test designed by the optimal time allocation.

We have studied the spectral features of Cl $L_{\mathrm{II},\mathrm{III}}$ resonant x-ray Raman scattering of HCl molecules in gas phase both experimentally and theoretically. The theory, formulated in the intermediate-coupling scheme, takes into account the spin-orbital and molecular-field splittings in the Cl $2p$ shells, as well as the Coulomb interaction of the core hole with unoccupied molecular orbitals. Experiment and theory display nondispersive dissociative peaks formed by decay transitions in both molecular and dissociative regions. The molecular and atomic peaks collapse in a single narrow resonance because the dissociative potentials of core-excited and final states are parallel to each other along the whole pathway of the nuclear wave packet.

The cross sections of the title reactions were calculated as functions of collision energy in the range $0.2–2.4\mathrm{eV}$ on a potential energy surface of Panda and Sathyamurthy [J. Chem. Phys. 121, 9343 (2004)]. The calculated results with the Coriolis coupled method were found to be more consistent with the experimental ones than the centrifugal sudden approximation, thus suggesting that Coriolis coupling plays an important role in those reactions. A pronounced isotopic effect was also revealed and attributed to the significant difference of the effective potential barrier height in both reactions.

Slow collisions of electrons with Rydberg sodium atoms have been quantum mechanically investigated by using the time-dependent close-coupling (TDCC) method. To make such large-scale calculations possible, it is essential to implement the TDCC method with the powerful finite-element discrete variable representation (FEDVR). Besides visualizing the slow collision dynamics, our quantum calculations show interesting features in the slow electron impact ionization of Rydberg atoms. The energy sharing between two continuum electrons changes dramatically as the incoming electron energy decreases. Predominant equal-energy sharing is observed in such a cold $(e,2e)$ process, even though the impact electron energy is still twice the binding energy of the Rydberg electron.

The output of a photodetector consists of a current pulse whose charge has the statistical distribution of the actual photon numbers convolved with a Bernoulli distribution. Photodetectors are characterized by a nonunit quantum efficiency, i.e., not all the photons lead to a charge, and by a finite resolution, i.e., a different number of detected photons leads to a discriminable values of the charge only up to a maximum value. We present a detailed comparison, based on Monte Carlo simulated experiments and real data, among the performances of detectors with different upper limits of counting capability. In our scheme the inversion of Bernoulli convolution is performed by maximum-likelihood methods assisted by measurements taken at different quantum efficiencies. We show that detectors that are only able to discriminate between zero, one and more than one detected photons are generally enough to provide a reliable reconstruction of the photon number distribution for single-peaked distributions, while detectors with higher resolution limits do not lead to further improvements. In addition, we demonstrate that, for semiclassical states, even on/off detectors are enough to provide a good reconstruction. Finally, we show that a reliable reconstruction of multipeaked distributions requires either higher quantum efficiency or higher resolution.

We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from $0.2\text{to}2.7\mathrm{mm}$. The oscillations in visibility depend predictably on the wavelength of incident electrons. This verifies that $5\mathrm{keV}$ electrons diffracted by nanostructures remain coherent after propagating farther than the Talbot length, and hence proves that a Talbot-Lau interferometer for electrons can be built with nanostructure gratings. Distorted fringes due to a phase object are used to demonstrate an application for this type of electron interferometer.

Decoherence causes the decay of the quantum information that is stored in highly correlated states during quantum computation. It is thus a limiting factor for all implementations of a quantum computer. Because a scalable quantum computer with hundreds or thousands of qubits is not available yet, experimental data about decoherence rates was restricted to small quantum registers. With solid state nuclear magnetic resonance we create highly correlated multiqubit states that serve as a model quantum register and measure their decay. By measuring the decay as a function of the system size, we determined the scaling of the decoherence rate with the number of qubits. Using the same system, we also used decoupling techniques to reduce the coupling between system and environment and thereby the decoherence rate by more than an order of magnitude, independent of the system size. For the free decay as well as for the decoupled case, we found a relatively weak scaling with system size, which could be fitted to a power law $\propto {\overline{K}}^p$ with an exponent $p\approx 1∕2$. This raises the prospect for large-scale quantum computation.