An erbium-doped microlaser is demonstrated utilizing $\mathrm{Si}{\mathrm{O}}_2$ microdisk resonators on a silicon chip. Passive microdisk resonators exhibit whispering-gallery-type modes (WGM’s) with intrinsic optical quality factors of up to $6\times {10}^7$ and were doped with trivalent erbium ions (peak concentration $\sim 3.8\times {10}^{20}{\mathrm{cm}}^{-3}$) using MeV ion implantation. Coupling to the fundamental WGM of the microdisk resonator was achieved by using a tapered optical fiber. Upon pumping of the ${}^{4}I_{15∕2}\to {}^{4}I_{13∕2}$ erbium transition at $1450\mathrm{nm}$, a gradual transition from spontaneous to stimulated emission was observed in the $1550\text{−}\mathrm{nm}$ band. Analysis of the pump-output power relation yielded a pump threshold of $43\mu \mathrm{W}$ and allowed measuring the spontaneous emission coupling factor: $\beta \approx 1\times {10}^{-3}$.

A coarse-grained Wigner distribution $p_W(x,\mu )$ obeying positivity derives out of information-theoretic considerations. Let $p(x,\mu )$ be the unknown joint probability density function (PDF) on position and momentum fluctuations $x$, $\mu$ for a particle in a pure state $\psi \left(x\right)$. Suppose that the phase part $\Psi (x,z)$ of its Fourier transform $T_F\left[p\right(x,\mu \left)\right]\equiv \mid G(x,z)\mid \exp \left[i\Psi \right(x,z\left)\right]$ is constructed as a hologram. (Such a hologram is often used in heterodyne interferometry.) Consider a particle randomly illuminating this phase hologram. Let its two position coordinates be measured. Require that the measurements contain an extreme amount of Fisher information about true position, through variation of the phase function $\Psi (x,z)$. The extremum solution gives an output PDF $p(x,\mu )$ that is the convolution of the Wigner $p_W(x,\mu )$ with an instrument function defining uncertainty in either position $x$ or momentum $\mu$. The convolution arises naturally out of the approach, and is one dimensional, in comparison with the ad hoc two-dimensional convolutions usually proposed for coarse graining purposes. The output obeys positivity, as required of a PDF, if the one-dimensional instrument function is sufficiently wide. The result holds for a large class of systems: those whose amplitudes $\psi \left(x\right)$ are the same at their boundaries [examples: states $\psi \left(x\right)$ with positive parity; with periodic boundary conditions; free particle trapped in a box].

By simulating four quantum key distribution (QKD) experiments and analyzing one decoy-state QKD experiment, we compare two data postprocessing schemes based on security against individual attack by Lütkenhaus, and unconditional security analysis by Gottesman-Lo-Lütkenhaus-Preskill. Our results show that these two schemes yield close performances. In QKD, since unconditional security is highly sought after, we conclude that one is better off considering unconditional security, rather than restricting to individual attacks.

We review a number of ideas related to area-law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory, and quantum information. An explicit computation in arbitrary dimensions of the geometric entropy of the ground state of a discretized scalar free field theory shows the expected area law result. In this case, area-law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations. Furthermore, the explicit control on all the eigenvalues of the reduced density matrix allows for a verification of entropy loss along the renormalization group trajectory driven by the mass term. A further result of our computation shows that single-copy entanglement also obeys area law scaling, majorization relations, and decreases along renormalization group flows.

We present an optical module to simulate one step of a quantum walk algorithm. The quantum state of a system with a $2N$-dimensional Hilbert space is encoded in the spatial distribution of the amplitude of the electromagnetic field in a plane. In such spatial encoding, the probability amplitude of each state of a basis is associated with the complex electromagnetic amplitude in a given slice of the laser wave front. We discuss the design and operation of an optical module that is used to implement one step of a quantum walk algorithm. Using this module, composed by standard optical elements, the evolution of the quantum state corresponds to the application of a Hadamard gate on a single qubit (representing the two-dimensional quantum coin) followed by a displacement of the $N$-dimensional quantum walker conditioned on the state of the coin. We show the actual implementation of the method and discuss its characteristics and limitations.

We have demonstrated direct imaging of interference fringes of total atomic density with periods $\lambda ∕4$ and $\lambda ∕2$ for optical wavelength $\lambda$ that have been produced in a de Broglie wave atom interferometer. The imaging was done by means of an “optical mask” technique, which allowed us to observe subwavelength periodic patterns with a resolution of up to $\lambda ∕16$. In addition, the dependence of the fringe pattern on the recoil phase and pulse area reveals quantum dynamics in the atomic center-of-mass motion. The behavior of the fringe patterns near the interference times distinguishes the effects of phase gratings from those of amplitude gratings.

We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after a sudden switch-on or switch-off of the superlattice potential, which can bring the system into insulating or superfluid phases, respectively. A collapse and revival of the zero-momentum peak can be seen in the first case. We study in detail the relaxation of these integrable systems towards equilibrium. We show how after relaxation time averages of physical observables, like the momentum distribution function, can be predicted by means of a generalization of the Gibbs distribution.

The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore, the change in both coherence length and shape of the correlation function, from Gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreement with existing predictions. Experimentalists often define a “quasi-condensate” via bimodal density fits, and this work reveals how consideration of local density-density correlations provides an alternative determination of this quantity.

Recent theoretical and experimental papers have shown how one can achieve Heisenberg-limited measurements by using entangled photons. Here we show how the photons in a noncollinear down-conversion process can be used for improving the sensitivity of magneto-optical rotation by a factor of 4 which takes us towards the Heisenberg limit. Our results apply to sources with arbitrary pumping. We also present several generalizations of earlier results for the collinear geometry. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used.

Millimeter-wave resonance spectroscopy has been used to measure the $(n+2)d_{5∕2}$ to $n{f}_{5∕2,7∕2}$ transition frequencies of cold ${}^{85}\mathrm{Rb}$ atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb $nf$ quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of ${\mathrm{Rb}}^{+}$.

Two XUV-photon double ionization of Kr and Ar by an intense superposition of higher-order harmonics of a Ti:sapphire laser is demonstrated. The logarithm of the ${\mathrm{Kr}}^{2+}$ and ${\mathrm{Ar}}^{2+}$ signals measured as a function of the logarithm of the XUV intensity depicts a linear dependence with a slope of $1.8\pm 0.2$. Under the XUV intensities and photon energies employed, this slope value provides evidence that to the observed double ionization the direct process has a significant contribution. Applications of the above process to attosecond pulse metrology are also discussed.

We study the nonequilibrium evolution of the phase coherence of a Bose-Einstein condensate in a one-dimensional optical lattice as the lattice array is suddenly quenched from a highly-number-squeezed to a superfluid state. We observe slowly damped phase coherence oscillations in the regime of large filling factor ($\sim 100$ bosons per site) at a frequency proportional to the generalized Josephson frequency.

For a generic interferometer, the conditional probability density distribution $p(\varphi \mid m)$, for the phase $\varphi$ given measurement outcome $m$ will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $\mathrm{\Delta }\varphi \sim 1∕\sqrt{N}$ (the standard limit), or $\mathrm{\Delta }\varphi \sim 1∕N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity—the fidelity of an interferometer—defined as the Shannon mutual information between the phase shift $\varphi$ and the measurement outcomes $m$. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. For the case where there exists no a priori information on the phase shift, we find the surprising result that maximally entangled state input leads to a lower fidelity than Fock state input, for the same photon number.

We present the general scheme for construction of noiseless networks detecting entanglement with the help of linear, hermiticity-preserving maps. We show how to apply the method to detect entanglement of an unknown state without its prior reconstruction. In particular, we prove there always exists noiseless network detecting entanglement with the help of positive, but not completely positive maps. Then the generalization of the method to the case of entanglement detection with arbitrary, not necessarily hermiticity-preserving, linear contractions on product states is presented.

We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in nuclear magnetic resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180° rotation in a two spin system. Finally, we show how these two approaches can be combined to produce more accurate frequency selective rotations.

Highly accurate ground-state nonrelativistic variational calculations of ${\mathrm{Ps}}_2$, ${}^1\mathrm{H}\mathrm{Ps}$, and ${}^{\infty }\mathrm{H}\mathrm{Ps}$ are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of the energies obtained are of the order of $4\times {10}^{-10}\mathrm{a.u.}$ for ${\mathrm{Ps}}_2$ and $2\times {10}^{-9}\mathrm{a.u.}$ for HP. Several expectation values have also been computed for each system, as well as electron-positron annihilation rates.

Radioactive beryllium isotope ions (${}^7\mathrm{Be}^{+}$ and ${}^{10}\mathrm{Be}^{+}$) that are provided by a projectile fragment separator with $\approx 1\mathrm{GeV}$ beams, as well as stable isotope ions $\left({}^9\mathrm{Be}^{+}\right)$ are stored and laser cooled in an online ion trap. Their absolute transition energies of the $2s{}^{2}S_{1∕2}\to 2p{}^{2}P_{3∕2}$ transition were measured with an accuracy of $\sim {10}^{-8}$. In this way isotope shifts of beryllium ions were obtained and the differential mass polarization parameter $\kappa =-\mathrm{0.286\hspace{0.17em}41}\left(70\right)\mathrm{a.u.}$ as well as the $2s{}^{2}S\to 2p{}^{2}P$ transition energy of an infinitely heavy beryllium ion $h{\nu }^{\infty }=\mathrm{0.145\hspace{0.17em}524\hspace{0.17em}290}\left(42\right)\mathrm{a.u.}$ were determined for the first time.

We consider the excitation dynamics of the two-photon $1S$-$2S$ transition in a beam of atomic hydrogen by $243\mathrm{nm}$ laser radiation. Specifically, we study the impact of ionization damping on the transition line shape, caused by the possibility of ionization of the $2S$ level by the same laser field. Using a Monte Carlo simulation, we calculate the line shape of the $1S$-$2S$ transition for the experimental geometry used in the two latest absolute frequency measurements [M. Niering et al., Phys. Rev. Lett. 84, 5496 (2000) and M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The calculated line shift and linewidth are in excellent agreement with the experimentally observed values. From this comparison we can verify the values of the dynamic Stark shift coefficient for the $1S$-$2S$ transition for the first time on a level of 15%. We show that the ionization modifies the velocity distribution of the metastable atoms, the line shape of the $1S$-$2S$ transition, and has an influence on the derivation of its absolute frequency.

Charge transfer processes due to collisions of ground state ${\mathrm{Si}}^{3+}\left(3s{}^{1}S\right)$ ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero et al. [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from $0.01\mathrm{eV}∕\mathrm{u}$ to $1\mathrm{MeV}∕\mathrm{u}$. Total and state-selective rate coefficients are also presented for temperatures from $2\times {10}^3\mathrm{K}$ to ${10}^7\mathrm{K}$. Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies.

Bound-state transitions in few-electron, heavy ions following radiative electron capture are studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock approach. Special attention is paid to the $K{\alpha }_1$ $(1s_{1∕2}2p_{3∕2}{}^{1,3}P_{J=1,2}\to 1s_{1∕2}^2{}^{1}S_{J=0})$ radiative decay of heliumlike uranium ${\mathrm{U}}^{90+}$ projectiles. This decay has recently been observed at the GSI facility in Darmstadt, giving rise to a surprisingly isotropic angular distribution, which is inconsistent with previous experiments and calculations based on a “one-particle” model. We show that the unexpected isotropy essentially results from the mutual cancellation of the angular distributions of the ${}^{1}P_1\to {}^{1}S_0$ electric dipole and ${}^{3}P_2\to {}^{1}S_0$ magnetic quadrupole transitions, both of which contribute to the $K{\alpha }_1$ radiation. Detailed computations on the anisotropy of the $K{\alpha }_1$ radiation have been carried out for a wide range of projectile energies and are compared to available experimental data.