We provide an analytical description of the entanglement dynamics of two qubits coupled to a common structured reservoir at zero temperature. We derive the conditions to maximize reservoir-induced entanglement for an initially factorized state of the two-qubit system. In particular, when the two qubits are placed inside a lossy cavity, we show that high values of entanglement can be obtained, even in the bad-cavity limit, in the dispersive regime. Finally we show that, under certain conditions, the entanglement dynamics exhibits quantum beats and we explain their physical origin in terms of the interference between two different transitions coupling the dressed states of the system.

We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the braiding gates for two qubits exhaust the entire two-qubit Clifford group. Analyzing the structure of the Clifford group for $n\ge 3$ qubits we prove that the image of the braid group is a nontrivial subgroup of the Clifford group so that not all Clifford gates could be implemented by braiding in the Ising topological quantum computation scheme. We also point out which Clifford gates cannot in general be realized by braiding.

The method of reduced-added Green’s function in quantum defect approximation [V. E. Chernov, D. L. Dorofeev, I. Yu. Kretinin, and B. A. Zon, Phys. Rev. A 71, 022505 (2005)] is generalized for calculation of dynamic polarizabilities of nonpolar molecules. The method is applied to alkali-metal dimers ${\text{Li}}_2$, ${\text{Na}}_2$, and ${\text{Rb}}_2$. The accuracy achieved in benchmark calculation (${\text{H}}_2$ molecule) is comparable to that of ab initio calculations.

Differential cross sections (DCSs) are presented for electron-impact excitation of the $C{}^3\Pi _u$, $E{}^3\Sigma _g^{+}$, and $a^{″}{}^1\Sigma _g^{+}$ states in ${\mathrm{N}}_2$ from the $X{}^1\Sigma _g^{+}(v^{″}=0)$ ground-state level. The DCSs were obtained from measurements of energy-loss spectra in the region of 10.75 to $12.75\mathrm{eV}$ measured at incident energies of 13, 15, 17.5, 20, 25, 30, 50, and $100\mathrm{eV}$, and for scattering angles ranging from 5° to 130°. The results are compared with existing measurements.

Vibrationally resolved differential cross sections (DCSs) for electron impact from the $X{}^1\Sigma _g^{+}(v^{″}=0)$ ground-state level in ${\mathrm{N}}_2$ are presented for excitation of the $C{}^3\Pi _u\left(v^{\prime }\right)$ state, where $v^{\prime }=0$, 1, 2, 3, and 4. DCSs for the full $C{}^3\Pi _u\left(v^{\prime }\right)$ state, where $v^{\prime }=0–4$, are also presented. The vibrationally resolved DCSs were obtained from energy-loss spectra in the region of $10.75\text{to}12.75\mathrm{eV}$ measured at incident energies of 13, 15, 17.5, 20, 25, 30, 50, and $100\mathrm{eV}$ and for scattering angles ranging from 5° to 130°. Relative excitation probabilities for the vibrational levels of the $C{}^3\Pi _u$ state are shown to demonstrate non-Franck-Condon behavior for excitation energies less than approximately $50\mathrm{eV}$. These results are compared with existing measurements.

We compare the generation of coherent extreme ultraviolet (xuv) photons in argon from three different high-order harmonic sources: a semi-infinite gas cell, a finite gas cell, and a pulsed valve. We demonstrate photoionization of the background gas by the coherent xuv photons as an alternative to xuv spectroscopy for real-time and in-line monitoring of the high-order harmonics. Using this technique for measuring photocurrent, we show that the gas cells produce 50–100-fold brighter harmonics than the pulsed valve, with an estimated conversion efficiency of ${10}^{-4}$. The spectral distribution of the harmonics produced in the gas cells peaks at the 27th harmonic compared to the 19th harmonic in the pulsed valve. We attribute this difference to the interplay between phase matching and absorption.

We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both $s$-wave and $p$-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor in the lowest Landau level and in terms of the ratio between $s$- and $p$-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or composed of spin-singlets. In the regime with no phase separation, we give evidence for fractional quantum Hall states. Most notably, we find two distinct singlet states at the filling $\nu =2/3$ for different interactions. One of these states is accounted for by the composite fermion theory, while the other one is a paired state for which we identify two competing descriptions with different topological structures. This paired state may be an Abelian liquid of composite spin-singlet Bose molecules with Laughlin correlations. Alternatively, it may be a known non-Abelian paired state, indicated by good overlaps with the corresponding trial wave function. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for $\nu =1/2$ and the permanent state of Moore and Read for $\nu =1$. For purely repulsive interactions, we also find evidence for a gapped Halperin state at $\nu =2/5$.

We present a scheme to realize a large cross-phase-modulation between two slow optical pulses by using the atomic configurations of coupled double dark resonances. In this scheme slow group velocities for these optical pulses can be automatically equalized in terms of the inherent symmetric atomic configuration, and the various absorptions can be overcome by using three-photon hyper-Raman amplification. Additionally, the switching between cross-type nonlinear amplification and absorption could be realized by just changing the sign of the difference between two pump detunings. This is useful for the implementations of all-optical switches. The linearity and cross nonlinearity in the Doppler-broadened medium with different laser propagating configurations have also been investigated.

A comparative study for the electron capture process ${\text{O}}^{+}\left({{}^{4}S}^0,{{}^{2}D}^0,{{}^{2}P}^0\right)+\text{He}\to \text{O}\left({}^{3}P\right)+{\text{He}}^{+}$ is reported. The cross sections are calculated using fully quantal and semiclassical molecular-orbital close-coupling (MOCC) approaches in the adiabatic representation. Detailed comparison of transition probabilities and cross sections is made from both MOCC approaches and displays close agreement above $\sim 125\text{eV}/\text{u}$. The remarkable discrepancies between the earlier semiclassical and quantal MOCC approaches may be attributed to the insufficient step-size resolution in their semiclassical calculation [M. Kimura et al., Phys. Rev. A 50, 4854 (1994)]. Our results have also been compared with experiment and found to be in good agreement.

Phase shift differences and ratios of radial dipole matrix elements of the outgoing $S$ and $D$ continuum waves from state-selected helium atoms are directly measured from the photoelectron angular distributions using pump-probe velocity map imaging. Aligned $1s3p$ ${}^{1}P_1$ and $1s4p$ ${}^{1}P_1$ states in helium are prepared by high-order harmonics and ionized with either 800, 400, or $267\mathrm{nm}$ light. The results allow for the determination of energy-dependent quantum defect differences and ratios of partial cross sections and agree favorably with theoretical calculations on electron scattering and photoionization.

Final-state probabilities are determined for different atomic fragments arising in the $\left({}^3\text{H}\text{e},n;p,t\right)$ reactions with slow neutrons. We consider the $\left({}^3\text{H}\text{e},n;p,t\right)$ reactions in the one-electron ${{}^3\text{H}\text{e}}^{+}$ ion and in the two-electron ${}^3\text{H}\text{e}$ atom. It is shown that highly exothermic nuclear reactions in light nuclei can be used as a very effective tool to study the electron-density distribution in light atoms and its redistribution during such reactions. The idea of bremsstrahlung amplifiers based on the $\left(n,Q;q_1,q_2\right)$ reactions in accelerated many-electron ions is proposed.

We report on precision laser spectroscopy of the ${{}^{2}S}_{1/2}\left(F=0\right)\text{−}{{}^{2}F}_{7/2}\left(F=3,m_F=0\right)$ clock transition in a single ion of ${{}^{171}\text{Y}\text{b}}^{+}$. A linewidth of $<40\text{Hz}$ is observed and frequency instability due to fluctuation of the ac Stark shift is reduced through improved stability of the beam alignment. The absolute value of the transition frequency, determined using an optical frequency comb, is $642121496772657\pm 12\text{Hz}$ with a fractional uncertainty of $2\times {10}^{-14}$. This is a factor of 50 better than the previously published value [Hosaka et al., IEEE Trans. Instrum. Meas. 54, 759 (2005)].

Motivated by an earlier proposal of splitting a one-dimensional atomic wave packet using two translating traps [Zhang et al., Phys. Rev. Lett. 97, 070403 (2006)], we report results of simulating the splitting dynamics for a three-dimensional Bose-Einstein condensate at zero temperature. Different from the single-atom case where the population in one of the traps shows full oscillations as a function of the translating velocity, we find that such oscillations are damped as the translating velocity decreases. As the interaction increases, we see a stronger damping effect. The damping mechanism is attributed to the formation of solitons which decay to vortex rings and cause complicated flow patterns to damp the population oscillations. Our conclusions are supported by results for $N=5400$ and $N=54000$ ${}^{87}\text{R}\text{b}$ atoms. In the adiabatically translating regime, the condensate can only be split 50:50. Therefore, a controlled splitting of the condensate in two symmetric traps can only be realized for a small number of atoms and away from the adiabatic regime.

The three types of defects—microcavity (linear media without resonant nanoparticles), groove (the defect span with reduced density of nanoparticles), and stripe (the defect with high density of resonant atoms)—are discussed here. The nonlinear polariton transmission, reflection, and trapping by defects in the resonantly absorbing Bragg grating (RABG) are demonstrated by numerical simulations. A geometric optics interpretation is proposed to estimate the solitary polaritonic wave velocity inside wide defects such as grooves and stripes when the reflection on the interface between the RABG and a defect is negligible. The values of solitary wave velocity calculated from geometric optics approximation gives a good agreement with the values computed numerically. It is shown that the electromagnetic field propagating through RABG can be captured inside the microcavity placed in the RABG.

A six-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum, and the indistinguishable emission produced by a two-crystal system operating with type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a witness criterion specifically presented for hyperentangled states. The experiment represents a realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given $2^3\times 2^3$ Hilbert space.

We consider a particle in the harmonic approximation coupled linearly to an environment modeled by an infinite set of harmonic oscillators. The system (particle environment) is considered in a cavity at thermal equilibrium. We employ the recently introduced notion of renormalized coordinates to investigate the time evolution of the particle occupation number. For comparison, we first present this study in bare coordinates. For a long elapsed time, in both approaches, the occupation number of the particle becomes independent of its initial value. The value of the occupation number of the particle is the physically expected one at the given temperature. So we have a Markovian process, describing the particle thermalization with the environment. With renormalized coordinates, no renormalization procedure is required, leading directly to a finite result.

We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while higher orders involve other multifractal exponents. These results can be applied to entanglement behavior near the Anderson transition.

We study the explicit relation between violation of Bell inequalities and bipartite distillability of multiqubit states. It has been shown that even though for $N\ge 8$ there exist $N$-qubit bound entangled states which violates a Bell inequality [W. Dür, Rev. Lett. 87, 230402 (2001)], for all the states violating the inequality there exists at least one splitting of the parties into two groups such that pure-state entanglement can be distilled [A. Acín, Rev. Lett. 88, 027901 (2002)]. We here prove that for all $N$-qubit states violating the inequality the number of distillable bipartite splits increases exponentially with $N$, and hence the probability that a randomly chosen bipartite split is distillable approaches 1 exponentially with $N$, as $N$ tends to infinity. We also show that there exists at least one $N$-qubit bound entangled state violating the inequality if and only if $N\ge 6$.

We study the modification by the presence of a plane wall of energy-level shifts of two-level atoms which are in multipolar coupling with quantized electromagnetic fields in a thermal bath in a formalism which separates the contributions of thermal fluctuations and radiation reaction and allows a distinct treatment to atoms in the ground and excited states. The position-dependent energy shifts give rise to an induced force acting on the atoms. We are able to identify three different regimes where the force shows distinct features and examine, in all regimes, the behaviors of this force in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, thus providing some physical insights into the atom-wall interaction at finite temperature. In particular, we show that both the magnitude and the direction of the force acting on an atom may have a clear dependence on the atomic polarization directions. In certain cases, a change in relative ratio of polarizations in different directions may result in a change in direction of the force.

We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra-atomic and interatomic interaction, the system is exactly solvable. Thus the exact ground-state wave-function and density distributions for the whole interacting regime can be obtained from the Bethe ansatz solutions. Since the ground state is a degenerate state with total spin $S=N/2$, the total density distributions are the same for each degenerate state. The total density distribution evolves from a Gauss-like Bose distribution to a Fermi-like one as the repulsive interaction increases. The distribution of each component is $N_{\alpha }/N$ of the total density distribution. This is approximately true even in the experimental situation. In addition the numerical results show that with the increase in interspecies interaction the distributions of two Tonks-Girardeau gases exhibit composite-fermionization crossover with each component developing $N$ peaks in the strongly interacting regime.