We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.

We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in noninertial frames and in other relativistic quantum-information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximations in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.

We study the discrete-time quantum-walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the position of the marked vertex, in particular, its centrality. We find that the maximum value of the search probability does not necessarily increase as the marked vertex becomes more central, and we investigate an interesting relationship between the frequency of the successful search probability and the centrality of the marked vertex.

We report a combined experimental and theoretical study of collision-induced dipolar relaxation in a cold spin-polarized gas of atomic nitrogen (N). We use buffer gas cooling to create trapped samples of ${}^{14}\mathrm{N}$ and ${}^{15}\mathrm{N}$ atoms with densities $(5\pm 2)\times {10}^{12}\hspace{0.5em}{\mathrm{cm}}^{-3}$ and measure their magnetic relaxation rates at milli-Kelvin temperatures. These measurements, together with rigorous quantum scattering calculations based on accurate ab initio interaction potentials for the ${}^7{\Sigma }_u^{+}$ electronic state of ${\mathrm{N}}_2$ demonstrate that dipolar relaxation in $\mathrm{N}+\mathrm{N}$ collisions occurs at a slow rate of $~{10}^{-13}\hspace{0.5em}{\mathrm{cm}}^3$/s over a wide range of temperatures (1 mK to 1 K) and magnetic fields (10 mT to 2 T). The calculated dipolar relaxation rates are insensitive to small variations of the interaction potential and to the magnitude of the spin-exchange interaction, enabling the accurate calibration of the measured N atom density. We find consistency between the calculated and experimentally determined rates. Our results suggest that N atoms are promising candidates for future experiments on sympathetic cooling of molecules.

Single- and double-ionization processes in ${\mathrm{C}}^{6+}$ collisions with the He atom at an incident energy of $100$ MeV/amu are studied by direct solution of the time-dependent Schrödinger equation. A time-dependent close-coupling method based on an expansion of a one-electron three-dimensional wave function in the field of He${}^{+}$ is used to calculate single-ionization cross sections. A time-dependent close-coupling method based on an expansion of a two-electron six-dimensional wave function in the field of He${}^{2+}$ is used to calculate single- and double-ionization cross sections. Electron energy and angle differential cross sections for single ionization are presented for various projectile impact parameters. For relatively large impact parameters, the differential cross sections are in qualitative agreement with ion-atom experiments. Electron energy and angle differential cross sections for double ionization are also presented for a relatively large projectile impact parameter.

Absolute cross sections for electron-impact dissociation of $X$H${}_2^{+}$ ($X=$ B, C, N, O, F) producing $X$H${}^{+}$ and $X^{+}$ ion fragments were measured in the 3- to 100-eV range using a crossed-electron-ion beams technique. Dissociative excitation of BD${}_2^{+}$ and CH${}_2^{+}$ producing ${\mathrm{B}}^{+}$ and ${\mathrm{C}}^{+}$, respectively, show a propensity toward a two-body dissociation while the remaining species all tend to show a three-body dissociation dynamic. The BD${}^{+}$ and CH${}^{+}$ dissociative excitation channels show a large resonant-type contribution to the cross sections at $~10$ eV. For the $X^{+}$ fragment ion production cross sections, a clear dependence on the threshold energy, as it relates to the rate of rise in the cross section above threshold, is observed.

A strong nonresonant, asymmetric ultrashort pulse drives an atomic transition and causes a complete population inversion because of a sudden nonadiabatic jump. This jump is probed in real time by propagating a weak ultrashort pulse in the system which is resonant on an adjacent transition. The probe at the exit of the medium presents an oscillatory structure with the nonadiabatic jump marked in time by the onset of oscillations. The nonadiabatic jump thus acts as a “turn-on” switch for the shaping of the probe.

Strong-field photoionization of ethane, butane, and octane are reported at intensities from $10$${}^{14}$ to $10$${}^{17}$ W/cm${}^2$. The molecular fragment ions, ${\mathrm{C}}^{+}$ and ${\mathrm{C}}^{2+}$, are created in an intensity window from $10$${}^{14}$ to $10$${}^{15}$ W/cm${}^2$ and have intensity-dependent yields similar to the molecular fragments ${\mathrm{C}}_m$H${}_n^{+}$ and ${\mathrm{C}}_m$H${}_n^{2+}$. In the case of ${\mathrm{C}}^{+}$, the yield is independent of the molecular parent chain length. The ionization of more tightly bound valence electrons in carbon (C${}^{3+}$ and ${\mathrm{C}}^{4+}$) has at least two contributing mechanisms, one influenced by the parent molecule size and one resulting from the tunneling ionization of the carbon ion.

Inner-shell photodetachment from ${\mathrm{Ru}}^{-}$ was studied near and above the $4p$ excitation region, 29-to-91-eV photon energy range, using a merged ion-photon-beam technique. The absolute photodetachment cross sections of ${\mathrm{Ru}}^{-}$ ($[\mathrm{Kr}]4d^{7}5s^2$) leading to ${\mathrm{Ru}}^{+}$, ${\mathrm{Ru}}^{2+}$, and ${\mathrm{Ru}}^{3+}$ ion production were measured. In the near-threshold region, a Wigner $s$-wave law, including estimated postcollision interaction effects, locates the $4p_{3/2}$ detachment threshold between 40.10 and 40.27 eV. Additionally, the ${\mathrm{Ru}}^{2+}$ product spectrum provides evidence for simultaneous two-electron photodetachment (likely to the ${\mathrm{Ru}}^{+}$ $4p^{5}4d^{6}5s^2$ state) located near 49 eV. Resonance effects are observed due to interference between transitions of the $4p$ electrons to the quasibound $4p^{5}4d^{8}5s^2$ states and the $4d\to \varepsilon f$ continuum. Despite the large number of possible terms resulting from the ${\mathrm{Ru}}^{-}$ $4d$ open shell, the cross section obtained from a 51-state $\mathit{LS}$-coupled $R$-matrix calculation agrees qualitatively well with the experimental data.

We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schrödinger (NLSE’s) or Gross-Pitaevskii equations (GPE’s), which are coupled by the linear mixing, with local strength $\Omega$, and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $\Omega$ an odd or even function of the coordinate ($x$). The sign flips of $\Omega (x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $\Omega$. Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system’s parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of $\Omega (x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.

We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states in the presence interactions. For weak interactions, our results coincide with those of Huang and Moore [Y. P. Huang and M. G. Moore, Phys. Rev. Lett. 100, 250406 (2008)], with an optimal initial number variance ${\sigma }_o\propto N^{1/3}$ and an optimal signal-to-noise ratio $s_o\propto N^{2/3}$ for the total atom number $N$. As the interaction strength $u$ increases past unity, phase diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number squeezing to initial phase squeezing with ${\sigma }_o\propto \sqrt{\mathit{uN}}$ and $s_o\propto \sqrt{N/u}$ shot-noise scaling. The initial phase squeezing translates into hold-time number squeezing, which is less sensitive to interactions than coherent states and improves $s_o$ by a factor of $\sqrt{u}$.

We investigate the strongly correlated effect of cold atoms in a triangular optical lattice using the dynamical cluster approximation combined with the continuous-time quantum Monte Carlo method. When the interaction increases, the Fermi surface evolves from a circular ring into a flat plane, and the system transitions from a Fermi liquid into a Mott insulator. The transition between the Fermi liquid and a pseudogap shows a reentrant behavior due to the Kondo effect. We give an experimental protocol to observe these phenomena in future experiments by varying the lattice depth and the atomic interaction via the Feshbach resonance.

Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin-population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature $T_c$. For a harmonically trapped Fermi gas at unitarity, we find that $(T_c){}_{\mathrm{upper}}<T_F$, where $T_F$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.

Classical theories of coherence for statistically stationary, as well as, nonstationary optical fields are frequently discussed both in the space-time and in the space-frequency domains. However, the quantum treatment of coherence theory is generally carried out in the space-time domain. In this paper, we present a quantum-mechanical theory of first-order coherence for statistically nonstationary light in the space-frequency domain.

Two solitons in an optical fiber can form pairs in which the double-humped shape is maintained even when the pair is shifted in frequency by the Raman effect. We show here analytically that this is possible even when the two solitons have unequal power. We discuss the forces that cause relative motion of the two solitons, and determine a condition for balance, i.e., for a pair to maintain their separation while the phase keeps evolving. At a specific parameter point we find a solution in which even the phase profile of the pulse pair is maintained. We then discuss that this special point exists also for multipeak structures, or soliton trains. These trains can move as an entity due to Raman shifting. The results are tested by numerical simulation. A comparison to literature reveals that both the rotating phase pair and the constant phase soliton pair apparently have been seen before by others in numerical simulations. Our treatment provides the general framework.

A recent Brief Report [Zhang et al., Phys. Rev. A 80, 045803 (2009)] presents experimental results in which dark pulses are generated in a fiber laser. Contrary to what is presented, the data published in that Brief Report do not support the claim that the duration of the dark dips are in the 8 ps range and that these pulses are related to genuine dark solitons.

We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom, interacting through collisions with a background ideal gas. When either internal or center-of-mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of internal degrees of freedom on center-of-mass decoherence is considered in this framework.

We have performed measurements of the dissociative electron recombination (DR) of ${\mathrm{H}}_3^{+}$ at the ion storage ring TSR utilizing a supersonic expansion ion source. The ion source has been characterized by continuous wave cavity ring-down spectroscopy. We present high-resolution DR rate coefficients for different nuclear spin modifications of ${\mathrm{H}}_3^{+}$ combined with precise fragment imaging studies of the internal excitation of the ${\mathrm{H}}_3^{+}$ ions inside the storage ring. The measurements resolve changes in the energy dependence between the ortho-${\mathrm{H}}_3^{+}$ and para-${\mathrm{H}}_3^{+}$ rate coefficients at low center-of-mass collision energies. Analysis of the imaging data indicates that the stored ${\mathrm{H}}_3^{+}$ ions may have higher rotational temperatures than previously assumed, most likely due to collisional heating during the extraction of the ions from the ion source. Simulations of the ion extraction shed light on possible origins of the heating process and how to avoid it in future experiments.

The generalized oscillator strengths and differential cross sections for electron-impact excitation of the $A^{\prime }\hspace{0.5em}{}^3{\Delta }_u$, Schumann-Runge continuum, and $E\hspace{0.5em}{}^3{{\Sigma }_u}^{-}({\nu }^{\prime }=0,1)$ states of oxygen have been determined at an incident electron energy of 2.5 keV. Good agreement is found between the present generalized oscillator strengths of the Schumann-Runge continuum and $E\hspace{0.5em}{}^3{{\Sigma }_u}^{-}({\nu }^{\prime }=1)$ states and the previous ones measured at higher impact energies, which indicates that the first Born approximation is satisfied at an impact energy of 400 eV. However, the large difference between the present generalized oscillator strengths of the $A^{\prime }{{}^3\Delta }_u$ and $E\hspace{0.5em}{}^3{{\Sigma }_u}^{-}({\nu }^{\prime }=0)$ states and the previous ones is observed, and the possible reasons are discussed. The $\mathit{BE}$-scaled (binding energy $B$ and excitation energy $E$) or $\mathit{BEf}$-scaled ($B$, $E$, and $f$ values) integral cross sections for the $A^{\prime }{{}^3\Delta }_u$, Schumann-Runge continuum, and $E\hspace{0.5em}{}^3{{\Sigma }_u}^{-}({\nu }^{\prime }=0,1)$ states from its threshold to 5 keV were calculated based on the present generalized oscillator strengths. The present scaled integral cross sections are in good agreement with the previous ones measured at the moderate impact energies except for that of the $A^{\prime }{{}^3\Delta }_u$ state.