Entanglement purification allows the creation of qubit pairs of arbitrarily high fidelity with respect to a maximally entangled state, starting from a larger number of low-fidelity pairs. Purification requires quantum memory, a role for which electron spins are well suited. However, using existing recurrence protocols involving symmetric local two-qubit operations for spin qubits turns out to be rather unpractical. We present an efficient purification protocol requiring only a single pulsed Heisenberg- or XY-type exchange interaction between two qubit pairs. In contrast to known protocols, we allow for asymmetric bilateral two-qubit operations where the two communication parties operate differently on their qubits. In the optimal version of our protocol, the local two-qubit interactions in the case of Heisenberg exchange correspond to the $\sqrt{swap}$ gate and its inverse.

The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.

In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in Li et al. [H.-W. Li, P. Mironowicz, M. Pawłowski, Z.-Q. Yin, Y.-C. Wu, S. Wang, W. Chen, H.-G. Hu, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 87, 020302(R) (2013)]. This method allows us to lower bound, with semi-definite programming, the randomness obtained from random number generators based on dimension witnesses. We also investigate the robustness of some randomness expanders using this method. We show the role of an assumption about the trace of the measurement operators and a way to avoid it. The method is also generalized to systems of arbitrary dimension and for a more general form of dimension witnesses than in our previous paper. Finally, we introduce a procedure of dimension witness reduction, which can be used to obtain from an existing witness a new one with a higher amount of certifiable randomness. The presented methods find an application for experiments [J. Ahrens, P. Badziag, M. Pawlowski, M. Zukowski, and M. Bourennane, Phys. Rev. Lett. 112, 140401 (2014)].

We perform spectroscopy on the optical dipole transitions $5s5p{}^3{P}_2–5snd{}^3{D}_{1,2,3}$, $n\in (5,6)$, for all stable isotopes of atomic strontium. We develop a spectroscopy scheme in which atoms in the metastable ${}^3{P}_2$ state are stored in a reservoir before being probed. The method presented here increases the attained precision and accuracy by two orders of magnitude compared to similar experiments performed in a magneto-optical trap or discharge. We show how the state distribution and velocity spread of atoms in the reservoir can be tailored to increase the spectroscopy performance. The absolute transition frequencies are measured with an accuracy of 5 MHz. The isotope shifts are given to within 200 kHz. We calculate the $A$ and $Q$ parameters for the hyperfine structure of the fermionic isotope at the MHz level. Furthermore, we investigate the branching ratios of the ${}^3{D}_J$ states into the ${}^3{P}_J$ states and discuss immediate implications on schemes of optical pumping and fluorescence detection.

The results of a theoretical investigation of prompt many-body ionization are reported. Our calculations address an experiment that reported ionization in Rydberg gases for densities two orders of magnitude less than expected from ionization between pairs of atoms. The authors argued that the results were due to the simultaneous interaction between many atoms. We performed classical calculations for many interacting Rydberg atoms with the ions fixed in space and have found that the many-atom interaction does allow ionization at lower densities than estimates from two-atom interactions. However, we found that the density fluctuations in a gas play a larger role. These two effects are an order of magnitude too small to account for the experimental results suggesting at least one other mechanism strongly affects ionization.

We study the spin-orbit-coupled ultracold Bose-Einstein condensate placed in a single-mode Fabry-Pérot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized modified Bose-Hubbard model whose zero-temperature phase diagram can be controlled by tuning the cavity parameters. In the noninteracting limit, where the atom-atom interaction is set to 0, the resulting atomic dispersion shows interesting features such as a bosonic analog of Dirac points, a cavity-controlled Hofstadter spectrum which bears the hallmark of pseudospin-1/2 bosons in the presence of Abelian and non-Abelian gauge fields (the latter due to spin-orbit coupling) in a cavity-induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose-Hubbard model of spin-orbit-coupled bosons in a classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be detected from the cavity transmission. This provides an alternative approach to detecting quantum magnetism in ultracold atoms. We discuss the effects of cavity-induced optical bistability on these phases and their experimental consequences.

We suggest a method to generate coherent short pulses by generating a frequency comb using lasing without inversion in the transient regime. We use a universal method to study the propagation of a pulse in various spectral regions through an active medium that is strongly driven on a low-frequency transition on a time scale shorter than the decoherence time. The results show gain on the sidebands at different modes can be produced even if there is no initial population inversion prepared. Besides the production of ultrashort pulses this frequency comb may have applications towards making short-wavelength or terahertz lasers.

In this paper we consider a two-dimensional quantum-state metamaterial comprising an array of qubits (two-level quantum objects). Here we propose that it should be possible to manipulate the propagation of quantum information. We show that a quantum metamaterial such as the one considered here exhibits several different modes of operation, which we have termed Aharonov-Bohm, intermediate, and quantum-Zeno. We also see interesting behavior which could be thought of as either quantum birefringence (where the material acts like a beam splitter) as well as the emergence of quantum correlations in the circuit's measurement statistics. Quantum-state metamaterials as proposed here may be fabricated from a variety of technologies from superconducting qubits to quantum dots and would be readily testable in existing state-of-the-art laboratories.

We study theoretically the nonlinear polarization dynamics of vertical-cavity surface-emitting lasers in the presence of an external cavity providing delayed optical feedback and cross-polarized reinjection. We show that, far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Poincaré sphere with a fixed radius. It entails that the evolution of the system is described by two phase variables: the orientation phase of the quasilinear polarization and the optical phase of the field. We explore the complex modal structure given by the double reinjection configuration and how it evolves between the cases of single cross-polarized reinjection and single optical feedback, hence disclosing the relationship with the Lang-Kobayashi model. We also reinterpret the square-wave switching observed by J. Mulet et al. [Phys. Rev. A 76, 043801 (2007)] in terms of phase kinks.

We discover long-lived (microsecond-scale) optical waveguiding in the wake of atmospheric laser filaments. We also observe the formation and then outward propagation of the consequent sound wave. These effects may be used for remote induction of atmospheric long-lived optical structures from afar which could serve for a variety of applications.

The Hamiltonian for a $\mathcal{PT}$-symmetric chain of coupled oscillators is constructed. It is shown that if the loss-gain parameter $\gamma$ is uniform for all oscillators, then as the number of oscillators increases, the region of unbroken $\mathcal{PT}$ symmetry disappears entirely. However, if $\gamma$ is localized in the sense that it decreases for more distant oscillators, then the unbroken $\mathcal{PT}$-symmetric region persists even as the number of oscillators approaches infinity. In the continuum limit the oscillator system is described by a $\mathcal{PT}$-symmetric pair of wave equations, and a localized loss-gain impurity leads to a pseudobound state. It is also shown that a planar configuration of coupled oscillators can have multiple disconnected regions of unbroken $\mathcal{PT}$ symmetry.

We investigate the role of electron-correlation effects in calculations of the electric-dipole polarizabilities $\alpha$ of elements belonging to three different groups (12–14) of the periodic table. To understand the propagation of the electron-correlation effects at different levels of approximations, we employ the relativistic many-body methods developed, based on first principles, at mean-field Dirac–Fock (DF), third-order many-body perturbation theory [MBPT(3)], random-phase approximation (RPA), and singly and doubly approximated coupled-cluster methods at the linearized (LCCSD) and nonlinearized (CCSD) levels. We observe a variance in the trends of the contributions of the correlation effects in a particular group of elements through the many-body method used; however, they resemble a similar tendency among the iso-electronic systems. Our CCSD results are within sub-1% agreement with the experimental values which are further ameliorated by including the contributions from the important triple excitations (${\mathrm{CCSD}}_p\mathrm{T}$ method).

We consider the behavior of Fermi atoms on optical superlattices with two-well structure for each node. Fermions on such lattices serve as an analog simulator of the Fermi-type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate $d$-electron compounds. The appropriate effective spin-orbital model appears to be a modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of the fermion arrangement on phases of complex hopping amplitudes is illustrated.

We present a coupled-pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of $N$ particles. A stochastically variational Gaussian expansion method is applied, focusing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The ground-state energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations.

Ionizing 800-nm femtosecond laser pulses propagating in silica glass and in potassium dihydrogen phosphate (KDP) crystal are investigated by means of a unidirectional pulse propagation code. Filamentation in fused silica is compared with the self-channeling of light in KDP accounting for the presence of defect states and electron-hole dynamics. In KDP, laser pulses produce intense filaments with higher clamping intensities up to 200 ${\mathrm{TW}/\mathrm{cm}}^2$ and longer plasma channels with electron densities above ${10}^{16}$ ${\mathrm{cm}}^{-3}$. Despite these differences, the propagation dynamics in silica and KDP are almost identical at equivalent ratios of input power over the critical power for self-focusing.

We study the dynamics of extended collective excitations in the pristine honeycomb lattice in the presence of the cubic nonlinearity. We show that not only band-gap excitations but also, stable and quasistable, extended excitations between the two lowest bands of the honeycomb system and labeled as in band exist. We also show that some solutions bifurcate from the saddle points of the Floquet band structure. Among other results, we report the existence of nontrivial stationary solutions even for the Floquet eigenvalue where the Dirac points occur. Numerical findings, in fair agreement with our theoretical predictions, are also reported.

Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play a crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for well-known catlike and compasslike states, in the rotating Morse system where sub-Planck scale structures originate in the dynamics of a suitably constructed SU(2) coherent state. A detail study of the sensitivity analysis reveals that rotational coupling in the vibrational wave packet can be used as a probe to enhance the sensitivity limit in a diatomic molecule. The maximum sensitivity limit is identified with the rotational amendment, and a quantitative measure of the angle of rotation for different rotational levels is also given. The correspondence of the numerical result with the angle of rotation is also delineated in phase-space Wigner representation.

A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Applications of quantum channels are most likely to be commercially important only in the multiparty regime, where such a correspondence does not exist even for pure quantum states. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits are the same as those of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of the former is the same as or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy-channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administration of a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.

The Anderson Talman theory of spectral line broadening is used together with potential energy curves calculated at the spin-orbit multi-reference configuration interaction level to compute broadening, shifting, and asymmetry coefficients of the $D_1$ and $D_2$ lines of alkali-metal atoms M, as they collide with noble gas atoms N, where $M=\mathrm{K},$ Rb, and Cs, and $N=\mathrm{He}$, Ne, and Ar. Our calculated coefficients are compared to experimental results for a variety of temperatures. In all cases general agreement is observed for the broadening coefficients, while significant disagreement is observed for the shifting coefficients. We also compare our $\mathrm{K}+\mathrm{He}$ broadening and shifting results with fully quantum-mechanical calculations that employ the Baranger theory of collisional line broadening, and we compare our results with other semiclassical calculations. As with the comparison to experiment, closer agreement is observed for the broadening coefficients while the shifting coefficients exhibit significant disagreement. We use the natural variation between the difference potentials of the nine $M+N$ pairs to explore the relationship between potential and line shape as determined by Anderson-Talman theory and develop a picture for the mechanism that underlies the general agreement between theoretical and experimental results on the broadening coefficient and the general disagreement on shifting coefficients.

We have extended the $ab$ $initio$ convergent close-coupling method to electron scattering from the vibrationally excited molecular hydrogen ion and its isotopologues. Calculations have been performed within the adiabatic-nuclei approximation. Results are presented for dissociative excitation and ionization as a function of the initial vibrational state of the molecules. Comparison with experiment is excellent across the energy range from near threshold to 1 keV.