We study the optimal generation of entanglement between two qubits subject to local unitary control. With only the assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagin minimum principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement. Unlike previous analyses of the entanglement generation process, our model considers an arbitrary interaction time, and it is possible to account for the energy cost associated with the controls. We can arbitrarily choose the relative weight between a large entanglement and a small energy cost.

By investigating the evolution of a moving spin-$\frac{1}{2}$ Dirac electron coupled with a background magnetic noise, we demonstrate that the effects of special relativity will significantly modify the decoherence properties of the spin state. The dephasing could be much suppressed, and for a sufficiently long time the decoherence even seems to halt. This interesting phenomenon stems from the dressed environment induced by special relativity.

We investigate the geometric characterization of pure state bipartite entanglement of $(2\times D)$- and $(3\times D)$-dimensional composite quantum systems. To this aim, we analyze the relationship between states and their images under the action of particular classes of local unitary operations. We find that invariance of states under the action of single-qubit and single-qutrit transformations is a necessary and sufficient condition for separability. We demonstrate that in the $(2\times D)$-dimensional case the von Neumann entropy of entanglement is a monotonic function of the minimum squared Euclidean distance between states and their images over the set of single qubit unitary transformations. Moreover, both in the $(2\times D)$- and in the $(3\times D)$-dimensional cases the minimum squared Euclidean distance exactly coincides with the linear entropy [and thus as well with the tangle measure of entanglement in the $(2\times D)$-dimensional case]. These results provide a geometric characterization of entanglement measures originally established in informational frameworks. Consequences and applications of the formalism to quantum critical phenomena in spin systems are discussed.

We describe a simple experiment that is ideally suited to analyze the high-dimensional entanglement contained in the orbital angular momenta (OAM) of entangled photon pairs. For this purpose we use a two-photon interferometer with a built-in image rotator and measure the two-photon visibility versus rotation angle. Mode selection with apertures allows one to tune the dimensionality of the entanglement; mode selection with spiral phase plates and fibers allows detection of a single OAM mode. The experiment is analyzed in two different ways: either via the continuous two-photon amplitude function or via a discrete modal (Schmidt) decomposition of this function. The latter approach proves to be very fruitful, as it provides a complete characterization of the OAM entanglement.

We report on the absolute total electron-trimethylphosphine scattering cross section (TCS) measured from 0.4 to 400 eV using a linear electron-beam attenuation method. The experimental TCS energy function exhibits very pronounced asymmetric enhancement peaked near 5.5 eV. Calculations were also carried out to obtain the integral elastic and ionization cross sections at intermediate and high energies using the independent atom and the binary-encounter-Bethe approximations, respectively. Their sum, the computed total cross section, is for intermediate energies in a reasonable agreement with the present experimental TCS data. Furthermore, the measured TCS for $\text{P}{\left({\text{CH}}_3\right)}_3$ is compared with the TCSs for some other phosphines $\left[{\text{PH}}_3,{\text{PF}}_3\right]$ and other methides $\left[\text{B}{\left({\text{CD}}_3\right)}_3,\text{N}{\left({\text{CH}}_3\right)}_3\right]$. Analysis clearly shows that exterior atoms of a molecule influence the scattering process more significantly than the central atom.

We analyze carrier-envelope phase (CEP) effects on electron wave-packet momentum and energy spectra produced by one or two few-cycle attosecond xuv pulses. The few-cycle attosecond pulses are assumed to have arbitrary phases. We predict CEP effects on ionized electron wave-packet momentum distributions produced by attosecond pulses having durations comparable to those obtained by Sansone et al. [Science 314, 443 (2006)]. The onset of significant CEP effects is predicted to occur for attosecond pulse field strengths close to those possible with current experimental capabilities. Our results are based on single-active-electron solutions of the three-dimensional, time-dependent Schrödinger equation including atomic potentials appropriate for the H and He atoms.

Using linear response theory, we demonstrate fractional quantum Hall features in a rotating Bose-Einstein condensate in a corotating two-dimensional optical lattice. The corotating lattice and trap potential allow for an effective magnetic field and compensation of the centrifugal potential. Fractional quantum Hall features in the current response are seen for the single-particle system and for a few strongly interacting many-particle systems.

We study experimentally and theoretically the effects of crossed-polarization reinjection (XPR) on the output characteristics of a vertical-cavity semiconductor laser. We find a set of parameters values for which each polarization component develops a square-wave modulation at a period close to twice the reinjection delay. We analyze the regularity of this modulation in terms of the laser pumping current and of the reinjection level. These observations are numerically reproduced within the spin-flip model modified to account for XPR. In particular, the degradation of the square-wave switching is linked to the finite value of the spin-flip rate, and it occurs when the current approaches the boundaries of polarization bistability.

We generalize Nielsen’s majorization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett. 83, 436 (1999)] to a special class of multipartite pure states with generalized Schmidt decompositions.

We propose a physical system where photons could exhibit strongly correlated effects. We demonstrate how a Mott-insulator phase of atom-photon excitations (polaritons) can arise in an array of individually addressable coupled electromagnetic cavities when each of these cavities is coupled resonantly to a single two-level system (atom, quantum dot, or Cooper pair). This Mott phase is characterized by the same integral number of net polaritonic excitations with photon blockade providing the required repulsion between the excitations in each site. Detuning the atomic and photonic frequencies suppresses this effect and induces a transition to a photonic superfluid. Finally, on resonance the system can straightforwardly simulate the dynamics of many-body spin systems.

We show that the quantum interference between down-converted photon pairs and photons from coherent laser light can produce a maximally path entangled $N$-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the two-photon coherence of down-converted light into an almost optimal $N$-photon coherence.

We introduce the concept of the Loschmidt echo (LE) to the space of the reduced density matrix of spin and fermionic systems to study the density matrix LEs (DMLEs) of the one-dimensional extended Hubbard model and the transverse field Ising model. Our results show that the DMLEs are remarkably influenced by the criticality of the system, and the method is a convenient way to study quantum phase transitions.

The radiative lifetimes of the $\left(3\right){}^1\Pi$ and $D\left(2\right){}^1\Pi$ states of the NaCs molecule have been directly measured in a thermal cell from fluorescence kinetics after modulated laser excitation. The experimental ${\tau }_{\left(3\right){}^1\Pi }^{\mathrm{rad}}$ values of the $\left(3\right){}^1\Pi (v^{\prime }∊[3,25];J^{\prime }∊[25,106])$ levels decrease from $29\text{to}21\mathrm{ns}$ as the $v^{\prime }$ values increase. The measured ${\tau }_{\left(3\right){}^1\Pi }^{\mathrm{rad}}$ values for two rotational $J^{\prime }=45$ and 106 levels of the $v^{\prime }=3$ state are 29 and $25\mathrm{ns}$, respectively, showing the effect of rotation. The experimental ${\tau }_{\left(2\right){}^1\Pi }^{\mathrm{rad}}$ value of the $D\left(2\right){}^1\Pi (v^{\prime }=0;J^{\prime }=16)$ level is about $37\mathrm{ns}$. The average measured effective quenching collision cross section of excited NaCs molecule with Cs atoms $\sigma =(3.5\pm 1.5)\times {10}^{-14}{\mathrm{cm}}^2$. The theoretical radiative lifetimes for the lowest $(1–3){}^1\Pi$ states have been evaluated in the framework of a pure $\mathbf{a}$ Hund’s coupling case using the approximate sum rule over the lower-lying vibronic states. The required quasirelativistic transition dipole moments were calculated by many-body multipartitioning theory. Propagation of the systematic errors of ab initio transition moments and potential energy curves (PECs) into the ${\tau }^{\mathrm{rad}}$ values is discussed. The best lifetime estimates predicted for particular rovibronic levels of the $\left(3\right){}^1\Pi$ and $D\left(2\right){}^1\Pi$ states agree with their experimental counterparts within 2–8 % which can be compared with the 1–3 % uncertainties in the measured ${\tau }^{\mathrm{expt}}$ values. The lifetimes of the $B\left(1\right){}^1\Pi$ and $\left(3\right){}^1\Pi$ states are almost exclusively determined by a single transition to the ground $X{}^1\Sigma ^{+}$ state while a contribution of the $D\left(2\right){}^1\Pi \to A{}^1\Sigma ^{+}$ transition into the ${\tau }_{\left(2\right){}^1\Pi }^{\mathrm{rad}}$ values reaches up to 10–15 %.

We investigate how gas phase $R$-matrix calculations for electron collisions with the water molecule can be efficiently used in a condensed environment. The electron band structure of cubic ice being fairly well studied, we try to reproduce it using a generalization of the Korringa-Kohn-Rostoker band calculation method. We find two cutoffs have to be applied to the $R$-matrix elastic scattering results in condensed matter: one on the range of the molecular dipole and another in the angular momentum components of the scattering matrix. Their origins and physical meaning are discussed.

The electron-ion recombination rate coefficient for $\mathrm{Si}\mathrm{IV}$ forming $\mathrm{Si}\mathrm{III}$ was measured at the heavy-ion storage-ring TSR. The experimental electron-ion collision energy range of $0$–$186\mathrm{eV}$ encompassed the $2p^{6}nl{n}^{\prime }{l}^{\prime }$ dielectronic recombination (DR) resonances associated with $3s\to nl$ core excitations, $2s2p^{6}3snl{n}^{\prime }{l}^{\prime }$ resonances associated with $2s\to nl$ $(n=3,4)$ core excitations, and $2p^{5}3snl{n}^{\prime }{l}^{\prime }$ resonances associated with $2p\to nl$ $(n=3,\dots ,\infty )$ core excitations. The experimental DR results are compared with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) method for DR via the $3s\to 3p{n}^{\prime }{l}^{\prime }$ and $3s\to 3d{n}^{\prime }{l}^{\prime }$(both $n^{\prime }=3,\dots ,6$) and $2p^{5}3s3l{n}^{\prime }{l}^{\prime }$ $(n^{\prime }=3,4)$ capture channels. Finally, the experimental and theoretical plasma DR rate coefficients for $\mathrm{Si}\mathrm{IV}$ forming $\mathrm{Si}\mathrm{III}$ are derived and compared with previously available results.

The energy spectra of $1–3\mathrm{keV}$ ${{\mathrm{C}}_{60}}^{+}$ ions reflected from a $\mathrm{KCl}\left(001\right)$ surface under grazing incidence are measured with an electrostatic spectrometer. Although both nuclear and electronic energy losses are expected to be almost completely suppressed in the grazing scattering of such extremely low energy ions $(v\sim 0.01\text{a.u.})$ from the wide-band-gap insulator surface, we observe anomalously large energy losses ranging from $\sim 25\mathrm{eV}$ $({\theta }_i=1°)$ to $\sim 100\mathrm{eV}$ $({\theta }_i=6°)$. Fragmentation of ${{\mathrm{C}}_{60}}^{+}$ ions via sequential ${\mathrm{C}}_2$ loss is also observed during grazing scattering. We find a strong correlation between the energy loss and the fragmentation. From these results the observed anomalous energy losses are attributed to the internal excitations of ${{\mathrm{C}}_{60}}^{+}$ ions.

We demonstrate an efficient scheme for continuous trap loading based upon spatially selective optical pumping. We discuss the case of ${}^{1}S_0$ calcium atoms in an optical dipole trap (ODT), however, similar strategies should be applicable to a wide range of atomic species, which do not permit efficient conventional trap loading. Our starting point is a moderately cold $(\approx 300\mu \mathrm{K})$ and dense $(\approx 9\times {10}^9{\mathrm{cm}}^{-3})$ reservoir of metastable ${}^{3}P_2$ atoms in a magneto-optic trap (triplet MOT). A focused $532\mathrm{nm}$ laser beam produces a strongly elongated optical potential for ${}^{1}S_0$ atoms with up to $350\mu \mathrm{K}$ well depth. A weak focused laser beam at $430\mathrm{nm}$, carefully superimposed upon the ODT beam, selectively pumps the ${}^{3}P_2$ atoms inside the capture volume to the singlet state, where they are confined by the ODT. The triplet MOT perpetually refills the capture volume with ${}^{3}P_2$ atoms, thus providing a continuous stream of cold atoms into the ODT at a rate of ${10}^7{\mathrm{s}}^{-1}$. Limited by evaporation loss, in $200\mathrm{ms}$ we typically load $5\times {10}^5$ atoms with $3.5\times {10}^{10}{\mathrm{cm}}^{-3}$ peak density and axial and radial temperatures of 300 and $85\mu \mathrm{K}$, respectively. After terminating the loading we observe evaporation during $50\mathrm{ms}$, typically leaving us with ${10}^5$ atoms with nearly equal radial and axial temperatures close to $40\mu \mathrm{K}$ and a peak density of $5\times {10}^{11}{\mathrm{cm}}^{-3}$. A simple model is presented, which identifies the relevant physical mechanisms of the loading and decay dynamics. We point out that a comparable scheme could be employed to load a dipole trap with ${}^{3}P_0$ atoms.

We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations.

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.