We report on an experimental study of direct and spectroscopic imaging of optically trapped Mie droplets in air. The scattering of the trapping beams gives glare points at the droplets’ azimuths. Spectroscopic measurements involving polarized light are performed to precisely determine both the droplet sizes and refraction index using Mie scattering theory. Experimental pictures are compared to rigorous numerical simulations. We also include some results on imaging of whispering gallery resonances and conclude with a brief discussion on the possibility of efficiently exciting whispering gallery resonances via radiative coupling.

A variant of a grazing-incidence pumping (GRIP) scheme for Ni-like x-ray lasers using a single shaped pulse from a 10-Hz Ti:sapphire laser system has been demonstrated. Experimental and numerical results show that efficient excitation leading to the lasing process can be achieved by controlled shaping of the pump laser pulse. Such a pulse has been defined for a silver slab target. A gain coefficient as high as $76{\mathrm{cm}}^{-1}$ was estimated. Results indicate that the nanosecond amplified spontaneous emission background of the leading edge of the driving pulse is decisive for an efficient pumping process in this version of GRIP.

We examine the effect of superluminal signal propagation through a birefringent crystal, where the effect is not due to absorption or reflection, but to the filtration of a special polarization component. We first examine the effect by a stationary phase analysis, with results consistent with those of an earlier analysis of the system. We supplement this analysis by considering the transit of a Gaussian wave and find bounds for the validity of the stationary phase result. The propagation of the Gaussian wave is illustrated by figures.

For finite systems that have the energetically highest-occupied molecular orbital (HOMO) with an asymptotic nodal surface, Joubert demonstrated recently [Phys. Rev. A 76, 012501 (2007)] strongly anisotropic behavior (in the asymptotic large-$r$ region) of the exact correlation potential of density-functional theory. As is shown by us, this result is a direct and simple consequence of the strong anisotropy of the exact exchange potential obtained by Della Sala and Görling [Phys. Rev. Lett. 89, 033003 (2002); Della Sala and GörlingJ. Chem. Phys. 116, 5374 (2002)] and the assumption about the asymptotic isotropy of the Kohn-Sham (KS) potential (based on the investigation of Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)] for atoms). Joubert’s result remains a hypothesis only, because the last assumption is in contradiction with the asymptotic strong anisotropy of the KS potential for systems with asymptotic nodal surface of the HOMO, demonstrated by Wu, Ayers, and Yang [J. Chem. Phys. 119, 2978 (2003)]. The correlation potential in the asymptotic region, stemming from their results, is given.

A large-scale configuration-interaction (CI) calculation is reported for the hyperfine splitting of the $2{}^{2}S$ and $3{}^{2}S$ states of ${}^7\mathrm{Li}$ and ${}^9\mathrm{Be}^{+}$. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a separate treatment of the QED, nuclear-size, nuclear-magnetization distribution, and recoil corrections. The nonrelativistic limit of the CI results is in excellent agreement with variational calculations. The theoretical values obtained for the hyperfine splitting are complete to the relative order of ${\alpha }^2$ and improve upon results of previous studies.

Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is contrasted with the decoherence effect of dynamic disorder having strength $W$, where a quantum to classical crossover at time $t_c\propto W^{-2}$ transforms the quantum walk into an ordinary random walk with diffusive spreading. We demonstrate these localization and decoherence phenomena in quantum carpets of the observed time evolution, we relate our results to previously studied models of decoherence for quantum walks, and examine in detail a dimer lattice which corresponds to a single qubit subject to randomness.

We measure the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold ${}^{85}\text{R}\text{b}$ atoms in a far-detuned 1D optical lattice. The lattice wells are so shallow as to support only two bound states, and we prepare the atoms in the ground state. The lattice is oriented vertically, leading to a tilted-washboard potential analogous to those encountered in condensed-matter systems. Experimentally, we find that a square pulse consisting of lattice displacements and a delay is more efficient than single-step pulses or Gaussian pulses. This is described as an example of coherent control. It is striking that contrary to the intuition that soft pulses minimize loss, the Gaussian pulse is outperformed by the square pulse. Numerical calculations are in strong agreement with our experimental results and show the superiority of the square pulse to the single-step pulse for all lattice depths and to the Gaussian pulse for lattice depths greater than seven lattice recoil energies. We also compare the effectiveness of these pulses for reviving oscillations of atoms in vibrational superposition states using the pulse-echo technique. We find that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These improved echo pulses allow us to probe coherence at longer times than in the past, measuring a plateau which has yet to be explained. In addition, we show numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices. The coupling probability for an optimized single-step pulse approaches $1/e$ as the depth goes to infinity (harmonic-oscillator limit), while in shallow lattices with large anharmonicity, the coupling probability reaches a maximum value of 0.51 for a lattice depth of five recoil energies. For square and Gaussian pulses the coupling in the lattice is even stronger, reaching maxima of 0.64 at 6 recoil energies and 0.67 at 5 recoil energies, respectively.

We report on a quantum key distribution effected with a two-way deterministic protocol over a standard telecommunication fiber. Despite the common belief of a prohibitive loss rate for such a scheme, our results show its feasibility on distances of few tenths of kilometers.

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of nonmaximally entangled qudits in a pure state $|\psi ⟩$. Our results include the following: (i) We prove that it is possible for a state $|\psi ⟩$ with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions $d=3$ and $d=4$, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of $d+j$ messages, $2\le j\le d-1$; moreover, we show that the $j=2$ and $j=d-1$ cases of the conjecture are valid in all dimensions. (iii) Given that $|\psi ⟩$ allows the sending of $K$ messages and has $\sqrt{{\lambda }_0}$ as its largest Schmidt coefficient, we show that the inequality ${\lambda }_0\le d/K$, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form ${\lambda }_0<d/K$ if $K=d+1$, while our constructions of local unitaries show that equality can be realized if $K=d+2$ or $K=2d-1$.

Radiative lifetimes of eight odd-parity states of Pt II, in the energy range from 51 408 to $64388{\text{cm}}^{-1}$, have been measured by means of the time-resolved laser-induced-fluorescence technique. Free, singly ionized platinum ions were obtained in a laser-produced plasma and a tunable laser with 1.5 ns duration pulse was used to selectively excite the ${\text{Pt}}^{+}$ ions. The comparison of the experimental results with relativistic Hartree-Fock calculations emphasizes the importance of valence-valence correlation and of core-polarization effects in this complex ion. A new and extensive set of calculated oscillator strengths and transition probabilities is reported in the present paper.

The partial cross sections for photoionization of $\text{H}_2{}^{+}$ present structures which are usually called Cooper-like minima. We analyze the physical origin of these features to determine if they are associated to the confinement of the target electron, as recently proposed by Férnandez et al., or to zero absorption as suggested here. A thorough analysis of the partial cross sections, the phase shifts, and the transition amplitude clearly shows that the Cooper-like minima correspond to zero absorption. To demonstrate this we show that the phase shifts have a maximum and the transition matrix is exactly zero at the electron momentum corresponding to where the Cooper-like minima appear. Finally, we show that the existence of the Cooper-like minima survive when the vibrational degree of freedom of the target is taken into account.

Large-scale relativistic close-coupling calculation of photoionization and photorecombination of $\mathrm{Fe}\mathrm{XVI}$ reveal strong resonance structures at low energies. The Breit-Pauli $R$-matrix method was employed in the calculations with the inclusion of 89 spectroscopic states in the close-coupling eigenfunction expansion. Our unified photorecombination cross sections show significant differences from previous results. The Gaussian averaged effective photorecombination cross sections to the $2p^{6}3d_{3/2,5/2}$ states of $\mathrm{Fe}\mathrm{XVI}$ are shown to be 24% larger than those used for normalization by Brown et al. [Phys. Rev. Lett. 96, 253201 (2006)]. This result should help resolve the issue raised in Brown’s paper on the puzzling large discrepancy between theoretical and experimental electron impact excitation cross sections of $\mathrm{Fe}\mathrm{XVII}$.

We study the Casimir-Lifshitz interaction out of thermal equilibrium, when the interacting objects are at different temperatures. The analysis is focused on the surface-surface, surface-rarefied body, and surface-atom configurations. A systematic investigation of the contributions to the force coming from the propagating and evanescent components of the electromagnetic radiation is performed. The large distance behaviors of such interactions is discussed, and both analytical and numerical results are compared with the equilibrium ones. A detailed analysis of the crossing between the surface-surface and the surface-rarefied body, and finally the surface-atom force is shown, and a complete derivation and discussion of the recently predicted nonadditivity effects and asymptotic behaviors is presented.

We have calculated the propagation of rovibrational wave-packet in the ${}^1\Sigma$ state of $\mathrm{CO}$ and the ${}^2\Pi$ state of $\mathrm{NO}$ manipulated by shaped midinfrared femtosecond laser pulses. The rotational states of the molecules were fully taken into account in the calculation and the effects of the rotational states in the vibrational wave-packet evolution were examined in detail. As a result, it is found that rotational excitations associated with the vibrational excitation affect the wave-packet propagation drastically, which suggests that the rotational states should not be ignored when vibrational states of molecules are used as the target state for coherent control and qubits for quantum computation. For the experimental detection of the amplitude and phase information on the rovibrational wave-packets, the time profiles of the transition intensities from the rovibrational wave-packet to an electronically excited state were calculated. It is shown that both ionization and laser induced fluorescence signals contain information necessary for the analysis of the phase and relative amplitude of the rovibrational wave-packets.

We calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a $J=1$ level in a magnetic field, and in control of entanglement of a pair of spin-$1∕2$ particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.

We study variational wave functions of the product form, factorizing according to the wave vectors $\mathbf{k}$, for the ground state of a system of bosons interacting via positive pair interactions with a positive Fourier transform. Our trial functions are members of different orthonormal bases in Fock space. Each basis contains a quasiparticle vacuum state and states with an arbitrary finite number of quasiparticles. One of the bases is that of Valatin and Butler (VB), introduced fifty years ago and parametrized by an infinite set of variables determining Bogoliubov’s canonical transformation for each $\mathbf{k}$. In another case, inspired by Nozières and Saint James the canonical transformation for $\mathbf{k}=0$ is replaced by a shift in the creation/annihilation operators. For the VB basis we prove that the lowest energy is obtained in a state with $\sim \sqrt{\text{volume}}$ quasiparticles in the zero mode. The number of $\mathbf{k}=0$ physical particles is of the order of the volume and its fluctuation is anomalously large, resulting in an excess energy. The same fluctuation is normal in the second type of optimized bases, the minimum energy is smaller and is attained in a vacuum state. Associated quasiparticle theories and questions about the gap in their spectrum are also discussed.

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).

A compact correlation-function expansion is developed for $n$-order optical susceptibilities in the frequency domain using the Keldysh-Schwinger loop. By not keeping track of the relative time ordering of bra and ket interactions at the two branches of the loop, the resulting expressions contain only $n+1$ basic terms, compared to the $2^n$ terms required for a fully-time-ordered density matrix description. Superoperator Green’s function expressions for ${\chi }^{\left(n\right)}$ derived using both expansions reflect different types of interferences between pathways. These are demonstrated for correlation-induced resonances in four-wave-mixing signals.

We describe a protocol capable of preparing an arbitrary state of two photons in several spatial modes using pairs of photons generated by spontaneous parametric down conversion, linear optical elements, and single-photon detectors or postselection. The protocol involves unitary and nonunitary transformations realizable by beam splitters and phase shifters. Nonunitary transformations are implemented by attenuation filters. The protocol contains several optimization capabilities with the goal of improving overall probability of its success. We also show how entangled two-photon states required for quantum computing with linear optics can be prepared using a very simple and feasible scheme.

We report an experiment in which two-photon interference occurs between degenerate single photons that never meet. The two photons travel in opposite directions through our fiber-optic interferometer and interference occurs when the photons reach two different, spatially separated, two-by-two couplers at the same time. We show that this experiment is analogous to the conventional Franson-type entanglement experiment where the photons are entangled in position and time. We measure wave-function overlaps for the two photons as high as $94\pm 3\%$.