In a recent paper [Phys. Rev. A 78, 020101(R) (2008)], Kim et al. have reported a large anomaly in the scaling law of the electrostatic interaction between a sphere and a plate, which was observed during the calibration of their Casimir force setup. Here we experimentally demonstrate that this behavior is not universal. Electrostatic calibrations obtained with our setup follow the scaling law expected from elementary electrostatic arguments, even when the electrostatic voltage that one must apply to minimize the force (typically ascribed to contact potentials) depends on the separation between the surfaces.

We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be estimated using a simple measurement procedure. We also compare this bound with the one provided in terms of fidelity.

We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schrödinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$, ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$, and ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimers.

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of $1∕4$, $1∕2$, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.

We present a theoretical study of vortices within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. We find that proximity to the Mott insulating state dramatically affects the vortex structures. To illustrate, we give examples in which the vortices (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. We also model time-of-flight expansion.

We discuss homogeneous and inhomogeneous Bell inequalities, following Santos’s classification. According to it, homogeneous inequalities entail only coincidence probabilities, whereas inhomogeneous inequalities entail coincidence probabilities together with single probabilities or with numbers. Because of technical limitations, all performed tests of Bell inequalities have been based on homogeneous inequalities whose derivation required additional assumptions besides realism and locality, thereby losing their genuine character. Here we derive, starting from the Clauser-Horne inequality, a homogeneous inequality that was at the basis of an experimental test performed some years ago by Torgerson et al. [Phys. Rev. A 51, 4400 (1995)]. We show that its derivation does not require anything but realism and locality, contrary to what has been previously assumed. It can thus be considered a genuine Bell inequality, appropriate for testing local realism. Similar, homogeneous inequalities can be analogously derived. They constitute a promising family that is likely to serve as a basis for loophole-free tests of local realism. The existence of such a family proves false the assertion that all genuine Bell inequalities must be inhomogeneous.

We propose a scheme for parameter estimation with cluster states. We find that phase estimation with cluster states under a many-body Hamiltonian and separable measurements leads to a precision at the Heisenberg limit. As noise models we study the dephasing, depolarizing, and pure damping channels. Decoherence reduces the sensitivity but our scheme remains superior over several reference schemes with states such as maximally entangled states and product states. For small cluster states and fixed evolution times it remains at the Heisenberg limit for approximately 2 times as many qubits than alternative schemes.

We demonstrate theoretically a scheme for cluster-state generation, based on atomic ensembles and the dipole-blockade mechanism. In the protocol, atomic ensembles serve as single-qubit systems. Therefore, we review single-qubit operations on qubit defined as collective states of atomic ensemble. Our entangling protocol requires nearly identical single-photon sources, one ultracold ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates in a single step $Q$-qubit GHZ states with success probability $p_{\text{success}}\sim {\eta }^{Q∕2}$, where $\eta$ is the combined detection and source efficiency. This is significantly more efficient than any known robust probabilistic entangling operation. GHZ states form the basic building block for universal cluster states, a resource for the one-way quantum computer.

We have experimentally investigated the structure of the ${\mathrm{Pt}}^{-}$ ion using laser photodetachment threshold spectroscopy. The experiment was conducted using a collinear laser-ion beam apparatus, in which the residual atoms created in the photodetachment process were detected. A $p$-wave threshold was observed in the photodetachment spectrum at an energy of $6851\left(13\right){\mathrm{cm}}^{-1}$. We conclude that this onset originates from a photodetachment transition in which the initial state of ${\mathrm{Pt}}^{-}$ is the previously unobserved $5d^{10}6s{}^{2}S_{1∕2}$ state and the final state of Pt is the $5d^{9}6s{}^{3}D_3$ ground state. The excitation energy of the ${}^{2}S_{1∕2}$ state is determined to be $10289\left(13\right){\mathrm{cm}}^{-1}$. This value can be compared with a multiconfiguration Dirac-Fock calculation performed by Thøgersen et al. [Phys. Rev. Lett. 76, 2870 (1996)], which yielded an excitation energy of $11301{\mathrm{cm}}^{-1}$. Our data show no indication of the presence of any other state of ${\mathrm{Pt}}^{-}$. We conclude that the structure of the ${\mathrm{Pt}}^{-}$ ion is now fully known.

We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends the scope of the available and successful multiconfigurational time-dependent Hartree methods—which were solely formulated for and applied to systems with a fixed number of particles—to a broader class of physical systems and problems. As a guiding example we treat explicitly a system where bosonic atoms can combine to form bosonic molecules and vice versa. In the theory for particle conversion, the time-dependent many-particle wave function is written as a sum of configurations made of a different number of particles, and assembled from sets of atomic and molecular orbitals. Both the expansion coefficients and the orbitals forming the configurations are time-dependent quantities that are fully determined according to the Dirac-Frenkel time-dependent variational principle. By employing the Lagrangian formulation of the Dirac-Frenkel variational principle we arrive at two sets of coupled equations of motion, one for the atomic and molecular orbitals and one for the expansion coefficients. The first set is comprised of first-order differential equations in time and nonlinear integrodifferential equations in position space, whereas the second set consists of first-order differential equations with coefficients forming a time-dependent Hermitian matrix. Particular attention is paid to the reduced density matrices of the many-particle wave function that appear in the theory and enter the equations of motion. There are two kinds of reduced density matrices: particle-conserving reduced density matrices which directly only couple configurations with the same number of atoms and molecules, and particle nonconserving reduced density matrices which couple configurations with a different number of atoms and molecules. Closed-form and compact equations of motion are derived for contact as well as general two-body interactions, and their properties are analyzed and discussed.

Highly charged ions have been used to study the sputtering of positive molecular fragments from mercaptoundecanoic acid and dodecanethiol self-assembled monolayers on gold surfaces. The samples were bombarded with ${\mathrm{Ar}}^{q+}$ $(4⩽q⩽10)$ ions with kinetic energies from $2\text{to}18\mathrm{keV}$. The main fragments detected were ${\mathrm{H}}^{+}$, ${\mathrm{C}}_n{\mathrm{H}}_{2n}^{+}$, and ${\mathrm{C}}_{n+1}{\mathrm{O}}_2{\mathrm{H}}_{2n+1}^{+}$ from mercaptoundecanoic and ${\mathrm{H}}^{+}$, ${\mathrm{C}}_n{\mathrm{H}}_{2n}^{+}$, and ${\mathrm{C}}_{n+1}{\mathrm{H}}_{2n+3}^{+}$ from dodecanethiol. The proton yields were increased with larger charge state $q$ of the highly charged ion (HCI) in both samples, scaling as $q^{\gamma }$, with $\gamma \sim 5$. The charge state dependence is discussed in terms of electron transfer to the HCI. The final yield of protons depends on molecular functional group characteristics, orientation on the surface, and reneutralization phenomena.

Within the framework of macroscopic quantum electrodynamics in linear, causal media, we study the van der Waals potentials of ground-state atoms in planar magnetodielectric host media. Our investigation extends earlier ones in two aspects: It allows for the atom to be embedded in a medium, thus covering many more realistic systems, and it takes account of the local-field correction. Two- and three-layer configurations are treated in detail both analytically and numerically. It is shown that an interplay of electric and magnetic properties in neighboring media may give rise to potential wells or walls. Local-field corrections as high as 80% are found. By calculating the full potential including the translationally invariant and variant parts, we propose a way to estimate the (finite) value of the dispersion potential at the surface between two media. Connection with earlier work intended for biological applications is established.

We describe theoretically and experimentally a laser-based method to control the rotations of asymmetric top molecules in three-dimensional space. Our method relies on keeping one axis of a molecule essentially fixed in space along the polarization vector of a nanosecond laser pulse (termed the long pulse) and forcing the molecule to rotate about the aligned axis by an orthogonally polarized, femtosecond laser pulse (termed the short pulse). Experimentally, we use femtosecond timed Coulomb explosion to image the three-dimensional (3D) alignment of the 3,5-difluoroiodobenzene molecule as a function of time after the short pulse. Strong 3D alignment is observed a few picoseconds after the short pulse and is repeated periodically, reflecting directly the revolution of the molecular plane about the aligned axis. Our numerical results, based on nonperturbative solution of the time-dependent Schrödinger equation, are in good agreement with the experimental findings and serve to unravel the underlying physical mechanism of the observations. The experiments and theory explore the influence of the laser parameters on the rotational control, in particular the role played by the intensity of the long and the short laser pulses. To illustrate the generality of our method, we illustrate its applicability to a molecule (3,4-dibromothiophene), with significantly different inertia and polarizability tensors. Finally, our theory shows that the strong 3D alignment obtained by the combined laser pulse method can be converted in to field-free alignment by rapid truncation of the long laser pulse.

A quantum theory of intense-field pump-probe experiments proposed by us recently [F. H. M. Faisal et al., Phys. Rev. Lett. 98, 143001 (2007) and F. H. M. Faisal and A. Abdurrouf, Phys. Rev. Lett. 100, 123005 (2008)] is derived here fully and applied to investigate the phenomena of dynamic alignment and high-order harmonic generation (HHG) from coherently rotating linear molecules. The theory is developed from the basic quantum transition amplitude for the HHG and used to relate the Fourier transform (FT) of the expectation value of the dipole operator to the rate of emission of the HHG photons. It permits us to give analytical expressions for the HHG signals and their simultaneous dependence on the two externally available control parameters—the delay-time, $t_d$, between the pump and the probe pulse, and the relative angle, $\alpha$, between their polarizations. A relation between the basic “one-molecule” and the macroscopic “many-molecule” HHG signals is obtained from the phase-matching condition for HHG in an ideal medium. The requirement for the coherent HHG signal and the “elastic” molecular transition, in contrast to the “inelastic” transitions and the “hyper-Raman” emission, is discussed. The effect of the “delayed” probe pulse on the dynamic alignment induced by the pump-pulse, the mean rotational energy of the molecule during the period between the pump and the probe pulse, as well as a method of estimating the effective temperature of the molecules are analyzed. A “revival theorem” on the number of fractional “revivals,” equal to the lowest power of the “cosine operator” in the Hamiltonian of the system, times the maximum powers of the “cosine-moments” present in the signal, is derived and used to interpret the observed fractional revivals and their relative phases. A “magic” polarization angle ${\alpha }_c=\arctan \sqrt{2}\approx 55°$, at which the signals for all $t_d$ approach each other closely, is identified as a generic signature of a ${\sigma }_g$ symmetry of the active orbital. Similarly, the presence of a “crossing neighborhood” near ${\alpha }_c$ is shown to be a generic signature of an active ${\pi }_g$ orbital. At an operational angle ${\alpha }_c\approx 55°$ in the laboratory, a steady emission of high-order harmonic radiation from coherently rotating molecules with ${\sigma }_g$ orbital symmetry (e.g., ${\mathrm{N}}_2$) can be obtained. Finally, explicit numerical calculations are performed at specific experimental parameter values in the time domain as well as in the frequency domain. The results well reproduce all the salient features of the experimental observations for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$, and provide a unified theoretical interpretation of the same.

Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground states in alkali-metal atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called “heading errors” of alkali-metal-vapor atomic magnetometers operating in the geophysical field range $(B\approx 0.2–0.7\mathrm{G})$. Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization, and frequency, a technique that can be readily applied in practical situations.

We show that the recently proposed ionic microscope setup [Kollath et al., Phys. Rev. A 76, 063602 (2007)] could be adapted to measure the local single-particle energy distribution of a degenerate Fermi gas in situ with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photoassociation rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photoassociation rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.

We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation, we derive a Korteweg–de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long-wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes nonmonotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations, and good agreement between them is found.

We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.

We calculated the coherent population trapping (CPT) for the open $D1$ line transition $F_g=2\to F_g=1$ in ${}^{87}\mathrm{Rb}$ by solving the time-dependent optical Bloch equations, integrating the results for the total excited state populations over atomic trajectories, and averaging over velocities (components perpendicular and parallel to the laser beam) and over atom incident angles to the laser beam. We obtained a square root dependence of the CPT linewidths as a function of the laser intensity for both steplike and Gaussian transverse beam profiles. The results obtained with the Gaussian transverse laser beam profile are in good agreement with recent experimental results. Results for both steplike and Gaussian profiles of the laser beam show asymptotic $1∕\sqrt{d}$ dependence ($d$ is the laser beam diameter) of the CPT linewidths, for a large range of the laser intensity.

For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration.