We study numerically the fluctuation-derived interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study the full crossover between nonretarded and retarded interactions as a function of separation. We use constrained factorizations in order to measure the interaction of a particle with a rough dielectric surface and compare with a scaling argument.

An alternative approach for the optimization strategy in quantum control experiments is proposed. Genetic algorithms are used frequently to improve the laser fields driving quantum processes. We present a flexible scheme based on ant-colony-optimization, which introduces a correlation of the mask function pixels and allows a decrease in the shaped pulse complexity and duration without loss of efficiency.

Using a nonselective broadband detection scheme we discovered an efficient mechanism of formation of ultracold ${\mathrm{Cs}}_2$ molecules in deeply bound vibrational levels $(v=1–9)$ of their electronic ground state $X{}^1\Sigma _g^{+}$. They are formed by a one-photon photoassociation of ultracold cesium atoms in a manifold of excited electronic states, followed by a two-step spontaneous emission cascade. This process creates about ${10}^5–{10}^6\text{molecules}\text{per}\text{second}$. This detection scheme is an advancement compare to previous ones and could be generalized to other molecular species for the systematic investigation of cold molecule formation mechanisms.

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.

We present cross sections for elastic collisions of low-energy electrons with acetic acid. We employed the Schwinger multichannel method with pseudopotentials in the static-exchange and static-exchange plus polarization approximations, for energies ranging from 0.1 to 10 eV. We found a ${\pi }^{\ast }$ shape resonance around 1.7 eV, corresponding to the $A^{″}$ symmetry of the $C_s$ group. This resonant state was assigned to the experimental dissociative electron attachment peak at 1.7 eV yielding ${\text{CH}}_3{\text{COO}}^{-}+\text{H}$. We also performed a series of electronic structure calculations using a small basis set for acetic, formic, and trifluoroacetic acids, which exhibit a similar behavior with respect to the dissociative electron attachment. We believe that hydrogen elimination triggered off by electron capture into a ${\pi }^{\ast }$ resonance could be a general property of carboxylic acids.

Relaxation of the off-diagonal density-matrix elements between the metastable $3{{}^{2}D}_{3/2}$ and $3{{}^{2}D}_{5/2}$ states in a single ${{}^{40}\text{C}\text{a}}^{+}$, which are separated from each other by 1.82 THz, is studied experimentally by using the Ramsey method of separated oscillating fields. The two metastable states are connected with a stimulated Raman transition by using two infrared lasers, which are phase locked with their frequency difference bridged by an optical frequency comb. By performing Ramsey measurements for two Zeeman components of the stimulated Raman transition with different sensitivities to magnetic fields, the coherence is investigated quantitatively and the effect of magnetic-field fluctuations on that is evaluated. By using a spin-echo $\pi$ pulse in a Ramsey sequence which is effective for inhomogeneous broadening processes, a visibility decay time of 5.1 ms is obtained. This is more than twice as long as that for normal sequences. This work is an essential step for realization of a qubit using the two metastable states and demonstrates coherent manipulation of the internal states separated by around a terahertz using phase-locked light sources.

A detailed theoretical study of ${\mathrm{H}}_2$ ionization by photons of a few hundreds of eV is presented. Bound and continuum states are accurately evaluated by using $B$-spline basis functions. The nuclear degrees of freedom are also included. A striking feature is observed when one analyzes the vibrational distribution of the residual $\mathrm{H}_2{}^{+}$ ion: this vibrational distribution does not follow the usual Franck-Condon behavior when ${\mathrm{H}}_2$ is parallel to the polarization direction. The origin of this anomaly is related to interference effects. Such effects are more clearly seen in the fully differential electron angular distributions associated with specific vibrational states of $\mathrm{H}_2{}^{+}$: for ${\mathrm{H}}_2$ molecules perpendicular to the polarization direction, the distributions clearly resemble those obtained in Young’s double-slit experiment, while, for molecules parallel to the polarization direction, they show that the electron is sometimes prevented to escape in the direction of the radiation field due to the suppression (or confinement) of a given partial wave. The calculations also show that, at these high photon energies, the nuclear asymmetry parameter exhibits a reminiscence of Cohen-Fano oscillations when it is plotted as a function of photon energy.

Coherence control is the key to success in the applications of atom-laser beams. A multiloop measurement feedback control scheme is proposed to improve atom-laser coherence. The first loop aims to cancel the decohering effects of the nonlinear atom-atom interactions via direct measurement feedback. However, there are nonlinear interactions with the optical probe field used in the measurement scheme which may also contribute to a degradation in atom-laser performance. Accordingly, a second feedback loop is used to reduce these effects based on linear quadratic Gaussian control. The multiloop design achieves improved atom-laser coherence.

This paper presents a unified theory for the $N\text{th}$-order $(N⩾1)$ coherence of thermal light. We wish to show that the $N\text{th}$-order coherence or correlation of thermal light is the result of $N$-photon interference, which involves the superposition of $N$-photon probability amplitudes, corresponding to different yet indistinguishable ways of triggering a $N$-photon joint detection event. The near-field third-order spatial coherence of thermal light is calculated and its use suggested for verifying the $N$-photon interference theory.

The general conditions required for complete tunneling of light through surface impedance-matched barrier layers were investigated. By analogy with the effective barrier length defined by Kim [Phys. Rev. E 70, 047603 (2004)], we define the extended effective barrier length and show that complete tunneling occurs when the extended effective barrier length becomes zero. The surface mode plays an important role in complete tunneling that arises from balancing field enhancement and decay. We need at least one interface which supports a local surface mode, and it is not necessary that every interface between adjacent barrier layers support a surface mode. Complete tunneling can still occur under arbitrary permutations of the order of the barrier layers. The effect of total barrier length on the angular dependence is also discussed.

Recently Parigi et al. [Science 317, 1890 (2007)] implemented experimentally the photon subtraction and addition processes from and to a light field in a conditional way, when the required operations were produced successfully only upon the positive outcome of a separate measurement. It was verified that for a low-intensity beam (quantum regime) the bosonic annihilation operator $a$ does indeed describe a single photon subtraction, while the creation operator $a^{†}$ describes a photon addition. Nonetheless, the exact formal expressions for these operations do not always reduce to these simple identifications, and in this connection here we deduce the general superoperators for multiple photon subtraction and addition processes and analyze the statistics of the resulting states for classical field states having an arbitrary intensity. We obtain closed analytical expressions and verify that for classical fields with high intensity (classical regime) the operators that describe photon subtraction and addition processes deviate significantly from simply $a$ and $a^{†}$. Complimentarily, we analyze in detail such a smooth quantum-classical transition as a function of beam intensity for both processes.

We give an example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be thought of as adding a number of small dimensions. This is a discrete time quantum walk using the Fourier transform coin, where the walk proceeds a distance $\Theta \left(1\right)$ in constant time compared to $\Theta \left(1/n\right)$ classically, independent of the number of these small dimensions. The analysis proceeds by reducing this walk to a walk with a two-dimensional coin.

We theoretically study the interaction of two time delayed, phase-locked, and nonresonant pulses with a two-level system in the strong field regime. The population transfer is shown to be extremely sensitive to the phase shift $\varphi$ between the pulses, with efficient population transfer taking place only for $\varphi$ close to $\pi$. This effect is explained in terms of nonadiabatic jump and rapid adiabatic passage phenomena.

In an experiment using the odd calcium isotope ${}^{43}\mathrm{Ca}^{+}$, we combine the merits of a high-fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two “clock” states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations, and mapping operations, errors smaller than 1% are achieved, whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when mapped to the hyperfine states. In the latter case, the entanglement is preserved for $96\left(3\right)\mathrm{ms}$, exceeding the duration of a single gate operation by three orders of magnitude.

We analyze atom-atom correlations in the $s$-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive-$P$ representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.

We show how quasiprobability distribution functions defined over $N^2$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin-tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics.

We explore theoretically the rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) in molecular electronic states including both the rotational and the vibrational degrees of freedom, with the LiH molecule as an example. By using a pure rovibrational state as initial state, we find that, under the condition of two-photon resonance, an efficient rovibrational population transfer can be achieved via STIRAP in molecular electronic states and the desired target state can be selected by adjusting laser-pulse parameters. Besides the interested rovibrational states, however, some unwanted rovibrational states may affect population transfer process, especially while the two-photon detuning is taken into account. By inspecting the evolution process of wave packet, we can easily search these unwanted rovibrational states and study their influences. Moreover, the effect of rotational temperature on the population transfer process is discussed using thermal mixed state as initial state.

Fermions in an optical lattice near a wide Feshbach resonance are expected to be described by an effective Hamiltonian of the general Hubbard model with particle-correlated tunneling rates resulting from the strong atomic interaction [Duan, Phys. Rev. Lett. 95, 243202 (2005)]. Here, we propose a scheme to test the predictions of this effective Hamiltonian through manipulation of ultracold atoms in an inhomogeneous optical superlattice. The structure of the low-energy Hilbert space as well as the particle-correlated tunneling rates can be inferred from measurements of the time-of-flight images.

The low-lying excitations of coreless vortex states in $F=1$ spinor Bose-Einstein condensates (BECs) are theoretically investigated using the Gross-Pitaevskii and Bogoliubov–de Gennes equations. The spectra of the elementary excitations are calculated for different spin-spin interaction parameters and ratios of the number of particles in each sublevel. There exist dynamical instabilities of the vortex state which are suppressed by ferromagnetic interactions, and, conversely, enhanced by antiferromagnetic interactions. In both of the spin-spin interaction regimes, we find vortex-splitting instabilities in analogy with scalar BECs. In addition, a phase-separating instability is found in the antiferromagnetic regime.

We investigate both analytically and numerically the dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction. The analytic solutions for the ring dark soliton are derived by using a transformation method. A shallow ring dark soliton is stable when the ring is slightly distorted, while for large deformation of the ring, vortex pairs appear and demonstrate different dynamical behaviors: the vortex pairs transform into dark lumplike solitons and revert to ring dark solitons periodically. Moreover, our results show that the dynamical evolution of the ring dark soliton can be dramatically affected by the Feshbach resonance, and the lifetime of the ring dark soliton can be greatly extended, which offers a useful method for observing ring dark solitons in future experiments.