We provide a quantum description of the vortex degrees of freedom for Bose gases in the lowest Landau level. The results can be used to interpret correlated many-particle wave functions in terms of superpositions of vortex configurations. These effects may be visible in the next generation of mesoscopic trap experiments. We expose the important role of nonorthogonality in using simple vortex descriptions, and formulate a basis set which does not experience these difficulties. We show that in general any correlated ground state (even completely fragmented) can be represented as a superposition of completely condensed states. We provide simple illustrations of these methods: a vortex interpretation of the exact, many-body, eigenstates for $L⩽N$, the determination of the energy levels of the single-vortex subspace and finally mention a more speculative description of the Laughlin state in vortex variables.

We introduce a tight-binding approach to model the emission dynamics of a quantum-dot in realistic, photonic-crystal-slab coupled-cavity systems. We apply our approach to a quantum-dot strongly coupled at the band edge of a lossy coupled-cavity waveguide and calculate the quantum-dot dynamics as well as the photon dynamics along the waveguide. We show that the condition for strong coupling is simply parametrized in terms of the waveguide loss and find that the key signature of the strong-coupling, Rabi oscillations, could be observed via time-resolved photon detection.

We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure and the second is the $q$-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same $q$-squashed entanglement.

We introduce a frequency-domain formalism for computing excited-state forces using linear response theory within the framework of time-dependent density-functional theory. We present an implementation of the formalism within a real-space computational framework. We demonstrate the validity and usefulness of the approach by comparing its results to those obtained with a Green’s function approach using the GW+Bethe-Salpeter-equation method, for the simple case of the CO molecule. We expect the method to be advantageous for computing excited-state dynamics in large systems.

In a quasiclassical framework, we formulate the quadruple ionization by single-photon absorption of the Coulomb five-body problem. We present the quadruple photoionization total cross section of the ground state of beryllium for energies up to 620 eV. Our results for energies close to threshold are in agreement with the Wannier threshold law for four-electron escape. In addition, the agreement of our results with a shape formula provides support for the overall shape of our total quadruple cross section. Finally, we find that the photon energy where the maximum of the total photoionization cross section occurs for single, double, triple, and quadruple photoionization of H, He, Li, and Be, respectively, seems to follow a linear relation with the threshold energy for complete breakup of the respective element.

We show that cold atom systems of simultaneously trapped Bose-Einstein condensates (BECs) and quantum degenerate fermionic atoms provide promising laboratories for the study of macroscopic quantum tunneling. Our theoretical studies reveal that the spatial extent of a small trapped BEC immersed in a Fermi sea can tunnel and coherently oscillate between the values of the separated and mixed configurations (the phases of the phase separation transition of BEC-fermion systems). We evaluate the period, amplitude, and dissipation rate for ${}^{23}\mathrm{Na}$ and ${}^{40}\mathrm{K}$ atoms, and we discuss the experimental prospects for observing this phenomenon.

Using resonant interaction of three Rydberg atoms with a single-mode microwave cavity, we consider a realization of the three-qubit Grover search algorithm in the presence of weak cavity decay, based on a previous idea for a three-qubit quantum gate [Chen et al., Phys. Rev. A 73, 064304 (2006)]. We simulate the searching process under the influence of the cavity decay and show that our scheme could be achieved efficiently to find a marked state with high fidelity. The required operations are very close to the capabilities of current cavity QED techniques.

We investigate entanglement properties of mixtures of short-range spin-$s$ dimer coverings in lattices of arbitrary topology and dimension. We show that in one spatial dimension nearest neighbor entanglement exists for any spin $s$. Surprisingly, in higher spatial dimensions there is a threshold value of spin $s$ below which the nearest neighbor entanglement disappears. The traditional “classical” limit of large spin value corresponds to the highest nearest neighbor entanglement that we quantify using the negativity.

We consider the Bose-Hubbard model in a two-dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller-type variational wave function, we find an analytical expression for the Mott insulator (MI)–superfluid (SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.

The present work tests the suitability of the narrow transitions $7s{}^{2}S_{1∕2}\to 6d{}^{2}D_{3∕2}$ and $7s{}^{2}S_{1∕2}\to 6d{}^{2}D_{5∕2}$ in ${\mathrm{Ra}}^{+}$ for optical frequency standard studies. Our calculations of the lifetimes of the metastable $6d$ states using the relativistic coupled-cluster theory suggest that they are sufficiently long for ${\mathrm{Ra}}^{+}$ to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities, and quadrupole moments of the appropriate states of this system.

We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influence on the entanglement dynamics due to the sensitive time dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case.

We employ conditional Tsallis $q$ entropies to study the separability of symmetric one parameter $W$ and GHZ multiqubit mixed states. The strongest limitation on separability is realized in the limit $q\to \infty$, and is found to be much superior to the condition obtained using the von Neumann conditional entropy ($q=1$ case). Except for the example of two qubit and three qubit symmetric states of GHZ family, the $q$-conditional entropy method leads to sufficient—but not necessary—conditions on separability.

Electron transmission through insulating polymer nanocapillary (diameter $200\mathrm{nm}$ and aspect ratio 50) foils has been investigated for incident energies 500 and $1000\mathrm{eV}$. Significant intensities of transmitted electrons were observed for foil tilt angles up to $\sim 10°$, and corresponding observation angles with respect to the incident beam direction, a phenomenon referred to as guiding. The transmitted electron spectra show substantial energy losses that increase with the capillary tilt angle, in sharp contrast to previous results for slow positive ions and lower energy electrons. Despite apparent close encounters with the capillary walls, inelastically scattered electrons are found to be guided at angles coinciding with elastically scattered electrons. These results suggest a means to study the dynamics of electron interactions with insulating materials, which is complicated by charge buildup in conventional surface scattering studies.

We study quantum turbulence in trapped Bose-Einstein condensates by numerically solving the Gross-Pitaevskii equation. Combining rotations around two axes, we successfully induce quantum turbulent state in which quantized vortices are not crystallized but tangled. The obtained spectrum of the incompressible kinetic energy is consistent with the Kolmogorov law, the most important statistical law in turbulence.

We apply the linear density response theory to the electron-impact ionization including autoionizing resonances of atoms. Such a single-electron-like method takes into account the electron-electron dynamic correlation effect through the first-order perturbation theory. The method allows us to study the dynamic correlation in the process of electron-impact excitation with ionization background. We take the autoionizing resonances of Ar atoms as an example to show the simpleness and effectiveness of the present method. Our calculated electron impact ionization cross sections including autoionizing resonances are in reasonable agreement with the experimental measurements.

We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by nonadiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photoswitch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in the literature. The laser pulses are computed by the multitarget optimal control theory with chirped pulses as trial fields. Very high fidelities are obtained. We also examine the stability of the control when the system is coupled to a bath of oscillators modeled by an ohmic spectral density. The bath correlation time scale being smaller than the pulse duration, the dynamics is carried out in the Markovian approximation

The framework of cyclostationary random processes is used to develop classical coherence theory for the measurement of statistically periodic stochastic optical fields, such as those produced by pulsed lasers. Cycloergodicity is invoked to show that precise and accurate inferences of the nonstationary process statistics can be made from a single field realization. In particular, many-pulse observations using nonlinear and/or nonstationary techniques, such as spectral shearing interferometry, can be used to fully characterize the standard two-time correlation function of a statistically periodic source. The theory is demonstrated through the simulation of spectral shearing interferometry and frequency-resolved optical gating measurements.

The Floquet perturbation theory represents an important technique for studying the response of atoms or molecules exposed to weak monochromatic fields. In this paper, we discuss an explicit implementation of the Floquet perturbation theory starting from different gauge representations of the matter-light Hamiltonian, namely, from the velocity gauge, the length gauge, and the acceleration gauge. Interestingly, the development of the second-order Floquet perturbation theory in different gauges gives rise to formally different quasienergy corrections, whose mutual equivalence is not self-evident. Nevertheless, our derivation shows how the perturbation formulas associated with different gauges can be converted to one another, provided that a complete basis set of the atomic-molecular electronic states has been used. On the other hand, it turns out that an inappropriate basis set truncation employed for a particular gauge (such as, e.g., the two-level approximation applied within the velocity gauge) may sometimes lead toward completely wrong results. This fact should serve as a warning against an uncautious use of various gauge transformations in practical calculations with a finite basis set.

Correlations between the entire conical spatial modes of signal and idler beams in a type II spontaneous parametric down-conversion (SPDC) under ultrashort pulse pumping are examined experimentally and theoretically. Statistical properties and theoretical analysis of “path-entangled” states formed using these beams suggest that the quantum state of SPDC photon pairs cannot be represented by a pure ensemble of identically prepared pairs.

The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. This proposal can efficiently use each physical electron spin as a logical qubit in the universal quantum computation.