The notion of “paired” fermions is central to important condensed-matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear, there exists no systematic and mathematical theory of pairing that would allow us to unambiguously characterize and systematically detect paired states. We propose a definition of pairing and develop methods for its detection and quantification applicable to current experimental setups. Pairing is shown to be a quantum correlation different from entanglement, giving further understanding in the structure of highly correlated quantum systems. In addition, we will show the resource character of paired states for precision metrology, proving that the BCS states allow phase measurements at the Heisenberg limit.

Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the ${\mathrm{Sr}}_2$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. ${\mathrm{Sr}}_2$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.

We report ab initio relativistic 20-electron correlation calculations of electric-dipole transition moments for nine low-lying electronic states of $\mathrm{Hf}{\mathrm{F}}^{+}$, which it is suggested to be used in experiments to search for the electric-dipole moment of the electron. Radiative lifetimes for the lowest vibrational levels of the first excited ${}^3\Delta _1$ electronic state are calculated and its population scheme is suggested. The influence of correlation of the $4f$ electrons of Hf is studied.

We apply the semiclassical propagation technique to tunneling ionization in atomic and molecular systems. Semiclassical wave functions and the tunneling flux are calculated from the solution of the classical equations of motion in the complex time plane. We illustrate this method by rederiving the known result for the decay rate of a negative ion in a weak electric field. We then obtain numerical results for atomic hydrogen, $\mathrm{H}_2{}^{+}$, ${\mathrm{H}}_2$, and Ar, and compare them with the results of the asymptotic [Ammosov-Delone-Krainov (ADK)] theory. The asymptotic theory gives surprisingly good results for the atomic and molecular ionization rates. In particular, our calculations for the simplest case of molecular suppression, ionization of ${\mathrm{H}}_2$ versus Ar, confirms the ADK analysis of Tong et al. [Phys. Rev. A 66, 013409 (2002)], explaining that the suppression is mainly due to the different symmetries of the ionized orbitals, $s$ in ${\mathrm{H}}_2$ and $3p_z$ in Ar.

We propose a simple three-wire-based magnetic trap potential for direct forced evaporative cooling of neutral atoms without using induced spin-flip technologies. We have devised a method for controlling the trap depth without sacrificing its frequencies by only varying wire currents and external magnetic fields. By having multiples of these wires on different levels integrated into an atom chip, it is possible to attain Bose-Einstein condensation without the conventional forced evaporation technique.

One important factor which determines efficiency of loading cold atoms into an optical dipole trap from a magneto-optical trap is the distance between the trap centers. By studying this efficiency for various optical trap depths $(2–110\mathrm{mK})$ we find that for optimum dipole trap loading, longitudinal displacements up to $15\mathrm{mm}$ are necessary. An explanation for this observation is presented and compared with other work and a simple analytical formula is derived for the optimum distance between the trap centers.

We investigate the existence and stability of spatial optical solitons supported by cylindrical Bessel lattices in a competing cubic-quintic (CQ) nonlinear medium. Various families of solitons, including vortex, multipole, and necklace solitons are presented. Vortex solitons with unit topological charge are stabilized by CQ nonlinearity almost in their entire existence domain. There exists a power threshold necessary for the existence of these solitons. Comparing with the defocusing cubic case, the CQ nonlinearity broadens the profiles of the solitons, and also broadens their existence and stability domains. The dark core of vortex solitons can be enlarged by selecting the higher order lattice. Especially, we reveal that this model supports stable vortex solitons with broad intensity distributions and higher topological charges. We also show that stable multiring higher-order necklacelike solitons which cannot be found in other schemes are possible.

We address the problem of an unambiguous comparison of a pair of unknown qudit unitary channels. Using the framework of process positive operator valued measures we characterize all solutions and identify the optimal ones. We prove that the entanglement is the key ingredient in designing the optimal experiment for comparison of unitary channels. Without entanglement the optimality cannot be achieved. The proposed scheme is also experimentally feasible.

The variational two-electron reduced-density-matrix (2RDM) method for electronic systems [Phys. Rev. Lett. 93, 213001 (2004)] is extended to compute ground-state distributions of electrons and hydrogen nuclei in molecules beyond the Born-Oppenheimer approximation. While traditional methods for nuclei rely on the construction of expensive potential energy surfaces or other approximations, the variational 2RDM method has the advantage of treating both electrons and hydrogen nuclei as quantum-mechanical particles simultaneously. Because these particles interact by pairwise Coulombic potentials, the ground-state energy is expressible as a linear functional of three 2RDMs corresponding to two electrons, two hydrogens, and one electron and one hydrogen. Nuclei other than hydrogen are treated in the Born-Oppenheimer approximation. Variational optimization of the ground-state energy requires that the 2RDMs be restricted by $N$-representability conditions to represent a realistic $N$-particle system where $N$ is the total number of electrons and hydrogens. Recent progress in electronic systems with (i) developing necessary $N$-representability conditions and (ii) optimizing the ground-state energy subject to these conditions is extended to systems with two types of particles, electrons and nuclei. The nuclear-electronic 2RDM method can be applied to studying macroscopic quantum phenomena in molecules with “floppy” or resonant hydrogens. Illustrative applications are made to (i) large-scale hydrogen motion in hydrogen-bonded molecules and protonated acetylene ${\mathrm{C}}_2\mathrm{H}_3{}^{+}$ and (ii) hydrogen resonance in malonaldehyde ${\mathrm{C}}_3{\mathrm{H}}_4{\mathrm{O}}_2$ and ammonia $\mathrm{N}{\mathrm{H}}_3$.

We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been fully investigated for electrons in two dimensions. We follow the approach originally proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. 23, 1915 (1983); J. Chem. Phys. 85, 7184 (1986)]. The resulting functional depends on two parameters that are adjusted to a test set of parabolically confined quantum dots. Our exchange functional is then tested on a variety of systems with promising results, reducing the error in the exchange energy by a factor of 4 with respect to the simple local density approximation.

Elastic differential cross sections have been measured for electron-$\mathrm{S}{\mathrm{F}}_6$ and electron-$\mathrm{C}{\mathrm{S}}_2$ collisions in the energy range from $30\mathrm{eV}\text{to}500\mathrm{eV}$ using a high resolution electron spectrometer. The measured cross sections have been put on an absolute scale using the relative flow technique. The total and momentum transfer cross sections have been determined by extrapolating the differential cross-section data using a least-squares fitting procedure based on standard Legendre polynomial expansion. The measured data are compared with theoretical and other experimental data wherever available. It is seen that the theoretical calculations based on independent-atom-model without polarization potential overestimates the cross sections at lower energies while at higher energies the model seems to be describing the interaction effects adequately.

We analyze the ac Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum.

Electrostatic velocity filtering and guiding is an established technique to produce high fluxes of cold polar molecules. In this paper we clarify different aspects of this technique by comparing experiments to detailed calculations. In the experiment, we produce cold guided beams of the three water isotopologs ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{D}}_2\mathrm{O}$, and HDO. Their different rotational constants and orientations of electric dipole moments lead to remarkably different Stark shift properties, despite the molecules being very similar in a chemical sense. Therefore, the signals of the guided water isotopologs differ on an absolute scale and also exhibit characteristic electrode voltage dependencies. We find excellent agreement between the relative guided fractions and voltage dependencies of the investigated isotopologs and predictions made by our theoretical model of electrostatic velocity filtering.

We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum Hall regime, which is reached when the rotation frequency $\Omega$ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency $\omega$ and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are always pinned at the maxima of the optical-lattice potential, similar to the slow-rotation case. At intermediate pinning strength, however, due to the competition between interactions and pinning energy, a structure arises for the two-component case where the vortices are pinned on lines of minimal potential.

We show that a $40\text{−}\mu \mathrm{m}$-diameter vertical-cavity surface-emitting laser (VCSEL) is capable of supporting spatially localized structures with linear polarization, orthogonal to the principal polarization. The VCSEL is biased above the lasing threshold and emits a well-defined linear polarization (principal polarization). A holding beam with orthogonal polarization is injected into the cavity, and a localized structure is spontaneously switched on. The orthogonally polarized localized structure is shown to be bistable when the injection current is varied. Numerical results based on a rate equation model support the experimental findings.

We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and vice versa. We also consider the different bipartitions of the system, finding similar relationships between their entanglement evolutions.

We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length of a quantum string is the maximal length in the superposition). This complements work by Schumacher and Westmoreland who calculated the corresponding rate for minimizing the output’s average length. Our compressed code words are prefix-free indeterminate-length quantum bit strings which can be concatenated in the case of multiple sources. Therefore, we generalize the known theory of prefix-free quantum codes to the case where strings have indeterminate length. Moreover, we describe a communication model which allows the lossless transmission of the compressed code words. The benefit of compression is then the reduction of transmission errors in the presence of noise.

The $m{\alpha }^6(m∕M)$-order corrections to the hyperfine splitting in the $\mathrm{H}_2{}^{+}$ ion are calculated. That allows a reduction of the uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about $10\mathrm{ppm}$. The results are in good agreement with the high-precision experiment carried out by Jefferts [Phys. Rev. Lett. 23, 1476 (1969)].

Two path integral representations for the $T$ matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of “phantom” degrees of freedom which take away explicit phases that diverge for asymptotic times. In addition, energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. These expressions may be useful for attempts to evaluate the path integral in real time and for alternative multiple scattering expansions. Standard eikonal-type high-energy approximations and systematic expansions immediately follow.

We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number $N=1$, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.