Primary and secondary interference structures attributed to coherent electron emission from the identical atomic centers of ${\mathrm{H}}_2$ have been observed in the velocity distributions of ejected electrons resulting from $(1–5)\text{−}\mathrm{MeV}$ ${\mathrm{H}}^{+}$ impact. The primary interference structures are found to depend on the projectile velocity, in addition to the previously observed dependence on electron ejection angle. In contrast, the secondary structures, attributed to intramolecular scattering, do not change with projectile velocity and show only slight variations with the electron ejection angle. The data also provide evidence for significantly higher-frequency structures for which no explanation currently exists.

Searches for $CP$-violating effects in atoms and molecules provide important constrains on competing extensions to the standard model of elementary particles. In particular, $CP$ violation in an atom leads to the $CP$-odd (T,P-odd) polarizability ${\beta }^{\mathrm{CP}}$: a magnetic moment ${\mu }^{\mathrm{CP}}$ is induced by an electric field ${\mathcal{E}}_0$ applied to an atom, ${\mu }^{\mathrm{CP}}={\beta }^{\mathrm{CP}}{\mathcal{E}}_0$. We estimate the $CP$-violating polarizability for rare-gas (diamagnetic) atoms He through Rn. We relate ${\beta }^{\mathrm{CP}}$ to the permanent electric dipole moment (EDM) of the electron and to the scalar constant of the $CP$-odd electron-nucleus interaction. The analysis is carried out using the third-order perturbation theory and the Dirac-Hartree-Fock formalism. We find that, as a function of nuclear charge $Z,{\beta }^{\mathrm{CP}}$ scales steeply as $Z^{5}R\left(Z\right)$, where slowly varying $R\left(Z\right)$ is a relativistic enhancement factor. Finally, we evaluate the feasibility of setting a limit on electron EDM by measuring $CP$-violating magnetization of liquid Xe. We find that such an experiment could provide competitive bounds on electron EDM only if the present level of experimental sensitivity to ultraweak magnetic fields [Kominis et al., Nature 422, 596 (2003)] is improved by several orders of magnitude.

A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian’s spectrum. Several decoherence times are estimated: ${10}^{-13}–{10}^{-15}\mathrm{s}$ for microscopic systems, and ${10}^{-37}–{10}^{-39}\mathrm{s}$ for macroscopic bodies. For the particular case of a thermal bath, the order of magnitude of our results agrees with that obtained by the einselection (environment-induced decoherence) approach.

We present an efficient strategy to translate a normal quantum algorithm into a sequence of operations on the quantum-cellular-automata-like architecture (QCALA) originally proposed by Lloyd. The QCALA assumes arrays of weakly coupled quantum systems where an interaction exists only between neighboring qubits and can only perform the same quantum operation onto all the qubits. The sequence obtained by the strategy proposed by Lloyd needs at most $12n$ operations, where $n$ is the number of qubits for the original circuit. The sequence obtained by our strategy needs at most $6n$ operations. We also clarified the relations between the upper bound of the number of translated operations and the period of the QCALA and between the upper bound of the number of qubits and the period of the QCALA.

The benzene cation $\left({\mathrm{C}}_6\mathrm{H}_6{}^{+}\right)$ has a doublet $\left(e_{1g}\right)$ ground state in hexagonal ring $\left(D_{6h}\right)$ geometry. Therefore a Jahn-Teller (JT) distortion will lower the energy. The present theoretical study yields a model Hückel-type Hamiltonian that includes an electron-phonon coupling of the $e_{1g}$ electronic ground state with the two $e_{2g}$ vibrational modes: in-plane ring-bending and C-C bond-stretching. We treat also a third $e_{2g}$ C-H bending mode which has less influence. We obtain the electron-phonon couplings from density functional theory which gives a JT energy lowering of $1024{\mathrm{cm}}^{-1}$ in agreement with previous quantum chemistry calculations. We find a nonadiabatic solution for vibrational spectra and predict frequencies shifts of both the benzene cation and anion.

We present a lifetime measurement of the $6s$ level of rubidium. We use a time-correlated single-photon counting technique on two different samples of rubidium atoms, a vapor cell with variable rubidium density, and a sample of atoms confined and cooled in a magneto-optical trap. The $5P_{1∕2}$ level serves as the resonant intermediate step for the two-step excitation to the $6s$ level. We detect the decay of the $6s$ level through the cascade fluorescence of the $5P_{3∕2}$ level at 780 nm. The two samples have different systematic effects, but we obtain consistent results that averaged give a lifetime of $45.57\pm 0.17\mathrm{ns}$.

The Friedel sum rule is generalized to relativistic systems of spin-$\frac{1}{2}$ particles. Its relation with the relativistic Levinson theorem is presented. Density oscillations in such systems are discussed.

A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A{}^1\Sigma _u^{+}\left(1{}^{1}S+1{}^{1}D\right),c{}^3\Pi _u\left(1{}^{3}P+1{}^{1}S\right)$, and $a{}^3\Sigma _u^{+}\left(1{}^{3}P+1{}^{1}S\right)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X{}^1\Sigma _g^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X{}^1\Sigma _g^{+}$ and excited $A{}^1\Sigma _u^{+}\left(1{}^{1}S+1{}^{1}D\right),c{}^3\Pi _u\left(1{}^{3}P+1{}^{1}S\right)$, and $a{}^3\Sigma _u^{+}\left(1{}^{3}P+1{}^{1}S\right)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A{}^1\Sigma _u^{+}\leftarrow X{}^1\Sigma _g^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $-3000\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the $J^{\prime }=1$ state of ${\mathrm{Ca}}_2$ that can mostly be assigned to the $c{}^3\Pi _u$ state. The two by far most intense lines at a detuning frequency around $-800\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the $1{}^{3}P+1{}^{1}S$ asymptote which are heavily mixed and can partly be assigned to the $A{}^1\Sigma _u^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.

The Compton profile of the neon atom is calculated from an accurate Kohn-Sham potential derived from accurate quantum Monte Carlo wave functions. Compared to the experiment, the results are better than the Hartree-Fock ones in the low-wave-vector region. This suggests that the systematic error in the Kohn-Sham formulation in momentum space is relatively small. The first-order Lam-Plazman correction is also calculated. This correction is less than 1% on the average.

We present a time-dependent method for calculating the energy-dependent atomic dipole phase that an electron acquires when it is ionized by the absorption of a single ultraviolet photon. Our approach exactly mirrors the method used to experimentally characterize a train of attosecond pulses. In both methods the total electron phase is measured (calculated) via a two-photon interference involving the absorption or emission of an additional infrared photon in the continuum. In our calculation we use a perfect (zero spectral phase) light field and so extract the atomic dipole phase directly from the electron wave packet. We calculate the atomic phase for argon, neon, and helium at low infrared intensities and compare them to previous perturbative calculations. At moderate infrared probe intensities, we find that that the dipole phase can still be reliably determined using two-photon interference, even when higher-order processes are non-negligible. We also show that a continuum structure, in this case a Cooper minimum in argon, significantly affects the probability for infrared absorption and emission over a range of energies around the minimum, even at low infrared intensities. We conclude that well-characterized attosecond pulse trains can be used to examine continuum structures in atoms and molecules.

We investigate the single-particle properties at $T=0$ of a trapped superfluid gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance leads to the BCS–Bose-Einstein condensate (BEC) crossover, where the character of superfluidity continuously changes from the BCS-type to a BEC of composite bosons. In this paper, we extend our previous work for a uniform superfluid Fermi gas [Y. Ohashi and A. Griffin, Phys. Rev. A 67, 063612 (2003)] to include the effect of a harmonic trap. We do not use the local density approximation (LDA), but directly solve the Bogoliubov–de Gennes (BdG) coupled equations. While our explicit numerical solutions are for a weak (narrow) Feshbach resonance, we argue that the single-particle BdG excitation spectrum will exhibit the same features for a strong (broad) Feshbach resonance. Using these equations, we find self-consistent values for the spatially dependent local density $n\left(\mathbf{r}\right)$ as well as the composite BCS order parameter $\tilde{\Delta }\left(\mathbf{r}\right)$, the latter describing both the Cooper-pair and molecular condensate contributions. Using these results, we calculate the single-particle density of states in the crossover region, and from this determine the true single-particle energy gap $\left(E_g\right)$ of the trapped Fermi superfluid. This is associated with the in-gap (or Andreev) states in the low-density region at the edge of the trap. We calculate the laser-induced tunneling current $I\left(\omega \right)$ into another hyperfine state, as measured in recent rf spectroscopy experiments. This rf spectrum gives a direct probe of the quasiparticle spectrum. We show how the high-energy part of $I\left(\omega \right)$ gives information about $\tilde{\Delta }(r=0)$ at the center of the trap (which is comparable to the Fermi energy ${\epsilon }_F$ in the crossover region). We show that $I\left(\omega \right)$ is very dependent on the spatial profile of the pair potential $\tilde{\Delta }\left(r\right)$ that is used. We also emphasize that the narrow “unpaired atom" peak in the rf data gives information about $E_g$ and the low-energy $(⪡{\epsilon }_F)$ in-gap states of a Fermi superfluid. While our calculations are limited to $T=0$, we use them to discuss the recent data of Chin et al. and the LDA calculations of Törmä and co-workers. The LDA, while useful, can lead to an incorrect physical picture of the low-density surface region of the Fermi superfluid.

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS’s) with large amplitudes out of CSS’s with small amplitudes using inefficient photon detection. The small CSS’s required to produce CSS’s with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.

We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely $W$ states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.

We present protocols for multiparty data hiding of quantum information that implement all possible threshold access structures. Closely related to secret sharing, data hiding has a more demanding security requirement: that the data remain secure against unrestricted attacks via local operation and classical communication. In the limit of hiding a large amount of data, our protocols achieve an asymptotic rate of one hidden qubit per local physical qubit. That is, each party holds a share that is the same size as the hidden state to leading order, with accuracy and security parameters incurring an overhead that is asymptotically negligible. The data-hiding states have very unusual entanglement properties, which we briefly discuss.

We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison of the optimal strategies where either entangled or unentangled input states are used.

A conditional protocol of transferring quantum correlations in a continuous variable regime was experimentally demonstrated. The quantum correlation in two pairs of twin beams, each characterized by intensity-difference squeezing of $7.0\pm 0.3\mathrm{dB}$, was transferred to two initially independent idler beams. The quantum-correlation transfer resulted in intensity-difference squeezing of $4.0\pm 0.2\mathrm{dB}$ between two idler beams. The dependence of the preparation probability and transfer fidelity on the selection bandwidth was also studied.

Within the framework of a fully quantum-mechanical molecular-orbital close-coupling (QMOCC) theory, charge transfer has been studied for collisions of S with ${\mathrm{H}}^{+}$. The multireference single- and double-excitation configuration-interaction method was utilized to evaluate the adiabatic potentials and nonadiabatic coupling matrix elements for the $S{\mathrm{H}}^{+}$ system. Cross sections and rate coefficients are presented for $S({}^{3}P,{}^{1}D)+{\mathrm{H}}^{+}\to S^{+}({}^{4}S^0,{}^{2}D^0,{}^{2}P^0)+\mathrm{H}$ with relative collision energies between $0.1\mathrm{meV}∕u$ and $10\mathrm{keV}∕u$ and temperatures between $10\mathrm{K}$ and $2.0\times {10}^6\mathrm{K}$. The investigation shows that the charge-transfer process is dominated by $S\left({}^{3}P\right)+{\mathrm{H}}^{+}\to S^{+}\left({}^{2}P^0\right)+\mathrm{H}$ and that the cross sections and rate coefficients vary by orders of magnitude over the energy and temperature range considered. The current rate coefficients are in disagreement with the often adopted value of $1.30\times {10}^{-9}{\mathrm{cm}}^3∕\mathrm{s}$ at low temperatures, and two orders of magnitude smaller than a previous estimate at $T={10}^4\mathrm{K}$, for the process $S\left({}^{3}P\right)+{\mathrm{H}}^{+}\to S^{+}({}^{2}D^0,{}^{2}P^0)+\mathrm{H}$. We also perfomed semiclassical close-coupling calculations, which give cross sections in excellent agreement agreement with the QMOCC results for energies above $30\mathrm{eV}∕u$. Application of the results to astrophysical environments is briefly discussed.

In ion-atom collisions, the charge transfer cross section is typically a strong function of the energy defect or $Q$ value, typically with smaller energy defects giving rise to higher capture probabilities. In some theoretical treatments, for example those based on the Demkov model, the cross section is a strong function of the magnitude of the $Q$ value, but is independent of its sign. In order to test this predicted sign independence, one must compare capture cross sections from energetically symmetric collision channels. In this work, relative capture cross sections, differential in scattering angle, are measured and compared for the energetically symmetric channels: ${\mathrm{Rb}}^{+}+\mathrm{Rb}\left(5s\right)\to \mathrm{Rb}\left(5p\right)+{\mathrm{Rb}}^{+}$ and ${\mathrm{Rb}}^{+}+\mathrm{Rb}\left(5p\right)\to \mathrm{Rb}\left(5s\right)+{\mathrm{Rb}}^{+}$. It is found that not only are the two cross sections not equal, but that in this case the endoergic channel was 3 times more likely. That is, the entropy reducing channel was preferred. An intuitive model, based on molecular potential curves, is suggested. The endoergic propensity is found to be consistent with this model.

Propagation of a Boson-Fermion (BF) pair in a BF environment is considered. The possibility of formation of stable strongly correlated BF pairs, embedded in the continuum, is pointed out. The Fermi gas of correlated BF pairs shows a strongly modified Fermi surface. The interaction between like particles is neglected in this exploratory study. Various physical situations where our pairing mechanism could be of importance are invoked.

We investigate dynamics in two-component Bose-Einstein condensates in the context of coupled Gross-Pitaevskii equations and derive results for the evolution of the total density fluctuations. Using these results, we show how, in many cases of interest, the dynamics can be accurately described with an effective one-component Gross-Pitaevskii equation for one of the components, with the trap and interaction coefficients determined by the relative differences in the scattering lengths. We discuss the model in various regimes, where it predicts breathing excitations, and the formation of vector solitons. An effective nonlinear evolution is predicted for some cases of current experimental interest. We then apply the model to construct quasistationary states of two-component condensates.