The best performance of a Mach-Zehnder interferometer is achieved with the input state $\mid N_T∕2+1⟩\mid N_T∕2-1⟩+\mid N_T∕2-1⟩\mid N_T∕2+1⟩$, $N_T$ being the total number of atoms or photons. This gives (i) a phase-shift error confidence $C_{68\%}=2.67∕N_T$ with (ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling $\sim 1∕N_T$ but with higher prefactors and at the price of a statistical analysis of two or more independent measurements.

Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions $W$ to represent quantum states in a Hilbert space with finite dimension. We show that such a class of Wigner functions $W$ can be defined so that the only pure states having non-negative $W$ for all such functions are stabilizer states, as conjectured by Galvão, [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of $W$ for all definitions of $W$ in the class form a subgroup of the Clifford group. This means pure states with non-negative $W$ and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.

A practical high-accuracy relativistic method of atomic structure calculations for univalent atoms is presented. The method is rooted in the coupled-cluster formalism and includes nonperturbative treatment of single and double excitations from the core and single, double, and triple excitations involving valence electron. Triple excitations of core electrons are included in the fourth order of many-body perturbation theory. In addition, contributions from the disconnected excitations are incorporated. Evaluation of matrix elements includes all-order dressing of lines and vertices of the diagrams. The resulting formalism for matrix elements is complete through the fourth order and sums certain chains of diagrams to all orders. With the developed method we compute removal energies, magnetic-dipole hyperfine-structure constants $A$, and electric-dipole amplitudes. We find that the removal energies are reproduced within 0.01–0.03 % and the hyperfine constants of the $3s_{1∕2}$ and $3p_{1∕2}$ states with a better than 0.1% accuracy. The computed dipole amplitudes for the principal $3s_{1∕2}\text{−}3p_{1∕2;3∕2}$ transitions are in an agreement with 0.05%-accurate experimental data.

The zero-range potential approach is extended for the description of situations where two-body scattering is resonant in arbitrary partial waves. The formalism generalizes the Fermi pseudopotential which can be used only for $s$-wave broad resonances. In a given channel, the interaction is described either in terms of a contact condition on the wave function or with a family of pseudopotentials. We show that it is necessary to introduce a regularized scalar product for wave functions obtained in the zero-range potential formalism (except for the Fermi pseudopotential). This metrics shows that the geometry of these Hilbert spaces depends crucially on the interaction.

Results of a theoretical study of photoionization cross sections and photoelectron angular asymmetry parameters of atoms confined by positively ${\mathrm{C}}_{60}^{+z}$ or negatively ${\mathrm{C}}_{60}^{-z}$ charged fullerene shells are presented. For negatively charged ${\mathrm{C}}_{60}$, entirely new confinement resonances, termed Coulomb confinement resonances, that dominate the spectra of the encapsulated atoms are predicted. In addition, the effect of a negative ${\mathrm{C}}_{60}$ shell is to move some of the oscillator strength of the encapsulated atom from the discrete excitation region into the continuum. For positively charged ${\mathrm{C}}_{60}$, the situation is much different; no Coulomb confinement resonances occur in the photoionization spectrum of the encapsulated atom, and charging the shell positively does nothing to the photoionization cross section (as a function of photon energy) except to increase the threshold energy. The findings result from model Hartree-Fock calculations of $1s$ photoionization of Ne confined by neutral, negative, and positive ${\mathrm{C}}_{60}$.

We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create coexistent quantum accelerator modes, and hence how momentum transfer that depends on the atoms’ internal state can be achieved. When combined with microwave driving of the transition between the states, a different type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes.

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.

Detection of weak forces with an accuracy beyond the standard quantum limit holds promise both for fundamental research and for technological applications. Schemes involving ultracold atoms for such measurements are now considered to be prime candidates for increased sensitivity. In this paper we use a combination of analytical and numerical techniques to investigate the possible subshot-noise estimation of applied force fields through detection of coherence dynamics of Bose-condensed atoms in asymmetric double-well traps. Following a semiclassical description of the system dynamics and fringe visibility, we present numerical simulations of the full quantum dynamics that demonstrate the dynamical production of phase squeezing beyond the standard quantum limit. Nonlinear interactions are found to limit the achievable amount to a finite value determined by the external weak force.

We consider a Bose-Einstein condensate confined in a “Mexican hat” or sombrero potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective-mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.

The polarization analysis of quantized probe light transmitted through an atomic ensemble has been used to prepare entangled collective atomic states. In a “balanced” detection configuration, where the difference signal from two detection ports is analyzed, the continuous monitoring of a component of the Stokes field vector provides a means for conditional projective measurements on the atomic system. Here, we make use of classical driving fields, in the pulsed regime, and of an “unbalanced” detection setup (single detector) where the effective photon number of scattered photons is the detected observable. Conditional atomic spin squeezed states and superpositions of such squeezed states can be prepared in this manner.

A nonperturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. This theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either ad hoc or perturbatively defined field operators. Moreover, our (exact) formalism remains valid beyond the quasimonochromatic paraxial limit.

We propose a method to decelerate polar molecules from a beam using a microwave field. A moving standing wave of a microwave electric field causes an ac Stark shift to polar molecules and decelerates them. The method is applicable to polar molecules in rotational ground states and can be used to directly load a microwave trap. Numerical simulations are presented indicating large phase-space acceptance volume.

We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.

We show that the generalized Bell-type inequality, explicitly involving rotational symmetry of physical laws, is very efficient in distinguishing between true $N$-particle quantum correlations and correlations involving less particles. This applies to various types of generalized partial separabilities. We also give a rigorous proof that the Bell inequalities are maximally violated by the GHZ states, and find a very handy description of the $N$-qubit correlation function.

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free (DF) subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d\left(n\right)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.

We study the quantum-state transfer (QST) of a class of tight-bonding Bloch electron systems with mirror symmetry by considering the mode entanglement. Some rigorous results are obtained to reveal the intrinsic relationship between the fidelity of QST and the mirror mode concurrence (MMC), which is defined to measure the mode entanglement with a certain spatial symmetry and is just the overlap of a proper wave function with its mirror image. A complementarity is discovered as the maximum fidelity is accompanied by a minimum of the MMC. At the instant that is just half of the characteristic time required to accomplish a perfect QST, the MMC can reach its maximum value of 1. A large class of perfect QST models with a certain spectral structure is discovered to support our analytical results.

A nine-state close coupling approximation has been employed to investigate the $e^{-}+\mathrm{Ps}$ scattering up to the incident energy $n=4$ excitation threshold of the Ps atom. The $s$- and $p$-wave Feshbach resonances predicted by Ho [Phys. Lett. 102A, 348 (1984) and Phys. Rev. A 60, 2834 (1999)] have been noticed below all the thresholds up to $n=4$. The present study shows the success of close coupling model in predicting the resonances in the elastic channel.

Measurements of the partial double differential ionization cross sections of argon atoms have been made by performing coincidences between recoil ions and energy- and angle-selected slow electrons produced in $12–24\mathrm{keV}$ $e^{-}\text{−}\mathrm{Ar}$ collisions. Results show that the ${\mathrm{Ar}}^{3+}$ ions are formed mainly by a two-step-one process via electron shake-off. These measurements have enabled determination of the shake-off probability $S=0.14\pm 0.01$ for $L_{2,3}$ subshell, which is in good agreement with a theoretical predication. Additionally, ${\mathrm{Ar}}^{2+}$ and ${\mathrm{Ar}}^{+}$ ions are found to arise respectively from the filling of $L$-shell vacancy by an auger transition and from the direct ionization of $M$-shell of the argon atom.

We have investigated the dependence of two electron processes leading to dissociation on the orientation of the ${\mathrm{H}}_2$ molecule, by measuring differential cross sections for proton fragment emission in coincidence with the outgoing projectile charge state. Proton energy spectra $(4–15\mathrm{eV})$ emerging at angles 10° and 90° were obtained for ${\mathrm{He}}^{+}$ and ${\mathrm{He}}^0$ charge states from ${\mathrm{He}}^{2+}+{\mathrm{H}}_2$ collisions at $E_P=25$ and $100\mathrm{keV}∕\mathrm{amu}$ ($v_P=1$ and $2\mathrm{a.u.}$). By means of the Franck-Condon approximation we found the contribution to the proton emission from the $2p{\pi }_u$, $2s{\sigma }_g$, $2p{\sigma }_u$, and Coulomb explosion dissociation channels, allowing us to obtain cross sections for double capture, transfer ionization, and transfer excitation processes. Cross sections for double ionization and ionization plus excitation were also obtained from the measured data. The results were discussed on the basis of a two-step model within the independent electron approximation, using a perturbative approach for the single capture process.

We make a systematic study of high-order harmonic generation (HHG) in a ${\mathrm{He}}^{+}$-like model ion when the initial state is prepared as a coherent superposition of the ground state and an excited state. It is found that, according to the degree of the ionization of the excited state, the laser intensity can be divided into three regimes in which HHG spectra exhibit different characteristics. The pulse-duration dependence of the HHG spectra in these regimes is studied. We also demonstrate evident advantages of using coherent superposition state to obtain high conversion efficiency. The conversion efficiency can be increased further if ultrashort laser pulses are employed.