Nagata [Phys. Rev. A 73, 066101 (2006)] questions whether a general no-go theorem of Malley [Phys. Rev. A 69, 022118 (2004)] applies to local hidden variables and outlines a “counterexample.” In fact this is not a counterexample at all, but in seeing why it fails we clarify the significance of Malley’s result and its relation to other no-go theorems.

The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control, Viola and Knill proposed a method called “Eulerian decoupling” that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the local structure of internal couplings and couplings to an environment that typically occur in multipartite quantum systems. In this paper we define a combinatorial structure called Eulerian orthogonal array. It merges the desirable properties of orthogonal arrays and Eulerian cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be used to remove both internal couplings and couplings to an environment of a multipartite quantum system. Furthermore, we show how to construct Eulerian orthogonal arrays having good parameters in order to obtain efficient decoupling schemes.

We review the entanglement properties in collective models and their relationship with quantum phase transitions. Focusing on the concurrence, which characterizes the two-spin entanglement, we show that for first-order transitions, this quantity is singular but continuous at the transition point, contrary to the common belief. We also propose a conjecture for the concurrence of arbitrary symmetric states which connects it with a recently proposed criterion for bipartite entanglement.

A joint measurement of two observables is a simultaneous measurement of both quantities upon the same quantum system. When two quantum-mechanical observables do not commute, then a joint measurement of these observables cannot be accomplished directly by projective measurements alone. In this paper we shall discuss the use of quantum cloning to perform a joint measurement of two components of spin associated with a qubit system. We introduce cloning schemes which are optimal with respect to this task. The cloning schemes may be thought to work by cloning two components of spin onto their outputs. We compare the proposed cloning machines to existing cloners.

Variational reduced-density-matrix theory is applied to calculating the ground-state energy and two-electron reduced density matrices (2-RDMs) of the one-dimensional Hubbard model for a range of interaction strengths. The 2-RDM is constrained to represent an $N$-particle wave function by two sets of $N$-representability conditions, known as the 2- and partial 3-positivity conditions. Variational optimization of the energy with the 2-RDM constrained by $N$-representability conditions is performed using a first-order semidefinite-programming algorithm that was developed for treating atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Accurate energies for a broad range of interaction strengths indicate that the variational 2-RDM method is a valuable tool for studying strongly correlated electrons.

The spectra of autoionizing Rydberg series of europium atoms are analyzed by a semiempirical multichannel quantum defect theory (MQDT). Experimental data were obtained using two-step resonance ionization spectroscopy below the $5d{}^{9}D_J$ ionic multiplet. The MQDT model involving five channels and three limits is used to analyze the observed four odd-parity Rydberg series. Theoretical energies are computed and compared with the experimental values. The Rydberg series are assigned on the basis of calculated admixture coefficients. The series having $J=3∕2$ are interpreted as $5dnd$ $(2,3∕2)$, $5dnd$ $(2,5∕2)$, $5dnd$ $(3,3∕2)$, and $5dnd$ $(3,5∕2)$. Interseries perturbations and perturbations due to levels of configuration $5dnd$ $(4,5∕2)$ are investigated. Some of the unobserved levels are also predicted.

Unimolecular decay rates and monomer-dimer branching ratios of gold clusters ${{\mathrm{Au}}_N}^{+}$ $(N=7–27)$ have been measured as a function of excitation energy in photodissociation experiments on size-selected clusters stored in a Penning trap. Part of the data set has previously been used to extract model-free values of dissociation energies [Vogel et al., Phys. Rev. Lett. 87, 013401 (2001)]. Other parts of the data set do not allow this analysis. We use these data to extract tentative dissociation energies, based on the systematics of deviations between an Arrhenius analysis and the model-free values. The observed systematics also allows an estimate of the true frequency factor which often is much higher than the Arrhenius value but in good agreement with the expected detailed balance value. The data are also reanalyzed including radiative cooling which may explain part of the discrepancy between model-free and Arrhenius dissociation-energy values.

We propose a laser cooling method for atomic species whose level structure makes traditional laser cooling difficult. For instance, laser cooling of hydrogen requires single-frequency vacuum-ultraviolet light, while multielectron atoms need single-frequency light at many widely separated frequencies. These restrictions can be eased by laser cooling on two-photon transitions with ultrafast pulse trains. Laser cooling of hydrogen, antihydrogen, and many other species appears feasible, and extension of the technique to molecules may be possible.

We investigate several mechanisms of vortex creation during splitting of a spinor Bose-Einstein condensate (BEC) in a magnetic double-well trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap [Y. Shin et al., Phys. Rev. A 72, 021604 (2005)], where an unexpected fork-like structure appeared in the interference fringes indicating the presence of a singly quantized vortex in one of the interfering condensates. It is well known that in a spin-1 BEC in a quadrupole trap, a doubly quantized vortex is topologically produced by a “slow” reversal of bias magnetic field $B_z$. Since in the experiment a doubly quantized vortex had never been seen, Shin et al. ruled out the topological mechanism and concentrated on the nonadiabatic mechanical mechanism for explanation of the vortex creation. We find, however, that in the magnetic trap considered both mechanisms are possible: singly quantized vortices can be formed in a spin-1 BEC topologically (for example, during the magnetic field switching-off process). We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. We also present a numerical example of creation of singly quantized vortices due to “fast” splitting; i.e., by a dynamical (nonadiabatic) mechanism.

We consider group delay and broadening using two strongly absorbing and widely spaced resonances. We derive relations which show that very large pulse bandwidths coupled with large group delays and small broadening can be achieved. Unlike single resonance systems, the dispersive broadening dominates the absorptive broadening which leads to a dramatic increase in the possible group delay. We show that the double resonance systems are excellent candidates for realizing all-optical delay lines. We report on an experiment which achieved up to 50 pulse delays with 40% broadening.

This paper is a theoretical work in support of a newly proposed experiment [R. Stutz and E. Cornell, Bull. Am. Soc. Phys. 89, 76 (2004)] that promises greater sensitivity to measurements of the electron’s electric dipole moment (EDM) based on the trapping of molecular ions. Such an experiment requires the choice of a suitable molecule that is both experimentally feasible and possesses an expectation of a reasonable EDM signal. We find that the molecular ions $\mathrm{Pt}{\mathrm{H}}^{+}$ and $\mathrm{Hf}{\mathrm{H}}^{+}$ are both suitable candidates in their low-lying ${}^3\Delta$ states. In particular, we anticipate that the effective electric fields generated inside these molecules are approximately 73 and $-17\mathrm{GV}∕\mathrm{cm}$, respectively. As a byproduct of this discussion, we also explain how to make estimates of the size of the effective electric field acting in a molecule, using commercially available nonrelativistic molecular structure software.

We present two quantum-state sharing protocols where the channels are not maximally entangled states. By properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state if the parties collaborate. We also show that contrary to the protocols where we have maximally entangled channels these protocols are probabilistic. We then compare the efficiency of both protocols and sketch the generalization of the protocols to $N$ parties.

Quantal calculations for scattering of ground-state antihydrogen by metastable $(n=2S)$ helium atoms have been performed using the nonadiabatic, atomic orbital expansion technique at thermal energies. The zero-energy elastic cross sections of the present systems are much greater than the corresponding value for the ground-state helium target. The low-energy elastic cross section for the singlet metastable helium $\left[\mathrm{He}\right(2{}^{1}S\left)\right]$ target is higher than the corresponding value when the target is in the metastable triplet state $\left[\mathrm{He}\right(2{}^{3}S\left)\right]$.

Stark deceleration relies on time-dependent inhomogeneous electric fields which repetitively exert a decelerating force on polar molecules. Fourier analysis reveals that such fields, generated by an array of field stages, consist of a superposition of partial waves with well-defined phase velocities. Molecules whose velocities come close to the phase velocity of a given wave get a ride from that wave. For a square-wave temporal dependence of the Stark field, the phase velocities of the waves are found to be odd-fraction multiples of a fundamental phase velocity $\lambda ∕\tau$, with $\lambda$ and $\tau$ the spatial and temporal periods of the field. Here we study explicitly the dynamics due to any of the waves as well as due to their mutual perturbations. We first solve the equations of motion for the case of single-wave interactions and exploit their isomorphism with those for the biased pendulum. Next we analyze the perturbations of the single-wave dynamics by other waves and find that these have no net effect on the phase stability of the acceleration or deceleration process. Finally, we find that a packet of molecules can also ride a wave which results from an interference of adjacent waves. In this case, small phase stability areas form around phase velocities that are even-fraction multiples of the fundamental velocity. A detailed comparison with classical trajectory simulations and with experiment demonstrates that the analytic “wave model” encompasses all the longitudinal physics encountered in a Stark decelerator.

We study one-dimensional fermions with photoassociation or with a narrow Fano-Feshbach resonance described by the boson-fermion resonance model. Using the bosonization technique, we derive a low-energy Hamiltonian of the system. We show that at low energy, the order parameters for the Bose condensation and fermion superfluidity become identical, while a spin gap and a gap against the formation of phase slips are formed. As a result of these gaps, charge density wave correlations decay exponentially in contrast with the phases where only bosons or only fermions are present. We find a Luther-Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions. This allows us to provide closed form expressions of the density-density correlations and the spectral functions. The spectral functions of the fermions are gapped, whereas the spectral functions of the bosons remain gapless. The application of a magnetic field results in a loss of coherence between the bosons and the fermion and the disappearance of the gap. Changing the detuning has no effect on the gap until either the fermion or the boson density is reduced to zero. Finally, we discuss the formation of a Mott insulating state in a periodic potential. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogoliubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.

We experimentally investigate the outcoupling of atoms from Bose-Einstein condensates using two radio-frequency (rf) fields in the presence of gravity. We show that the fringe separation in the resulting interference pattern derives entirely from the energy difference between the two rf fields and not the gravitational potential difference between the two resonances. We subsequently demonstrate how the phase and polarization of the rf radiation directly control the phase of the matter wave interference and provide a semiclassical interpretation of the results.

The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized Fermi gas with infinitely strong attractive zero-range odd-wave interactions, arising from a confinement-induced resonance reachable via a three-dimensional $p$-wave Feshbach resonance. We investigate the off-diagonal long-range order (ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by analyzing the two-particle reduced density matrix for which we derive a closed-form expression. Using a variational approach and numerical diagonalization we find that the largest eigenvalue of the two-body density matrix is of order $N∕2$, where $N$ is the total particle number, and hence a partial ODLRO is present for a FTG gas in the trap.

We demonstrate that the output of a frequency comb laser can be amplified and upconverted to the vacuum ultraviolet (vuv) in a gaseous medium while its phase coherence is maintained to a high degree ($<\frac{1}{30}$ of a vuv cycle). The produced vuv pulses are well suited to perform frequency comb spectroscopy with sub-MHz accuracy, which is experimentally verified using a Ramsey-type quantum interference scheme to excite a transition in xenon at $125\mathrm{nm}$. The achieved resolution constitutes an improvement of six orders of magnitude compared to previous demonstrations of frequency domain quantum interference in this wavelength range.