The possibility of using neutral and double ionized erbium for atomic clocks of high precision is investigated. In both cases the narrow electric quadrupole clock transition between the ground and first exited states of the same configuration lies in optical region. The estimated ratio of decay width to transition energy is less then ${10}^{-20}$. We demonstrate that these transitions are not sensitive to blackbody radiation, and if other perturbations are also considered the relative accuracy of the clocks can probably reach the level of ${10}^{-18}$ or better.

A density-functional-theory method for analyzing effects of strong electron correlation is presented, based on a single Kohn-Sham determinant. It yields the population of effectively unpaired (odd) electrons and depicts the strength of nondynamic correlation, both locally and globally. It provides also a quantitative estimate of localized magnetic moments without invoking symmetry-breaking procedures. Preliminary tests on some exemplary systems of strong correlation such as C${}_2$, Cr${}_2$, the NO dimer, and dissociating H${}_2$ and N${}_2$ are discussed in comparison with available post-Hartree-Fock wave-function studies. We show that the bond in C${}_2$ is unlikely to have diradical character in its ground state, but may have it in some excited state. The singlet ground state of the NO dimer, however, does have a diradical character of the bonding. Quite interestingly, the bond in Cr${}_2$ has a quad-radical nature.

The chiral $p$-wave ($p_x\pm i{p}_y$) superfluid has attracted significant attention in recent years, mainly because its vortex core supports a Majorana fermion which, due to its non-Abelian statistics, can be explored for implementing topological quantum computation. Mixing dipolar bosons with fermions in quasi-two-dimensional space offers the opportunity to use the roton minimum as a tool for engineering the phonon-induced attractive interaction between fermions. We study, within the Hartree-Fock-Bogoliubov approach, the $p$-wave superfluid pairings in a quasi-two-dimensional dipolar Bose-Fermi mixture. We show that enhancing the induced interaction by lowering the roton minimum can affect the stability property of the mixture as well as the effective mass of the fermions in an important way. We also show that one can tune the system to operate in stable regions where chiral $p$-wave superfluid pairings can be resonantly enhanced by lowering the energy cost of the phonons near the roton minimum.

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate from a Bardeen-Cooper-Schrieffer state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field, our Hamiltonian includes the leading postadiabatic effects that arise because the crossover proceeds at a nonzero sweep rate. We apply a path-integral approach and a stationary phase approximation for the molecular $\mathbf{k}=\mathbf{0}$ background, which is a good approximation for narrow resonances [see, e.g., Diehl and Wetterich, Phys. Rev. A 73, 033615 (2006) as well as Diehl, Gies, Pawlowski, and Wetterich, Phys. Rev. A 76, 053627 (2007)]. We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the $\mathbf{k}\ne \mathbf{0}$ molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a postadiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs.

By means of a mean-field method, we have studied the zero-temperature structure and excitation spectrum of a three-dimensional soft-core bosonic system for a value of the interaction strength that favors a crystal structure made of atomic nanoclusters arranged with fcc ordering. In addition to the longitudinal and transverse phonon branches expected for a normal crystal, the excitation spectrum shows a soft mode related to the breaking of gauge symmetry, which signals a partial superfluid character of the solid. Additional evidence of supersolidity is provided by the calculation of the superfluid fraction, which shows a first-order drop, from 1 to 0.4, at the liquid-supersolid transition and a monotonic decrease as the interaction strength parameter is increased. The conditions for the coexistence of the supersolid with the homogeneous superfluid are discussed, and the surface tension of a representative solid-liquid interface is calculated.

High-order harmonics generated from multiple orbitals of aligned O${}_2$ molecules are studied theoretically and we focus on the effect of two-center interference during photoexcitation. We find that the contribution of the harmonics generated from different molecular orbitals to the total harmonics varies distinctively with the laser intensity. The total harmonic spectra are dominated by the harmonics generated from a 1${\pi }_g$ valence shell at lower intensities, but are dominated by those generated from a 1${\pi }_u$ valence shell at higher intensities. This change is a sequence of the structure-induced two-center interference during photoexcitation of harmonic generation. This study indicates that by properly choosing the intensity of driving laser pulses, one can extract the orbital information of both the 1${\pi }_g$ and the 1${\pi }_u$ valence shells by the generated harmonics. This provides a potential way to tomographically reconstruct the low-lying 1${\pi }_u$ valence shell.

In a recent article [Phys. Rev. A 87, 022340 (2013)], Yan et al. have studied geometric discord for a well-known class of bound entangled states. Based on their calculation, they claim “It is found that there exists a nondynamic sudden change in quantum discord” for these states. In this Comment, we criticize their work by pointing out that what has been calculated is actually a bound and is not the exact value of discord. Since, generally, it is not possible to infer the exact value (or property) of a quantity just from its bound, we cannot conclude about (exact) discord and its change. Thus, the above-mentioned conclusion cannot be drawn from the calculations of the paper.

We exhibit an operational connection between mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exist in dimension 6.

The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et al. [T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Phys. Rev. Lett. 111, 030501 (2013)] showed how to make this statement quantitative, using semidefinite programming to calculate how much entanglement is certified by a given violation. Here I adapt their techniques to the case in which Bob's measurement devices are in fact trusted, the setting for Einstein-Podolsky-Rosen steering inequalities. Interestingly, all of the steering inequalities studied turn out to require negativity for their violations. This supports a significant strengthening of Peres's conjecture that negativity is required to violate a bipartite Bell inequality.

We consider the application of the minimax strategy to discrimination between quantum states with a certain fraction of inconclusive results. An inconclusive minimax solution is defined as the pair of a collection of prior probabilities and a quantum measurement that achieves the minimax probability of a detection error subject to the constraint that the highest probability of an inconclusive result does not exceed a given value. We first show a necessary and sufficient condition for an inconclusive minimax solution, and derive that the problem of obtaining an inconclusive minimax measurement can be expressed as a semidefinite programming problem. We then present a condition under which there exists a solution such that at least one of the prior probabilities is a zero. We finally show that for any state set with a certain symmetry, an inconclusive minimax solution exists having the same symmetry.

We have measured and analyzed the hyperfine structure of two lines, one at 583 nm and one at 401 nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the $J\to J+1$ laser cooling transitions from the $\left[\text{Xe}\right]4f^{12}6s^2{(}^3{H}_6)$ ground state to two levels of the excited $\left[\text{Xe}\right]4f^{12}6s6p$ configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401 nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are $A_e/h=-100.1\left(3\right)\mathrm{MHz}$ and $B_e/h=-3079\left(30\right)\mathrm{MHz}$, respectively. The hyperfine spectrum of the narrow transition at 583 nm, was previously observed and accurate $A_e$ and $B_e$ coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the $A_e$ and $B_e$ constants, respectively.

The recent adiabatic saddle-point approach of Shearer et al. [Phys. Rev. A 84, 033409 (2011)] is extended to multiphoton detachment of negative ions with outer $p$-state electrons. This theory is applied to investigate the strong-field photodetachment dynamics of F${}^{-}$ ions exposed to few-cycle femtosecond laser pulses, without taking into account the rescattering mechanism. Numerical calculations are considered for mid-infrared laser wavelengths of 1300 and 1800 nm at laser intensities of 7.7 $\times$ 10${}^{12}$, 1.1 $\times$ 10${}^{13}$, and 1.3 $\times$ 10${}^{13}$ W/cm${}^2$. Two-dimensional momenta saddle-point spectra exhibit a distinct distribution in the shape of a “smile” in the complex-time plane. Electron momentum distribution maps of direct electrons are investigated. These produce a distinct pattern of above-threshold detachment (ATD) concentric rings due to constructive and destructive quantum interference of electrons detached from their parent ions. Probability detachment distributions presented, capturing the influence of saturation effects that are found to become more significant with increasing laser intensity at a fixed wavelength. ATD photoangular distributions as functions of laser intensity and wavelength near channel closings are also investigated and found to be sensitive to initial-state symmetry. Nonmonotonic structures observed in the ejected photoelectron energy spectra are attributed to interference effects from coherent electronic wave packets. Additionally the profiles of all the photoelectron emission spectra show strong dependence on the carrier-envelope phase, indicating that it is a reliable parameter for characterizing the wave form of the pulse.

We report a simple scheme to achieve ultrafast and selective population transfer in four-level atoms by utilizing a single nonlinearly chirped femtosecond pulse. It is demonstrated that the almost complete population may be transferred to the preselected state of atoms just by manipulating the so-called frequency offset parameter. The robustness of the scheme against the variation of laser pulse parameters is also investigated. The proposed scheme may be useful for selective population transfer in molecules.

We investigate the propagation of localized three-dimensional spatiotemporal Airy self-accelerating parabolic-cylinder light bullets in a linear medium. In particular, we consider the effects resulting from utilizing initial finite-energy Airy wave packets to accelerate these localized beams in the absence of any external potential. A general localized light bullet solution with the joint Airy pulse characteristics and parabolic-cylinder spatial characteristics is obtained in the Cartesian coordinates, using parabolic-cylinder and Airy functions. Our results show that the localized wave packets can retain their intensity features and still be accelerated over several Rayleigh lengths.

We study spontaneous symmetry breaking in localized modes trapped by a pair of defects embedded in a Bragg grating written in a Kerr-nonlinear material. While the system has two symmetric modes at low energies, the nonlinearity renders one of these unstable in favor of an asymmetric mode emerging at sufficiently high energies. Using a simple semianalytic model, we explain this transition as originating from the degeneracy between a state in a grating with two defects and state in a grating with a single defect.

We calculate magnetic dipole transition amplitudes in $s-s$ and $s-d$ transitions of Rb, Cs, Ba${}^{+}$, Fr, Ra${}^{+}$, Yb${}^{+}$, Ac${}^{2+}$ and Th${}^{3+}$. These transitions were used or considered to be used for parity-nonconservation (PNC) measurements. We also calculate the magnetic $g$-factor anomalies for a selection of states, along with electric quadrupole transition amplitudes for $s-d$ transitions in these systems.

We conjecture uncertainty relations that restrict correlations between the results of measurements performed by two separate parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from the Maassen-Uffink uncertainty relation and is much stronger than the Hall uncertainty relation derived from the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two observables. We provide numerical evidence for the validity of the conjectured uncertainty relations, and we prove them for large classes of states and observables.

Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In particular, quantum control techniques and orthogonal function theory have been applied to the reconstruction of the complete profiles of time-varying magnetic fields. Here, we provide a detailed theoretical analysis of the reconstruction method based on the Walsh functions, highlighting the relationship between the orthonormal Walsh basis, sensitivity of field reconstructions, data compression techniques, and dynamical decoupling theory. Specifically, we show how properties of the Walsh basis and a detailed sensitivity analysis of the reconstruction protocol provide a method to characterize the error between the reconstructed and true fields. In addition, we prove various results about the negligibility function on binary sequences which lead to data compression techniques in the Walsh basis and a more resource-efficient reconstruction protocol. The negligibility proves a fruitful concept to unify the information content of Walsh functions and their dynamical decoupling power, which makes the reconstruction method robust against noise.

Using the core-mass approach, we have generated a vibrational-mass surface for the triatomic ${\mathrm{H}}_3{}^{+}$. The coordinate-dependent masses account for the off-resonance nonadiabatic coupling and permit a very accurate determination of the rovibrational states using a single potential energy surface. The new, high-precision measurements of 12 rovibrational transitions in the ${\nu }_2$ bending fundamental of ${\mathrm{H}}_3{}^{+}$ by Wu et al. [Phys. Rev. A 88, 032507 (2013)] are used to scale this surface empirically and to derive state-dependent vibrational and rotational masses that reproduce the experimental transition energies to ${10}^{-3}{\mathrm{cm}}^{-1}$. Rotational term values for $J\le 10$ are presented for the two lowest vibrational states and equivalent transitions in D${}_3{}^{+}$ considered.