We calculate the excitation modes of a one-dimensional (1D) dipolar quantum gas confined in a harmonic trap with frequency ${\omega }_0$ and predict how the frequency of the breathing $n=2$ mode characterizes the interaction strength evolving from the Tonks-Girardeau value ${\omega }_2=2{\omega }_0$ to the quasi-ordered, superstrongly interacting value ${\omega }_2=\sqrt{5}{\omega }_0$. Our predictions are obtained within a hydrodynamic Luttinger-liquid theory after applying the local density approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from reptation quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.

We propose a technique for the creation of maximally entangled symmetric Dicke states in an ion trap using adiabatic passage, which requires only a pair of chirped pulses from a single laser and is applicable to any number of ions and excitations. By utilizing a particular factorization of the Hilbert space for multilevel ladders we show that the problem can be reduced to “bow-tie”-configuration energy-level crossings. This technique is naturally robust against fluctuations in the laser intensity and the chirp rate. Even when realistic heating rates are considered, we estimate that the overall fidelity should remain high (e.g., 98% for a ten-ion Dicke state), which represents a significant improvement over traditional approaches.

We present a general scheme allowing for construction of scalar separability criteria from positive, but not completely positive, maps. The concept is based on a decomposition of every positive map $\Lambda$ acting on $M_d\left(\mathbb{C}\right)$ into a difference of two completely positive maps ${\Lambda }_1$, ${\Lambda }_2$, i.e., $\Lambda ={\Lambda }_1-{\Lambda }_2$. The scheme may also be treated as a generalization of the known entropic inequalities, which are obtained from the reduction map. Analyses performed on a few classes of states show that the scalar criteria are stronger than the entropic inequalities and when derived from indecomposable maps allow for detection of bound entanglement.

Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.

Recently it was shown that if a given state fulfils the reduction criterion, it must also satisfy the known entropic inequalities. The natural question arises as to whether it is possible to derive some scalar inequalities stronger than the entropic ones, assuming that stronger criteria based on positive but not completely positive maps are satisfied. In the present paper we show that if certain conditions hold, the extended reduction criterion [H.-P. Breuer, Phys. Rev. Lett 97, 080501 (2006); W. Hall, J. Phys. A 40, 6183 (2007)] leads to some entropiclike inequalities, much stronger than their entropic counterparts. The comparison of the derived inequalities with other separability criteria shows that such an approach might lead to strong scalar criteria detecting both distillable and bound entanglement. In particular, in the case of SO(3)-invariant states it is shown that the present inequalities detect entanglement in regions, in which linear entanglement witnesses based on the extended reduction map fail. It should also be emphasized that in the case of $2\otimes d$ states the derived inequalities detect entanglement efficiently, while the extended reduction maps are useless, when acting on the qubit subsystem. Moreover, there is a natural way to construct a many-copy entanglement witnesses based on the derived inequalities so, in principle, there is a possibility of experimental realization. Some open problems and possibilities for further research are outlined.

Radiative decay spectra of doubly excited states in He have been measured after selective excitation with monochromatized synchrotron radiation. The decay spectra are in excellent agreement with predictions based on calculations.

Relativistic energy shifts of the low-energy levels of Fe have been calculated using the Dirac-Hartree-Fock and configuration interaction techniques. The results are to be used in the search for the space-time variation of the fine-structure constant in quasar absorption spectra. The values of the shifts are the largest among those used in the analysis so far. This makes Fe a good candidate for the inclusion into the analysis.

By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the $s$-wave scattering lengths of all 28 pairs of the seven stable isotopes. The $s$-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for ${}^{168}\text{Y}\text{b}$, 3.38(11) nm for ${}^{170}\text{Y}\text{b}$, $-0.15\left(19\right)\text{nm}$ for ${}^{171}\text{Y}\text{b}$, $-31.7\left(3.4\right)\text{nm}$ for ${}^{172}\text{Y}\text{b}$, 10.55(11) nm for ${}^{173}\text{Y}\text{b}$, 5.55(8) nm for ${}^{174}\text{Y}\text{b}$, and $-1.28\left(23\right)\text{nm}$ for ${}^{176}\text{Y}\text{b}$. The coefficient of the lead term of the long-range van der Waals potential of the ${\text{Yb}}_2$ molecule is $C_6=1932\left(30\right)$ atomic units $\left(E_h{a}_0^6\approx 9.573\times {10}^{-26}\text{J}{\text{nm}}^6\right)$.

Projectile angular-differential cross sections for single-transfer and transfer excitation have been calculated with the two-center extension of the nonperturbative basis generator method for 5–200 keV proton-helium collisions. The calculations are based on the independent electron model, and the eikonal approximation has been used to extract angular-differential cross sections from impact-parameter-dependent transition amplitudes. The present results are compared with experimental and previous theoretical data where available. In particular, we consider the ratio of transfer excitation to single capture versus double excitation to single excitation at intermediate energies. An experimentally observed structure in this ratio at a scattering angle about 0.5 mrad is qualitatively reproduced, while a previous classical evaluation failed in this respect. Therefore, we conclude that this structure is caused by quantum mechanical heavy-particle-electron couplings.

We present a simple quantum-field model for photon frequency conversion processes in dispersive dielectric microcavities, allowing practical calculations of conversion rates and efficiency optimization. The model incorporates the effect of dispersion into the structure of spatial cavity eigenmodes, while the material nonlinear properties enter the calculations through the coupling coefficients. Similar to the radiative atomic transitions, cavity photon-to-photon decay rates are derived for stimulated and spontaneous photon conversion. The phase matching requirement for a nonlinear process in a cavity is shown to be translated into a nonlinear mode overlap, manifesting the momentum conservation in a $k$ space spanned by the cavity eigenmodes. We illustrate the efficiency of the model by calculating degenerate two-photon and three-photon parametric down-conversion rates and analyze the photon lifetime dependence on various cavity and material parameters.

For two qubits belonging to Alice and Bob, we derive an approach to set up the bound of the Bell operator in the condition that Alice and Bob continue to perform local vertical measurements. For pure states we find that if the entanglement of the two qubits is less than 0.2644 (measured with von Neumann entropy) the violation of the Bell inequality will never be realized, and only when the entanglement is equal to 1 can the maximal violation $\left(2\sqrt{2}\right)$ occur. For a specific form of mixed states, we prove that the bound of the Bell inequality depends on the concurrence. Only when the concurrence is greater than 0.6 can the violation of the Bell inequality occur and the maximal violation can never be achieved. We suggest that the bound of the Bell operator in the condition of local vertical measurements may be used as a measure of the entanglement.

The mechanism underlying the substantial amplification of the high-order harmonics $q\pm 2K$ ($K$ integer) upon the addition of a weak seed extreme uv (XUV) field of harmonic frequency $q\omega$ to a strong IR field of frequency $\omega$ is analyzed in the framework of the quantum-mechanical Floquet formalism and the semiclassical recollision model. According to the Floquet analysis, the high-frequency field induces transitions between several Floquet states and leads to the appearance of new dipole cross terms. The semiclassical recollision model suggests that the origin of the enhancement lies in the time-dependent modulation of the ground electronic state induced by the XUV field.

We study vibrational wave packet dynamics on realistic surfaces of diatomic molecules and focus on the loss of coherence induced by rovibrational coupling at finite temperature $T$. The expected revivals of the wave packet depend sensitively on the coherence between the vibrational states, and their suppression indicates decoherence. In order to investigate this loss of vibrational coherence more quantitatively, we focus on purity decay and observe, apart from an overall decay, a remarkable oscillatory behavior of purity on the vibrational time scale. We present fully quantum-mechanical calculations of purity decay and the signal measured in a typical femtosecond pump-probe experiment.

We present a theoretical study of a superconducting charge qubit dispersively coupled to a transmission line resonator. Starting from a master equation description of this coupled system and using a polaron transformation, we obtain an exact effective master equation for the qubit. We then use quantum trajectory theory to investigate the measurement of the qubit by continuous homodyne measurement of the resonator out field. Using the same polaron transformation, a stochastic master equation for the conditional state of the qubit is obtained. From this result, various definitions of the measurement time are studied. Furthermore, we find that in the limit of strong homodyne measurement, typical quantum trajectories for the qubit exhibit a crossover from diffusive to jumplike behavior. Finally, in the presence of Rabi drive on the qubit, the qubit dynamics is shown to exhibit quantum Zeno behavior.

The exchange coupling between two spins has been proposed as a control parameter over the states of the two-qubit space, so that it can be used to produce quantum gate operations, and in particular, the ${\left(\text{SWAP}\right)}^{\alpha }$ two-qubit quantum gate. In this work, we study the effect that the Dzyaloshinski-Moriya term (DM) has on the ${\left(\text{SWAP}\right)}^{\alpha }$ gate operation. By considering a time-dependent exchange interaction we have calculated dynamical properties for the probability of the two spin states, magnetization, concurrence, and fidelity of the required quantum gate to determine the effect of the anisotropic term on the ${\left(\text{SWAP}\right)}^{\alpha }$ gate operation. We present an analytical relation, valid in the subspace $S_z=0$, between the concurrence (measurement of entanglement) and the on-site magnetization as an observable. We also show, with calculation of the fidelity of the system, that the DM term, will add an intrinsic error to the gate that depends on its amplitude and the concurrence of the $\alpha$ state.

In this paper we classify the four-qubit states that commute with $U\otimes U\otimes V\otimes V$, where $U$ and $V$ are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC.

Measuring the hyperfine structure (HFS) of long-lived ${{}^{3}P}_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in ${}^{87}\text{S}\text{r}$ needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. The results of similar analyses for ${}^9\text{B}\text{e}$, ${}^{25}\text{M}\text{g}$, and ${}^{43}\text{C}\text{a}$ are also reported.

A protocol to take a Rydberg wave packet that is trapped in a period-1 island, i.e., that is synchronized with the period of the driving field, and transfer it to a period-2 island such that the wave packet evolves with twice the period is theoretically analyzed and experimentally demonstrated. Such period-doubling transitions are realized using two superposed trains of half-cycle pulses whose relative time delay is varied adiabatically. It is shown that this protocol provides a tool to manipulate the angle variable of a Rydberg wave packet while its conjugate principal action is maintained constant.

The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive $1/r$ interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, nonsymmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.