We have observed the diatomic $nsns\to ns\left(n+1\right)s\to \left(n+1\right)s\left(n+1\right)s$ microwave transitions of pairs of cold Rb Rydberg atoms for $36<n<48$. The $ns\left(n+1\right)s$ state has by far the largest van der Waals shift due to its near degeneracy with the nearby $n{p}_{3/2}n{p}_{3/2}$ state. In fact, the energy difference and the van der Waals shift change sign at $n=38$ and we observe shifts of both signs. The combined excitation of the $ns\left(n+1\right)s$ and $\left(n+1\right)s\left(n+1\right)s$ states leads to an unusual line shape which can be described by a three-level Floquet model.

We study the dynamics of a vortex in an atomic Bose-condensed gas at finite temperature within the Zaremba-Nikuni-Griffin formalism. In a harmonically trapped pancake-shaped condensate, an off-centered vortex is known to decay by spiraling out toward the edge of the condensate. We quantify the dependence of this decay on temperature, atomic collisions, and thermal cloud rotation. Near the trap center where the density varies slowly, we show that our numerical results agree with the predictions of the Hall-Vinen phenomenological friction force model used to describe quantized vorticity in superfluid systems. Our result thus clarifies the microscopic origin of the friction and provides an ab initio determination of its value.

We investigate the appearance of vortices and vortex lattices in two-dimensional, anisotropic, and rotating Bose-Einstein condensates. Once the anisotropy reaches a critical value, the positions of the vortex cores in the ground state are no longer given by an Abrikosov lattice geometry but by a linear arrangement. Using a variational approach, we determine the critical stirring frequency for a single vortex as well as the equilibrium positions of a small number of vortices.

The possibility of adiabatically cooling a spin-1 polar Bose gas to a spin-nematic phase is theoretically discussed. The relation between the order parameter of the final spin-nematic phase and the starting temperature of the spinor Bose gas is obtained both using the mean-field approach for high temperature and spin-wave approach for low temperature. We find that there exists a good possibility to reach the spin-nematic ordering starting with spinor antiferromagnetic Bose gases.

We present a proof of principle demonstration of signal processing using atom-optical methods. A Bose-Einstein condensate diffracted by a phase shifted periodic potential realizes the discrete Fourier transform for several test signals. We demonstrate that the quantum probability distribution of output momenta can yield more accurate frequency spectra than the usual classical method in terms of linewidth and noise rejection. Extensions to superposition states are shown and ideas for implementing continuous signal analysis are discussed.

We present a theoretical description of the response of a dynamic slab, with time-periodic dielectric function $ϵ\left(t\right)$, to a normally incident monochromatic plane wave of frequency ${\omega }_o$. As a consequence of the interaction of this incoming wave with the dynamic slab, the reflected and transmitted waves contain harmonics of the modulating frequency $\Omega$, namely, the slab itself becomes a polychromatic source of frequencies ${\omega }_o-n\Omega \left(n=0,\pm 1,\pm 2,\dots \right)$. We establish a general formalism to quantify the reflected and transmitted fields for any periodic variation in the dielectric function. To achieve this, a description of wave propagation in a dynamic bulk is needed. A theoretical framework to treat such propagation, based on the concept of a temporal photonic crystal, is developed. As a consequence of the Bloch-Floquet theorem, the dispersion relation is a band structure that is periodic with frequency and exhibits forbidden wave vector gaps. The Poynting vectors of the transmitted and reflected fields are analyzed in detail. Our theory is applied to the case in which the dielectric function is modulated sinusoidally. We calculate numerically the magnitudes and phases of the reflection and transmission coefficients for several harmonics ${\omega }_o-n\Omega$ and slab thicknesses. Three modulation regimes are considered: weak, moderate, and strong. The response in the weak regime is similar to that of a Fabry-Perot etalon—the strengths of the harmonics are weak. For the strong-modulation regime, the strengths of reflection and transmission coefficients of the harmonics become large; they can even exceed one due to the openness of the system in which an external modulating agent can provide part of the invested energy. Dynamic variation in the dielectric properties of materials can give rise to new effects in wave propagation and to novel optical applications and is readily attainable with present-day technology.

We explain the spin segregation seen at Duke in a two-component gas of ${}^6\text{L}\text{i}$ [X. Du, L. Luo, B. Clancy, and J. E. Thomas, Phys. Rev. Lett. 101, 150401 (2008)] as a mean-field effect describable via a collisionless Boltzmann equation. As seen in experiments, we find that slight differences in the trapping potentials in the two spin states drive small spin currents. The Hartree-Fock-type interactions convert these currents into a redistribution of populations in energy space, and consequently a long-lived spin texture develops. We explore the interaction strength dependence of these dynamics, finding nontrivial dependence on system parameters and close agreement with experiment.

The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp observables to be jointly measurable. The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.

Using an open quantum system we calculate the time dependence of the concurrence between two maximally entangled electron spins with one accelerated uniformly in the presence of constant electric and magnetic fields, and the other at rest and isolated from fields. We find at high Rindler temperature that the proper time for the entanglement to be extinguished is proportional to the inverse of the acceleration cubed.

We present a family of entanglement measures $R_m$ which act as indicators of separability of $n$-qubit quantum states into $m$ subsystems for arbitrary $2\le m\le n$. The measure $R_m$ vanishes if the state is separable into $m$ subsystems, and for $m=n$ it gives the Meyer-Wallach measure, while for $m=2$ it reduces, in effect, to the one introduced recently by Love et al. [Quantum Inf. Process. 6, 187 (2007)]. The measures $R_m$ are evaluated explicitly for the Greenberger-Horne-Zeilinger state and the $W$ state (and its modifications, the $W_k$ or Dicke states) to show that these globally entangled states exhibit rather distinct behaviors under the measures, indicating the utility of the measures $R_m$ for characterizing globally entangled states as well.

When a two-qubit system is initially maximally entangled, two independent decoherence channels, one per qubit, would greatly reduce the entanglement of the two-qubit system when it reaches its stationary state. We propose a method on how to minimize such a loss of entanglement in open quantum systems. We find that the quantum entanglement of general two-qubit systems with controllable parameters can be controlled by tuning both the single-qubit parameters and the two-qubit coupling strengths. Indeed, the maximum fidelity $F_{\text{max}}$ between the stationary entangled state, ${\rho }_{\infty }$, and the maximally entangled state, ${\rho }_m$, can be about $2/3\approx \text{max}\left\{\text{tr}\left({\rho }_{\infty }{\rho }_m\right)\right\}=F_{\text{max}}$, corresponding to a maximum stationary concurrence, $C_{\text{max}}$, of about $1/3\approx C\left({\rho }_{\infty }\right)=C_{\text{max}}$. This is significant because the quantum entanglement of the two-qubit system can be produced and kept, even for a long time. We apply our proposal to several types of two-qubit superconducting circuits and show how the entanglement of these two-qubit circuits can be optimized by varying experimentally controllable parameters.

The $1S\text{−}2S$ two-photon transition in singly ionized helium is a highly interesting candidate for precision tests of bound-state quantum electrodynamics (QED). With the recent advent of extreme ultraviolet frequency combs, highly coherent quasi-continuous-wave light sources at 61 nm have become available, and precision spectroscopy of this transition now comes into reach for the first time. We discuss quantitatively the feasibility of such an experiment by analyzing excitation and ionization rates, propose an experimental scheme, and explore the potential for QED tests.

The electron capture in ${\text{O}}^{8+}-\text{H}$ collisions is studied by the two-center atomic-orbital close-coupling method when the interactions of charged particles are screened and have a Yukawa form. Atomic orbitals and eigenenergies of $n\le 7$ states on ${\text{O}}^{7+}$ and $n\le 2$ states on H are calculated as a function of the interaction screening parameter and used in the atomic-orbital close-coupling dynamics scheme to calculate the electron capture cross sections in the energy range of 0.2–50 keV/u. It is shown that the degree of interaction screening determines the reduction in electron binding energies, the number of open electron capture channels, and the strength of the exchange couplings, thus affecting the entire collision dynamics and the magnitude and energy behavior of state-selective cross sections. The changes in electron binding energies and capture cross sections when the interaction screening varies introduce dramatic changes in the radiation spectrum of ${\text{O}}^{7+}\left(nl\right)$ capture states with respect to the unscreened interaction case. The state-selective electron capture cross sections in this collision system, as well as the intensities of a number of charge exchange spectral lines, for a number of representative screening parameter values are presented and discussed.

Using a crossed electron-ion beams method, we measured absolute cross sections for electron-impact dissociation of the $\text{CD}_3{}^{+}$ molecular ions producing $\text{CD}_2{}^{+}$ fragment ions and $\text{CH}_3{}^{+}$ ions yielding ${\text{CH}}^{+}$ and ${\text{C}}^{+}$ fragment ions over a collision energy range from a few eV up to 100 eV. The total experimental uncertainties are about 12% at the maximum of the curves of cross sections (peak of the cross section for the ${\text{CH}}^{+}$ channel). The obtained results suggest important roles played by predissociation of bound states in the production of both the ${\text{CH}}^{+}$ and ${\text{C}}^{+}$ fragment ions. Good agreement is found with other results reported for the ${\text{CH}}^{+}$ fragment, but some differences are found for the $\text{CD}_2{}^{+}$ and ${\text{C}}^{+}$ fragments.

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrödinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.

A collective photon-number-splitting attack strategy is proposed, which combines photon-number-splitting attack with an unambiguous set discrimination of quantum state. Verified by this attack strategy, it is shown that a two-way quantum secure direct communication protocol with qubits is insecure in real circumstance. Finally, we present a possible improved version of this kind of quantum secure direct communication protocol.

We present a perfect state transfer protocol via a qubit chain with the evolution governed by the $xx$ Hamiltonian. In contrast to the recent protocol announced in Phys. Rev. Lett. 101, 230502 (2008), our method does not demand any remote-cooperated initialization and sending classical information about measurement outcomes. We achieve the perfect state transfer only with the assumption of access to two spins at each end of the chain, while the initial state of the whole chain is irrelevant.

There are two alternative methods used in the literature to calculate the incoherent part of the spectrum of light scattered by an atomic system. In the first, one calculates the spectrum of the total light scattered by the system and obtains the incoherent part by subtracting the coherent part. In the second method, one introduces the fluctuation operators and obtains the incoherent part of the spectrum by taking the Fourier transform of the two-time correlation function of the fluctuation operators. These two methods have been recognized for years as completely equivalent for evaluating the incoherent part of the spectrum. In a recent paper, Xu et al. [Phys. Rev. A 78, 013407 (2008)] showed that there are discrepancies between the incoherent parts of the stationary spectrum of a three-level $\Lambda$-type system calculated with these two methods. The predicted discrepancies can be severe that over a wide range of the Rabi frequencies and atomic decay rates, the spectrum calculated with the variance method can have negative values. In this Comment, we show that there are no discrepancies between these two methods. We show the equivalence of these two methods that leads to the same incoherent spectra which are positive for all frequencies independent of values of the parameters involved. We also identify the source of the discrepancy, that is, in an incorrect treatment of the incoherent part of the spectrum calculated with the two-time correlation function of the fluctuation operators.