The excitation spectrum for the three-dimensional Bose gas in the Bose-Einstein condensation phase is calculated nonperturbatively with the modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From improved $\Phi$-derivable theory, the diagrams needed to preserve the Ward-Takahashi identity are re-summed in a systematic and nonperturbative way. It is valid up to the critical temperature where the dispersion relation of the low-energy excitation spectrum changes from linear to quadratic. Because including the higher-order fluctuation, the results show significant improvement on the calculation of the shift of critical temperature with other conserving and gapless theories.

We derive one-dimensional effective Hamiltonians for spin-orbit-coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For an energy regime around the two-body bound-state energy, the effective Hamiltonian takes a two-channel form, where the populations in transverse excited levels are described by dressed molecules in the closed channel. For an energy regime slightly above the continuum threshold, the effective Hamiltonian takes a single-channel form, where low-energy physics is governed by the one-dimensional interacting strength determined by three-dimensional scattering length and transverse confinement. We further discuss the effect of spin-orbit coupling and effective Zeeman field on the position of confinement-induced resonances and show that these resonances can be understood as Feshbach resonances between the threshold of the transverse ground state and the two-body bound state associated with the transverse excited states. We expect that the shift of confinement-induced resonances can be observed under present experimental technology at attainable temperatures.

We analyze the ground-state phase diagram of two-component Fermi gases loaded into a two-dimensional checkerboard superlattice, i.e., a double-well optical lattice, potential within the BCS mean-field theory. We show that, by coupling the two $s$-wave sublattice superfluid order parameters, a checkerboard potential gives rise to an effectively two-band model with three (two intraband and an interband) nonlocal order parameters. We study the evolution of these order parameters as a function of particle filling, interaction strength, and checkerboard potential and find that the system always prefers the 0-phase solutions, i.e., where the phase difference between sublattice order parameters is 0, but never the $\pi$-phase one. In addition, we find that the ground state of the system undergoes a superfluid-normal quantum phase transition at half fillings beyond a critical checkerboard potential $C$, the threshold of which is precisely determined by the magnitude of the order parameter at $C=0$, and that the normal state rapidly turns into a checkerboard insulator as $C$ increases.

We establish through analytical and numerical studies of thermodynamic quantities for noninteracting atomic gases that the isotropic three-dimensional spin-orbit coupling, the Weyl coupling, induces interaction which counters “effective” attraction (repulsion) of the exchange symmetry present in zero-coupling Bose (Fermi) gas. The exact analytical expressions for the grand potential and hence for several thermodynamic quantities have been obtained for this purpose in both uniform and trapped cases. It is enunciated that many interesting features of spin-orbit-coupled systems revealed theoretically can be understood in terms of coupling-induced modifications in statistical interparticle potential. The temperature dependence of the chemical potential, specific heat, and isothermal compressibility for a uniform Bose gas is found to have signature of the incipient Bose-Einstein condensation in the very weak coupling regime although the system does not really go in the Bose-condensed phase. The transition temperature in the harmonically trapped case decreases with an increase of coupling strength consistent with the weakening of the statistical attractive interaction. Anomalous behavior of some thermodynamic quantities, partly akin to that in dimensions less than two, appears for uniform fermions as soon as the Fermi level goes down the Dirac point on increasing the coupling strength. It is suggested that the fluctuation-dissipation theorem can be utilized to verify anomalous behaviors from studies of long-wavelength fluctuations in bunching and antibunching effects.

Frequency conversion of single photons in a nonlinear crystal is theoretically discussed. Losses and noise are included within a Heisenberg-Langevin formalism for the propagating photon field. We calculate the first- and second-order correlation functions of the frequency-converted light when the input is a train of single-photon pulses. This model allows one to identify the requirements on the nonlinear device so that it can be integrated in a quantum network.

The force density induced by electromagnetic fields in electrically and magnetically polarizable media is studied analytically. Different formulations of the force density as a function of field-related quantities, including the spatial derivatives of the fields, gradients of the field intensity, phase gradients, electromagnetic power flow (Poynting vector field), and kinetic momentum flow, are introduced. These formulations retain certain symmetries with respect to the force expressions introduced in previous works for an isolated particle but also point out fundamental differences, such as the suppression of recoil forces, negative radiation pressure, and far-field gradient forces. It is shown how these analytical formulations also provide the necessary means to elucidate the sign of the force density in complex media and how they can assist the design of sources to manipulate clouds of particles. The theory is illustrated with numerical examples of an insulated Hertzian dipole immersed in different media, including lossy dielectrics, media with negative permittivity and permeability, and zero-index media.

We investigate the onset of parity-time ($\mathcal{PT}$) symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss-gain regions in the presence of an advective term. Similarly to the instability properties of hydrodynamic open flows, it is shown that $\mathcal{PT}$ symmetry breaking can be either absolute or convective. In the former case, an initially localized wave packet shows a secular growth with time at any given spatial position, whereas in the latter case the growth is observed in a reference frame moving at some drift velocity while decay occurs at any fixed spatial position. In the convective unstable regime, $\mathcal{PT}$ symmetry is restored when the spatial region of gain or loss in the lattice is limited (rather than extended). We consider specifically a non-Hermitian extension of the Rice-Mele tight-binding lattice model, and show the existence of a transition from absolute to convective symmetry breaking when the advective term is large enough. An extension of the analysis to ac-dc driven lattices is also presented, and an optical implementation of the non-Hermitian Rice-Mele model is suggested, which is based on light transport in an array of evanescently coupled optical waveguides with a periodically bent axis and alternating regions of optical gain and loss.

Uncertainty relations for light pulses found in our previous paper [Phys. Rev. A 86, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the two-dimensional plane perpendicular to the direction of the beam propagation which is more interesting for realistic beams. This uncertainty relation connects the area of the focal spot with the spectrum of transverse photon momenta. The shape of the beam that saturates the uncertainty relation is very close to a Gaussian. The directions of the electric and magnetic field vectors are those of the circularly polarized plane wave. Our uncertainty relation for the focal spot is quite general but we were able to determine the value of the lower bound only for beams made of many photons.

We propose a family of sifting-less quantum-key-distribution protocols which use reverse reconciliation, and are based on weak coherent pulses (WCPs) polarized along $m$ different directions. When $m=4$, the physical part of the protocol is identical to most experimental implementations of BB84 [Bennett and Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, New York, 1984)] and SARG04 [Scarani, Acín, Ribordy, and Gisin, Phys. Rev. Lett. 92, 057901 (2004); Acín, Gisin, and Scarani, Phys. Rev. A 69, 012309 (2004)] protocols and they differ only in classical communications and data processing. We compute their total key rate as a function of the channel transmission $T$, using general information theoretical arguments, and we show that they have a higher key rate than the more standard protocols, both for fixed and optimized average photon number of the WCPs. When no decoy-state protocols (DSPs) [Hwang, Phys. Rev. Lett. 91, 057901 (2003); Lo, Ma, and Chen, Phys. Rev. Lett. 94, 230504 (2005); Wang, Phys. Rev. A 72, 012322 (2005)] are applied, the scaling of the key rate with transmission is improved from $T^2$ for BB84 to $T^{1+\frac{1}{m-2}}$. If a DSP is applied, we show how the key rates scale linearly with $T$, with an improvement of the prefactor by 75.96% for $m=4$. High values of $m$ allow one to asymptotically approach the key rate obtained with ideal single-photon pulses. The fact that the key rates of these sifting-less protocols are higher compared to those of the aforementioned more standard protocols show that the latter are not optimal, since they do not extract all the available secret keys from the experimental correlations.

The atomic masses of ${}^{82,83}$Kr and ${}^{131,134}$Xe have been measured using the Florida State Penning trap mass spectrometer with ${}^{84,86}$Kr and ${}^{129,132}$Xe used as reference masses. The results are $M$(${}^{82}$Kr) $=$ 81.913 481 159(9) u, $M$(${}^{83}$Kr) $=$ 82.914 126 519(12) u, $M$(${}^{131}$Xe) $=$ 130.905 084 137(14) u, and $M$(${}^{134}$Xe) $=$ 133.905 393 032(13) u.

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled-channel calculations for several cases of overlapping resonances in the collisions of two ${}^7$Li atoms or two Cs atoms.

X-ray spectra following charge-exchange collisions between C${}^{6+}$ and He are presented for collision energies between 460 and 32 000 eV/u. Spectra were obtained at the Oak Ridge National Laboratory Multicharged Ion Research Facility using a microcalorimeter x-ray detector capable of fully resolving the C vi Lyman series lines through Ly-$\gamma$. These line ratios are sensitive to the initial electron $\ell$ distribution and test our understanding of the charge-exchange process. In addition, these line ratios are important for identifying charge exchange in astrophysical contexts involving the interaction of solar wind ions with neutrals. Our measurements are performed at collision velocities (300–2500 km/s) which overlap most of the solar wind range. Additional data of this type can be combined with computations to provide an extensive set of reliable line ratios and absolute cross sections for the interpretation of a variety of astrophysical situations.

Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO${}_2$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in “targeted” Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the $ns$, $np$, and $nd$ Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the $m_z=0$ Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted $l=0$ states.

We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.

We demonstrate nanowatt-level saturated absorption using a subwavelength diameter tapered optical fiber (TOF) suspended in a gas of metastable xenon atoms. This ultralow-power nonlinearity is enabled by a small optical mode area propagating over a relatively long distance through the Xe gas. The use of inert noble gases in these kinds of TOF experiments may offer practical advantages over the use of reactive alkali-metal vapors, such as rubidium.

The enhanced cooperative decay rate and the enhanced cooperative Lamb shift from a slab of two-level atoms placed in between two noble-metal slabs are analyzed within the context of the interacting polariton of the resonant medium and the metallic plasmon eigenmodes.

In this paper we present theoretical and experimental studies of the modifications of the thermal spectrum inside a microwave resonator due to a parametric amplification process. Both the degenerate and nondegenerate amplifiers are discussed. Theoretical calculations are compared with measurements performed with a microwave cavity parametric amplifier.

Bell inequalities and nonlocality have been widely studied in one-dimensional quantum systems. As a kind of quantum correlation, it is expected that bipartite nonlocality should be present in quantum systems, just as bipartite entanglement does. Surprisingly, for various models, two-qubit states do not violate Bell inequalities, i.e., they are local. Recently, it is realized that the results are related to the monogamy trade-off obeyed by bipartite Bell correlations, thus it is believed that for general translation invariant systems, two-qubit states should not violate the Bell inequality [Oliveira, Europhys. Lett. 100, 60004 (2012)]. In this Brief Report, we demonstrate that in perfect translation-invariant systems with an even number of sites, the Bell inequality can be violated. A nontrivial model is constructed to confirm the conclusion.

We present a simple yet effective theory that predicts the existence of resonant radiation bands in the deep normal group-velocity dispersion region of a medium, even in the absence of a zero-group-velocity dispersion point. This radiation is evident when the medium is pumped with high-energy ultrashort pulses, and it is driven by the interplay between the Kerr and the shock terms in the nonlinear Schrödinger equation. Accurate experiments performed in bulk silica fully support the theoretical phase-matching condition found by our theory.

We investigate from a practitioner's point of view the computation of the ionization potential (IP) within density-functional theory (DFT). DFT with (semi)local energy-density functionals is plagued by a self-interaction error which hampers the computation of the IP from the single-particle energy of the highest occupied molecular orbital (HOMO). The problem may be cured by a self-interaction correction (SIC) for which there exist various approximate treatments. We compare the performance of the SIC proposed by Perdew and Zunger with the very simple average-density SIC (ADSIC) for a large variety of atoms and molecules up to larger systems such as carbon rings and chains. Both approaches to the SIC provide a large improvement to the quality of the IP if calculated from the HOMO level. The surprising result is that the simple ADSIC performs even better than the original Perdew-Zunger SIC in the majority of the studied cases.