We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant, and we determine various parameters in the unitarity limit.

We calculate the single-particle spectral density of a normal (nonsuperfluid) two-component gas of fermions in the BCS-BEC crossover within a $T$-matrix approximation. We review how noncondensed pairs lead to a spectral density reminiscent of the ordered state, and explore how a gaplike feature in the spectrum evolves as one changes the polarization of the gas. As the gas is polarized, we find that this pseudogap becomes more diffuse and moves away from the Fermi level, reflecting the fact that fewer pairs are present but that they still play an important role in the excitations.

We show that the use of path-entangled states of photons, having nonzero orbital angular momentum (OAM), increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. In the ideal case of maximally path-entangled states, the resolution of angular-displacement measurements increases by a factor of $\mathit{Nl}$, while the uncertainty in the measurement of angular displacements scales as $1/\mathit{Nl}$, where $N$ is the number of entangled photons, half of which carry, on average, an OAM of $+l\hslash$ per photon and the other half carry an OAM of $-l\hslash$ per photon. We analyze measurement schemes for two- and four-photon entangled states produced by parametric down-conversion and, by employing a 4$\times$4 matrix formalism to study the propagation of entangled OAM modes, obtain explicit expressions for the resolution and sensitivity in these schemes. These results constitute an improvement over what could be obtained with $N$ nonentangled photons carrying an orbital angular momentum of $\left|l\right|\hslash$ per photon.

We analyze the longitudinal Lorentz forces that a propagating continuous-wave light exerts on a subwavelength-diameter optical fiber. Our theoretical results show that, during the propagating process, the guided light exerts no net time-averaged force on the fiber. Via numerical simulation, we find a significant overall pull force of 0.4 pN/mW acting on a 450-nm-diam fiber tip at a wavelength of 980 nm due to the scattering of the end face and a calculated force distribution reveals the feature of a near-field accumulation. Our results may be helpful to the configuration of optomechanical components or devices based on these fibers.

We present quantum-mechanical studies on above-threshold ionization of molecular ions in two and three dimensions. The momentum distributions show signatures of interfering emissions from the molecular centers. These structures deviate from a simple double-slit model that ignores the electron-ion interaction, but they are reproduced by an eikonal model. Such distortions of the interference pattern are partly responsible for the absence of clear interference patterns in the angle-integrated electron energy spectra.

We investigate the effect of a nonuniform deformation applied to one-dimensional (1D) quantum systems, where the local energy scale is proportional to $g_j=[\sin (j\pi /N)]{}^m$ determined by a positive integer $m$, site index $1⩽j⩽N-1$, and system size $N$. This deformation introduces a smooth boundary to systems with open-boundary conditions. When $m⩾2$, the leading $1/N$ correction to the ground-state energy per bond $e_0^{(N)}$ vanishes and one is left with a $1/N^2$ correction, the same as with periodic boundary conditions. In particular, when $m=2$, the value of $e_0^{(N)}$ obtained from the deformed open-boundary system coincides with the uniform system with periodic boundary conditions. We confirm the fact numerically for correlated systems, such as the extended Hubbard model, in addition to 1D free-fermion models.

A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the effects of network instabilities in the form of broken links, and examine the response of the quantum walk to such failures. It is shown that the reconfiguration of the quantum walk is determined by the community structure of the network. In this context, quantum walks based on the adjacency and Laplacian matrices of the network are compared, and their responses to link failures is analyzed.

Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum error-correcting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-$d$ representation. In operating the algorithm, the number $n<N=d^K$ is read into a $K$-qudit register through its interaction with a stream of $n$ particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number $n$ in the base-$d$ representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semiclassical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where $d$ is a prime number, with a simpler single-shot measurement allows us to find the powers of 2, 3, and other primes $d$ in the number $n$. We show that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-$d$ systems, $d$-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter’s performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure voltage (an analog to digital converter) and a simple procedure to entangle multiparticle states.

The cascade $L$-shell x-ray emission as an incident polarized and unpolarized monochromatic radiation overpass the $1s$ ionization threshold is investigated for the metallic Fe by means of moderate resolution, quantitative x-ray spectrometry. A full ab initio theoretical investigation of the $L$-shell x-ray emission processes is performed based on a detailed straightforward construction of the cascade decay trees within the Pauli-Fock approximation. The agreement obtained between experiments and the presented theory is indicated and discussed with respect to the accuracy of advanced atomic models as well as its significance for the characterization capabilities of x-ray fluorescence (XRF) analysis.

The structure of $\{a^{\pm },a^{\pm },b^{\mp }\}$-type Coulombic systems is characterized by the effective ground-state density of the $a$-type particles, computed via nonrelativistic quantum mechanics without introduction of the Born-Oppenheimer approximation. A structural transition is observed when varying the relative mass of the $a$- and $b$-type particles, e.g., between atomic ${\mathrm{H}}^{-}$ and molecular ${\mathrm{H}}_2$${}^{+}$. The particle-density profile indicates a molecular-type behavior for the positronium ion, Ps${}^{-}$.

We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine-structure constant $\alpha$. The method used follows the ideas of Chin and Flambaum [Phys. Rev. Lett. 96, 230801 (2006)], where the sensitivity to the variation of the electron-to-proton mass ratio $\beta$ was considered. We demonstrate that for heavy systems, the sensitivity to the variation of $\alpha$ is of the same order of magnitude as to the variation of $\beta$. Near narrow Feshbach resonances, the enhancement of the sensitivity may exceed nine orders of magnitude.

Coherent transport by adiabatic passage has recently been suggested as a high-fidelity technique to engineer the center-of-mass state of single atoms in inhomogeneous environments. While the basic theory behind this process is well understood, several conceptual challenges for its experimental observation have still to be addressed. One of these is the difficulty that currently available optical or magnetic micro-trap systems have in adjusting the tunneling rate time dependently while keeping resonance between the asymptotic trapping states at all times. Here we suggest that both requirements can be fulfilled to a very high degree in an experimentally realistic setup based on radio-frequency traps on atom chips. We show that operations with close to $100\%$ fidelity can be achieved and that these systems also allow significant improvements for performing adiabatic passage with interacting atomic clouds.

Based on a general beam-propagation model, we derive in the paraxial approximation the analytical expressions for the spatial transverse shift (TS) and the angular TS of a beam reflected from the air-chiral interface. The results show that the TSs are closely related to the propagation behaviors of the right-circularly polarized (RCP) and the left-circularly polarized (LCP) waves in the chiral medium. When the L(R)CP wave becomes evanescent, the left (right)-elliptically polarized incident beam suffers a smaller TS. When the L(R)CP wave propagates, the left (right)-elliptically polarized incident beam experiences a greater TS. When the total internal reflection happens, neither of the two elliptically polarized incident beams suffers TSs. TSs can be controlled not only by adjusting the central angle of incidence, but also by tailoring the permittivity, permeability, and chirality parameter of the chiral medium.

We show that a semiconductor nanocavity where the dominant nonlinear mechanism is the refractive index change induced by carriers generated through two-photon absorption can become unstable, exhibiting the onset of spontaneous oscillations (self-pulsing). The linear stability analysis, validated through numerical integration of a mean-field model, leads us to predict oscillations to take place typically in the 10-ps range at input power levels of the order of 15 mW.

We propose a scheme for three-level cascade atoms to entangle two optomechanical oscillators as well as two-mode fields. We show that two movable mirrors and two-mode fields can be entangled even for bad cavity limits. We also study entanglement of the output of two-mode fields in the frequency domain. The results show that the frequency of the mirror oscillation and the injected atomic coherence affect the output entanglement of the two-mode fields.

The absorption line shape of a given ${\mathrm{H}}_2$${}^{18}\mathrm{O}$ vibration-rotation line at 1.38 $\mu$m was deeply investigated using a spectroscopic approach based upon the use of a pair of offset-frequency locked extended-cavity diode lasers. This dual-laser apparatus ensures extreme levels of accuracy in controlling and measuring any variation of the laser frequency around a given absolute reference. As a result, high levels of precision and accuracy were reached in the observation of a molecular absorption line shape in the near infrared. A variety of semiclassical models, accounting for Dicke narrowing and speed-dependent effects, were implemented and tested in order to describe the physical situation of self-colliding ${\mathrm{H}}_2$${}^{18}\mathrm{O}$ molecules. Our study demonstrates that the molecular confinement alone is unable to explain entirely the departures from the Voigt profile and that the speed dependence of pressure-induced broadening and shift cannot be ignored, even in the case of pure water samples at relatively small pressures. The absorption spectrum was successfully interpolated using the uncorrelated version of the speed-dependent Galatry profile, with a hypergeometric dependence on the absorber speed for both pressure broadening and pressure shift parameters, thus reaching an agreement between theory and experiment at the level of $5\times {10}^{-5}$.

We have investigated the $4s\hspace{0.5em}{}^2{S}_{1/2}\to 5p\hspace{0.5em}{}^2{P}_{1/2}$ transition ($D_1$ line) of the potassium isotopes ${}^{39}\mathrm{K}$, ${}^{40}\mathrm{K}$, and ${}^{41}\mathrm{K}$ using Doppler-free laser saturation spectroscopy. Our measurements reveal the hyperfine splitting of the $5p\hspace{0.5em}{}^2{P}_{1/2}$ state of ${}^{40}\mathrm{K}$, and we have determined the specific mass shift and the nuclear field shift constants for the blue (405 nm) $D_1$ line.

Systematic study of Rb atomic properties is carried out using a high-precision relativistic all-order method. Excitation energies of the $\mathit{ns}$, $\mathit{np}$, $\mathit{nd}$, and $\mathit{nf}$ ($n⩽10$) states in neutral rubidium are evaluated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to $n=8$. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole ($5s-\mathit{np}$, $n=5-26$), electric-quadrupole ($5s-{\mathit{nd}}_j$, $n=4-26$), and electric-octupole ($5s-{\mathit{nf}}_j$, $n=4-26$) matrix elements are calculated to obtain the ground state $E1$, $E2$, and $E3$ static polarizabilities. Scalar polarizabilities of the $\mathit{ns}$, $\mathit{np}$, and $\mathit{nd}$ states, and tensor polarizabilities of the ${\mathit{np}}_{3/2}$ and $\mathit{nd}$ excited states of Rb are evaluated. The hyperfine $A$ and $B$ values in ${}^{87}\mathrm{Rb}$ are determined for the first low-lying levels up to $n=9$. These calculations provide recommended values critically evaluated for their accuracy for a number of Rb atomic properties useful for a variety of applications.

We present a high-precision measurement of the isotope shift of the narrow quadrupole-allowed 5 ${}^2{S}_{1/2}$ – 4 ${}^2{D}_{5/2}$ transition in ${}^{86}\mathrm{Sr}$${}^{+}$ relative to the most abundant isotope ${}^{88}\mathrm{Sr}$${}^{+}$. This was accomplished using high-resolution laser spectroscopy of individual trapped ions, and the measured shift is $\Delta {\nu }_{\mathrm{meas}}^{88,86}=570.281(4)$ MHz. We also tested a recently developed and successful method for ab initio calculation of isotope shifts in alkali-metal-like atomic systems against this measurement, and our initial result of $\Delta {\nu }_{\mathrm{calc}}^{88,86}=457(28)$ MHz is also presented. While the measurement and the calculation are in broad agreement, there is a clear discrepancy between them, and we believe that the specific mass shift was underestimated in our calculation. Our measurement provides a stringent test for further refinements of theoretical isotope shift calculation methods for atomic systems with a single valence electron.