We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.

We explore the zero-temperature phase diagram of bosons interacting via Feshbach resonant pairing interactions in one dimension. Using DMRG (density matrix renormalization group) and field theory techniques we characterize the phases and quantum phase transitions in this low-dimensional setting. We provide a broad range of evidence in support of an Ising quantum phase transition separating distinct paired superfluids, including results for the energy gaps, correlation functions, and entanglement entropy. In particular, we show that the Ising correlation length, order parameter and critical properties are directly accessible from a ratio of the atomic and molecular two-point functions. We further demonstrate that both the zero-momentum occupation numbers and the visibility are in accordance with the absence of a purely atomic superfluid phase. We comment on the connection to recent studies of boson pairing in a generalized classical $\mathit{XY}$ model.

We investigate, theoretically and experimentally, absorption on an excited-state atomic transition in a thermal vapor where the lower state is coherently pumped. We find that the transition linewidth can be subnatural, that is, less than the combined linewidth of the lower and upper state. For the specific case of the $6P_{3/2}\to 7S_{1/2}$ transition in room temperature cesium vapor, we measure a minimum linewidth of 6.6 MHz compared with the natural width of 8.5 MHz. Using perturbation techniques, an expression for the complex susceptibility is obtained which provides excellent agreement with the measured spectra.

We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle, with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.

We propose a scheme for generating many-atom maximal entanglement states in spin-1 Bose-Einstein condensates. By applying a far-off-resonate blue-detuned linear-polarized laser to the condensates, the hyperfine level $F=1,m=0$ ground state and the hyperfine $F=0$ excited state are conveniently coupled. Such a configuration is more efficient and provides a fast implementation of the maximally entangled GHZ state, using only half of the time that is required in single-atom Raman-transition-based schemes [You, Phys. Rev. Lett. 90, 030402 (2003)].

Lossless dielectric nanospheres (made of nonmagnetic materials) with relatively low refraction index may present strong electric and magnetic dipolar resonances. We establish a relationship between the optical force from a plane wave on small electric and magnetic dipolar particles, the transport cross section, and the scattering asymmetry parameter $g$. In this way we predict negative $g$ (that minimize the transport mean free path below values of the scattering mean free path) for a dilute suspension of both perfectly reflecting spheres as well as of lossless dielectric nanospheres made of moderate permittivity materials, e.g., silicon or germanium nanospheres in the infrared region. Lossless dielectric Mie spheres of relatively low refraction index (as low as 2.2) are shown to present negative $g$ in specific spectral ranges.

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed Lévy-type distribution. Based on recent predictions made for 1D coherent transport with Lévy-type disorder, we show numerically that for a system of length $L$ (i) the average $\langle -\ln T\rangle \propto L^{\alpha }$ for $0<\alpha <1$, while $\langle -\ln T\rangle \propto L$ for $1⩽\alpha <2$, $\alpha$ being the exponent of the power-law decay of the layer-thickness probability distribution, and (ii) the transmission distribution $P\left(T\right)$ is independent of the angle of incidence and the frequency of the electromagnetic wave, but it is fully determined by the values of $\alpha$ and $\langle \ln T\rangle$. Additionally we have found and numerically verified that $\langle T\rangle \propto L^{-\alpha }$ with $0<\alpha <1$.

The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e., the Schrödinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-not (cnot) gates, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.

We have measured the absolute frequency of a clock transition at the 10${}^{-15}$ level with a single, trapped, laser-cooled ${}^{40}$Ca${}^{+}$ ion in a miniature Paul trap. In our measurement, an optical frequency comb is referenced to a hydrogen maser, which is calibrated to the SI second through the Global Positioning System (GPS). By analyzing the experimental data obtained within 32 days of a total averaging time $>$2 $\times$ 10${}^6$ s, the absolute frequency of the ${}^{40}$Ca${}^{+}$ 4$s$ ${}^2{S}_{1/2}$–3$d$ ${}^2{D}_{5/2}$ clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 $\times$ 10${}^{-15}$.

We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide a quantitative description of the full momentum distribution measurements of Van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)]. We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry.

We study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically we focus on the experimentally available mixture of ${}^6$Li and ${}^{40}$K atoms. In this regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency (rf) spectrum and the momentum distribution for the spin polarons for experiments with ${}^6$Li and ${}^{40}$K atoms. Subsequently we study the relaxation of the motion of the Fermi polaron due to spin drag.

We show that high-angle Bessel beams may significantly reduce nonlinear pulse distortions due, for example, to nonlinear Kerr effects (self-phase-modulation and self-focusing) yet enhance ionization and plasma generation. Holographic reconstruction of Bessel beams in water show intensity clamping at increased intensities and evidence of nontrivial plasma dynamics as the input energy is increased. The solvated electron density increases significantly and the cavitation-induced bubbles are ejected from the focal region indicating a significant excess plasma heating in the Bessel-pulse wake.

We theoretically and numerically investigate the interaction of an electromagnetic wave with structured metamaterial under the excitation of linearly polarized light. A polarization map of the transmitted electromagnetic wave can reveal electromagnetic spin-to-orbital angular momentum conversion. The spatial splitting of spin states described by the Stokes parameter $S_3$ may be viewed as the photonic version of a Stern-Gerlach experiment in the absence of a magnetic field. Our idea is ideally suitable for demonstration of electromagnetic spin-to-orbital angular momentum conversion, which offers an alternative way to comprehend the conversion. Moreover, it could enrich a variety of optical phenomena in subwavelength structured metallic systems.

We demonstrate a direct relationship between tunneling delays in a one-dimensional potential barrier and the delays observed in frustrated total internal reflection. Expressions relating the group delays in these two cases have been formulated in the past [A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994)], but only for certain limits of the normalized particle energy $E/V_0$. Here, we derive a single expression relating these two group delays that is valid for arbitrary particle energy by decomposing the group delay into dwell-time and self-interference components. This decomposition also explains why the predicted delay differs in the limiting cases observed by Steinberg and Chiao.

Within the linear combination of atomic orbitals (LCAO) approximation, one can distinguish two different Kohn-Sham potentials. One is the potential available numerically in calculations, and the other is the exact potential corresponding to the LCAO density. The latter is usually not available, but can be obtained from the total density by a numerical inversion procedure or, as is done here, analytically using only one LCAO Kohn-Sham orbital. In the complete basis-set limit, the lowest-lying Kohn-Sham orbital suffices to perform the analytical inversion, and the two potentials differ by no more than a constant. The relation between these two potentials is investigated here for diatomic molecules and several atomic basis sets of increasing size and quality. The differences between the two potentials are usually qualitative (wrong behavior at nuclear cusps and far from the molecule even if Slater-type orbitals are used) and $\delta$-like features at nodal planes of the lowest-lying LCAO Kohn-Sham orbital. Such nodes occur frequently in LCAO calculations and are not physical. Whereas the behavior of the potential can be systematically improved locally by the increase of the basis sets, the occurrence of nodes is not correlated with the size of the basis set. The presence of nodes in the lowest-lying LCAO orbital can be used to monitor whether the effective potential in LCAO Kohn-Sham equations can be interpreted as the potential needed for pure-state noninteracting $v$-representability of the LCAO density. Squares of such node-containing lowest-lying LCAO Kohn-Sham orbitals are nontrivial examples of two-electron densities which are not pure-state noninteracting $v$-representable.

We study high-order harmonic generation (HHG) spectra by a focused truncated Bessel beam versus a Gaussian beam, including macroscopic propagation of the fundamental laser and harmonic fields in the gas medium, with the single-atom-induced dipole response calculated from the recently developed quantitative rescattering theory. We first simulate the HHG spectra of Ar by an 8-fs and 780-nm short laser pulse, reported by Wörner et al. [Phys. Rev. Lett. 102, 103901 (2009)], assuming the incident beam is a truncated Bessel beam or a Gaussian beam. Both simulations fail to reproduce the observed wide and deep Cooper minimum in the HHG spectra. However, we are able to reproduce the HHG spectra of Ar generated by few-cycle 1800-nm near-infrared lasers, reported recently by Shiner et al. [Nature Phys. 7, 464 (2011)]. We also provide a systematic phase-mismatch analysis in the gas jet to examine the spatial growth of harmonics for tight-focusing versus loose-focusing lasers. The dependence of phase mismatch on the gas-jet position and gas pressure is investigated. Finally, we check the divergence of the harmonic beam generated by a tight-focusing versus loose-focusing truncated Bessel beam. These studies show that for a typical gas-jet experiment, whether the spatial mode is a truncated Bessel beam or a Gaussian beam is important only when the laser beam is tightly focused.

We present a finite-temperature analysis of a quasi-two-dimensional (Q2D) dipolar gas. To do this, we use the Hartree-Fock-Bogoliubov method within the Popov approximation. This formalism is a set of nonlocal equations containing the dipole-dipole interaction and the condensate and thermal correlation functions, which are solved self-consistently. We detail the numerical method used to implement the scheme. We present density profiles for a finite-temperature dipolar gas in Q2D and compare these results to those for a gas with zero-range interactions. Additionally, we analyze the excitation spectrum and study the impact of the thermal exchange.

We investigate numerically and theoretically solitons in highly nonlocal three-dimensional nematic liquid crystals. We calculate the fundamental soliton profiles using the modified Petviashvili method. We apply the variational method to the widely accepted scalar model of beam propagation in uniaxial nematic liquid crystals and compare the results with numerical simulations. To check the stability of such solutions, we propagate them in the presence of noise. We discover that the presence of any noise induces the fundamental solitons—the so-called nematicons—to breathe. Our results explain the difficulties in experimental observation of steady nematicons.

We report on the real-space experimental observation of whispering-gallery modes in coupled disk microresonators excited by a tapered optical fiber. Using a high-resolution scattering scanning near-field optical microscope (SNOM) technique, the resonator modes can be perturbed, leading to altered transmission and reflection through the tapered fiber. The correlation of the perturbed signals with the position of the perturbing SNOM tip results in intensity maps of the optical resonator modes under investigation. A combination of a coupled-mode theory of the excited microresonator including the SNOM tip and a two-dimensional modal expansion technique can be used to understand different regimes of the perturbation, leading to qualitatively different transmission and reflection maps for the same optical resonator mode. Detailed measurements of the intensity distributions of eigenmodes of two and three coupled disks in different arrangements are presented and compared to theoretical calculations.