We find that the Feynman relation of Bose-Einstein condensates with spin-orbit coupling, which relates the energy of excitations, the static structure factor in condensed phase, and the dispersion of free bosons, is not satisfied in the whole momentum space. The dispersion is highly anisotropic and more divergent in the infrared limit compared to that without spin-orbit coupling because of spontaneous breaking of the O(2) symmetry of the ground state. And the dispersion also exhibits time reversal asymmetry for plane-wave condensates, which is condensed on a momentum with a finite value. We also find that larger spin-orbit coupling makes the excitations out of condensates more coherent.

A scheme for directed transport of quantum particles in a static bipartite lattice driven by an ac force, based on a sequence of Landau-Zener transitions, is proposed theoretically. As compared to directed transport in bipartite lattices exploiting the phenomenon of coherent destruction of tunneling recently suggested by Creffield [Phys. Rev. Lett. 99, 110501 (2007)], the present scheme realizes a robust quantum state transport owing to the adiabaticity of the particle transfer. The transport is realized by an external force with a sawtooth profile and does not require modulation of lattice parameters (intersite couplings and energy levels). The effects of lattice disorder and particle interaction on the directed quantum transport are discussed.

We propose a scheme to observe the crossover from weakly to strongly bound pairs with stationary polaritons. We first show how stationary light-matter excitations (polaritons) can realize an optically tunable two-component Bose-Hubbard model with repulsive intraspecies interactions and attractive interspecies interactions. We then discuss the feasibility of generating an effective Fermi-Hubbard model of polaritons exhibiting the crossover behavior. The predicted behavior of the system characterized by a crossover from short- to long-range spatial correlations as interactions are tuned can be efficiently observed by measuring correlation functions on the light exiting the waveguide.

We consider shapes and dynamics of semidiscrete solitons (SDSs) in the known model of the set of linearly coupled waveguides with intrinsic cubic nonlinearity. The model applies to the description of a planar array of optical fibers or of a stack of parallel planar waveguides, in the temporal and spatial domains, respectively, as well as to the self-attractive Bose-Einstein condensate (BEC) loaded into an array of parallel tunnel-coupled cigar-shaped traps. It was found previously that the interplay of the group-velocity dispersion, discrete diffraction (in the longitudinal and transverse directions, respectively), and intrinsic self-focusing gives rise to SDSs in the array. We here develop the variational approximation (VA) and additional analytical methods for the description of the SDSs, and study their mobility and collisions by means of systematic simulations. The VA and an exact solution of the linearized equation in the cores adjacent to the central one produce an accurate description for the family of stable fundamental on-site-centered SDS solutions, as well as of surface SDSs in the semi-infinite array. The VA is also presented for transversely unstable intersite-centered solitons. In simulations, the solitons are not mobile in the discrete direction (nonsoliton semidiscrete modes may be mobile across the array). Collisions between SDSs traveling in the longitudinal direction feature a threshold separating the passage and merger or destruction. The exact shape of the threshold, considered as a function of the solitons’ energy, features irregularities, while its average form is explained analytically. “Shifted” collisions between SDSs centered at adjacent cores are also studied.

We report experiments and numerical simulations on the self-focusing and filamentation of ultraintense femtosecond Airy waveforms in water. The accelerating property of Airy waveforms results in the generation of distinct features in the angularly resolved spectra of forward-propagating supercontinuum emission. Fitting these features with appropriate phase-matching conditions allows for the quantification of the propagation history of the waveforms.

Quantum coherence can affect the thermodynamics of small quantum systems. Coherences have been shown to affect the power generated by a quantum heat engine (QHE) which is coupled to two thermal photon reservoirs and to an additional cavity mode. We show that the fluctuations of the heat exchanged between the QHE and the reservoirs strongly depend on quantum coherence, especially when the engine operates as a refrigerator, i.e., heat current flows from the cold bath to the hot bath. Intriguingly, we find that the ratio of positive and negative (with respect to the thermodynamic force) fluctuations in the heat current satisfies a universal coherence-independent fluctuation theorem.

We have investigated multiphoton-ionization passages of rubidium atoms initiated from the excited $5P_{3/2}$ energy state. For this we used coherent control schemes based on femtosecond laser pulse shaping applied to cold atoms spatially isolated in a magneto-optical trap. With programed laser pulses of spectral $\pi$-phase step, of which location was varied within the laser spectrum, the sequential two-photon-ionization passage along the $5P_{3/2}$-$5D$ continuum was probed in terms of trap-loss spectroscopy. The coherent control two-photon-ionization method unveiled not only the resonantly enhanced two-photon ionization but also the asymmetric nature of the ionization profile structure given as a function of the spectral phase step location. Experimental results show good agreement with the second-order perturbation calculation of the constituent possible ionization passages.

Quantum correlations may be measured by means of the distance from the state to the subclass of states $\Omega$ having well-defined classical properties. In particular, a geometric measure of asymmetric discord [Dakić et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance from a given two-qubit state to the closest classical-quantum (CQ) correlated state. We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance from a given state to the closest classical-classical (CC) correlated state. The optimal member of $\Omega$ is just a specially measured original state for both the CQ and CC discords. This implies that this measure is equal to the quantum deficit of postmeasurement purity. We discuss some general relations between the CC discords and explain why an analytical formula for the CC discord, contrary to the CQ discord, can hardly be found even for a general two-qubit state. Instead of such an exact formula, we find simple analytical-measurement-based upper bounds for the CC discord which, as we show, are tight and faithful in the case of two qubits and may serve as independent indicators of two-party quantum correlations. In particular, we propose an adaptive upper bound, which corresponds to the optimal states induced by single-party measurements: optimal measurement on one of the parties determines an optimal measurement on the other party. We discuss how to refine the adaptive upper bound by nonoptimal single-party measurements and by an iterative procedure which usually rapidly converges to the CC discord. We also raise the question of optimality of the symmetric measurements realizing the CC discord on symmetric states and give a partial answer for the qubit case.

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft interparticle potential. In order to make contact with a real system, we use an attractive Gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used ${}^4$He-${}^4$He interactions, the LM2M2 potential of Aziz and Slaman. The intensity of the potential is varied in order to explore the clusters’ spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four-, five-, and six-particle systems. In all the regions explored, we have found that these systems present two states, one deep and one shallow close to the $A-1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continua using the two-body Gaussian potential. They agree with recent measurements and theoretical predictions.

The method for the evaluation of the self-energy of bound electron is proposed. The integration over four-momenta of virtual photons is done in a way that preserves manifest Lorentz invariance. The resulting expression can then be decomposed into high- and low-energy parts in a Lorentz invariant fashion. The high-energy part depends only on the behavior of the wave function of the reference state in the immediate vicinity of the nucleus and can be calculated analytically. The low-energy part depends on further details of the atomic structure and has to be calculated numerically. The results accurate at least up to $\alpha {\left(Z\alpha \right)}^6$ are obtained for non-$S$ states and normalized difference $n^3\Delta E_n-\Delta E_1$ of the $S$ states. The method is applied to the states with the principal quantum number $n$ ranging from 2 to 10, with the orbital quantum number $l$ ranging from 0 to 3 and with the nuclear charges $Z$ ranging from 1 to 30. In the cases that were already considered in literature a very good agreement with previous calculations is found, especially for the atoms with lower nuclear charges. The advantages of the present method over the previous ones are pointed out.

We demonstrate the trapping of a single ion in the focus of a deep parabolic mirror that covers 81$\%$ of the solid angle surrounding the ion. Accounting for the reflectivity of the mirror we infer a photon collection efficiency of 54.8$\%$ for our setup. The underlying experimentally detected maximum fluorescence rate is $1.91\times {10}^6$ s${}^{-1}$ from a single ${}^{174}$Yb${}^{+}$ ion, mainly limited by the quantum efficiency of our photon detector. Besides the high collection efficiency, the integration of an ion trap into a parabolic mirror is a key ingredient for efficient coupling of light to a single ion in free space.

We study the carrier-envelope-phase (CEP) effect of a few-cycle laser pulse on bound-bound transitions in helium in the high-frequency region. Specifically, for the one-photon transition from the $1{}^{1}S$ to the $2{}^{1}P$ state, the CEP effect increases as the frequency increases; while for the two-photon transition from the $1{}^{1}S$ to the $3{}^{1}D$ state, the CEP effect shows a peak at a frequency that is almost equal to the energy difference between the $1^{1}S$ and $3{}^{1}D$ states. By using a four-level model, we find that the CEP effect on the $1{}^{1}S$–$2{}^{1}P$ transition is attributed to the quantum interference between the positive-frequency and negative-frequency subpaths of the one-photon transition; whereas the CEP effect on the $1{}^{1}S$–$3{}^{1}D$ transition is attributed to the interference between the sum-frequency and difference-frequency components of the two-photon transition. These results indicate that the CEP effect can occur not only due to the interference between neighboring multiphoton-transition paths, but also due to the interference between two components inside one multiphoton-transition path. Therefore, this work, together with our previous work for the low-frequency region [Peng et al., Phys. Rev. A 82, 053407 (2010)], may provide a complete picture of the CEP effect on bound-bound transitions in the whole range of laser frequency.

Resonantly enhanced multiphoton ionization photoelectron spectroscopy (REMPI-PS) has proven to be a well-established tool to study the excited-state structure. However, femtosecond-induced REMPI-PS suffers from poor selectivity between neighboring excited states due to the large spectral bandwidth. In this paper, we present a feasible scheme to realize the selective excitation of (2+1) REMPI-PS in sodium atoms. We show that, by shaping the femtosecond laser pulse with a cubic phase modulation, a high-resolution (2+1) REMPI-PS is obtained, and the (2+1) REMPI-PS signal from one excited state is enhanced while that from the other excited state is effectively suppressed. Furthermore, we explain the physical control mechanism of the selective excitation of (2+1) REMPI-PS by considering the two-photon power spectrum.

Exploratory simulations of Bose-Fermi mixtures on the three-dimensional optical lattice at finite temperature are performed by adopting the lattice quantum chromodynamics technique. We analyze the bosonic superfluid transition and its dependence on the strength of the boson-fermion coupling. The particle densities and the pair occupancies are also studied to understand the effect of the boson-fermion coupling to the microscopic properties of the system. The effect of the induced fermion-fermion interaction by the boson density fluctuation is clearly seen.

The Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar systems has been studied recently by path integral Monte Carlo simulations [A. Filinov et al., Phys. Rev. Lett. 105, 070401 (2010)]. Here, we complement this analysis and study temperature-coupling strength dependence of the density (particle-hole) and single-particle (SP) excitation spectra both in superfluid and normal phases. The dynamic structure factor, $S(q,\omega )$, of the longitudinal excitations is rigorously reconstructed with full information on damping. The SP spectral function, $A(q,\omega )$, is worked out from the one-particle Matsubara Green's function. A stochastic optimization method is applied for reconstruction from imaginary times. In the superfluid regime sharp energy resonances are observed in both the density and SP excitations. The involved hybridization of both spectra is discussed. In contrast, in the normal phase, when there is no coupling, the density modes, beyond acoustic phonons, are significantly damped. Our results generalize previous zero-temperature analyses based on variational many-body wave functions [F. Mazzanti et al., Phys. Rev. Lett. 102, 110405 (2009); D. Hufnagl et al., Phys. Rev. Lett. 107, 065303 (2011)], where the underlying physics of the excitation spectrum and the role of the condensate has not been addressed.

Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons ($XY$ model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.

We investigate the wavelength scaling of high-order-harmonic-generation (HHG) efficiency by few-cycle laser pulses where the influence of the carrier-envelope phase (CEP) becomes prominent. Based on the numerical solution of time-dependent Schrödinger equation, in the infrared region of $\lambda$ (0.8–1.8 $\mu$m), we observe that the power law of the form ${\lambda }^{-x}$ ($x\approx 5$–6) is still present; but for constant intensity and a fixed energy interval, it differs markedly in the CEP. We find that for a specific value of CEP the wavelength dependence follows a ${\lambda }^{-4.6}$ scaling in high-harmonic yield. We also perform classical trajectory calculations to gain some understanding of the CEP dependence of the wavelength scaling.

We measure the time-energy correlation of broadband, spontaneously seeded four-wave mixing (FWM), and demonstrate time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband ($>100$ nm) sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down-conversion, its unique dependence on pump intensity due to self- and cross-phase-modulation effects yields spectral and temporal structure in the correlations. While these effects are minute compared to the time duration and bandwidth of the FWM sidebands, they are well observed using sum-frequency generation as a precise, ultrafast, wide-bandwidth correlation detector.

We study the interference pattern of biphotons passing through a dispersive medium, and devise a method for measuring dispersion in coincidence counting of entangled photons. By measuring the Gouy phase shift accompanying dispersion, we show that it fundamentally differs from the Gouy phase expected from classical models. Finally, we show that the second-order correlation function of the dispersed biphoton can be much wider than the pattern predicted from classical analog.