We compare and contrast the wide Feshbach resonances and the corresponding weakly bound states in the lowest scattering channels of ultracold ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$. We use high-precision measurements of binding energies and scattering properties to determine interaction potentials that incorporate non-Born-Oppenheimer terms to account for the failure of mass scaling between ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$. Correction terms are needed for both the singlet and the triplet potential curves. The universal formula relating binding energy to scattering length is not accurate for either system. The ${}^6\mathrm{Li}$ resonance is open-channel-dominated and the van der Waals formula of Gao [J. Phys. B 37, 4273 (2004)] gives accurate results for the binding energies across much of the resonance width. The ${}^7\mathrm{Li}$ resonance, by contrast, is weakly closed-channel-dominated and a coupled-channel treatment of the binding energies is required. Plotting the binding energies in universal van der Waals form helps illustrate subtle differences between the experimental results and different theoretical forms near the resonance pole.

We experimentally investigate the radiative force and laser-induced fluorescence (LIF) in cold rubidium atoms induced by pulse-train (frequency-comb) excitation. Three configurations are studied: (i) single-pulse-train excitation, (ii) two in-phase counterpropagating pulse trains, and (iii) two out-of-phase counterpropagating pulse trains. In all configurations, measured LIF is in agreement with calculations based on the optical Bloch equations. The observed forces in the first two configurations are in qualitative agreement with the model(s) used for calculating mechanical action of a pulse train on atoms; however, this is not the case for the third configuration. Possible resolution of the discrepancy is discussed.

We theoretically investigate the free-carrier-induced spatiotemporal dynamics of continuous waves in silicon waveguides embedded in an amplifying medium. Optical propagation is governed by a cubic Ginzburg-Landau equation coupled with an ordinary differential equation accounting for the free-carrier dynamics. We find that, owing to free-carrier dispersion, continuous waves are modulationally unstable in both anomalous and normal dispersion regimes and chaotically generate unstable accelerating pulses.

We give a detailed account of an efficient search algorithm for the data-pattern tomography proposed by J. Rehacek, D. Mogilevtsev, and Z. Hradil [Phys. Rev. Lett. 105, 010402 (2010)], where the quantum state of a system is reconstructed without a priori knowledge about the measuring setup. The method is especially suited for experiments involving complex detectors, which are difficult to calibrate and characterize. We illustrate the approach with the case study of the homodyne detection of a nonclassical photon state.

We study breathers, their collision, and the interaction between breathers and other types of nonlinear localized waves (solitons and rogue waves) in a three-mode optical fiber. We find that there exist three types of breathers with different structures, i.e., bright, dark, and four-petaled breathers. We present some inelastic interaction structures of the breather collision and the interplay of breathers and other types of nonlinear localized waves. In particular, we find that one breather and two rogue waves with different structures can coexist and interact with each other. It is interesting that the breather gets twisted by the attractive interactions between the breather and rogue waves, and its intensity between the rogue waves changes.

We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. We show that the two clouds are anticorrelated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with nonlocal Einstein-Podolsky-Rosen entanglement.

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong-coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases is investigated with the density matrix renormalization group technique. Other magnetic phases are seen and phase transitions between them within the superfluid regime are discussed. Possible experimental detection is discussed.

We address the propagation of the spin along classical trajectories for a spin-1/2 particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities, we find an explicit spin-transport law for the case of the Dirac oscillator. In the general case we examine the spin propagation along classical trajectories emerging as an approximation of the quantum dynamics via the mechanical analog of the optical eikonal asymptotic approach. Throughout we establish as many parallels as possible with the equivalent situation for the electromagnetic field.

Pendlebury $\mathit{et}\mathit{al}.$ [Phys. Rev. A 70, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.

Photon-photon interactions mediated by an atomic gas can effect efficient polarization exchanges between two beams, leaving the medium exactly in its initial state. In, e.g., hydrogen, the distance required for macroscopic exchange is of the order of one-tenth the distance in which the ordinary nonlinear index of refraction would induce a phase change of $\pi$. Several examples are worked out that show the variety of behaviors that can result, depending on the initial respective polarizations stated and the angle between the beams. Of particular interest are initial conditions in which there is no exchange at a mean-field level, conventionally believed to apply when the number of photons N is large. Then the full theory leads both to large exchange and to large entanglement between the beams. Our most solid results indicate that one would have to wait a time proportional to log[N] to see this effect, but there are some indications that this behavior can be circumvented.

In this work, we revisit the problem of finding an admissible region of fidelities obtained after the application of an arbitrary $1\to N$ universal quantum cloner which has been recently solved in A. Kay et al. [Quant. Inf. Comput 13, 880 (2013)] from the side of cloning machines. Using group-theory formalism, we show that the allowed region for fidelities can be alternatively expressed in terms of overlaps of pure states with recently found irreducible representations of the commutant $U\otimes U\otimes \cdots \otimes U\otimes U^{*}$, which gives the characterization of the allowed region where states being cloned are a figure of merit. Additionally, it is sufficient to take pure states with real coefficients only, which makes calculations simpler. To obtain the allowed region, we make a convex hull of possible ranges of fidelities related to a given irrep. Subsequently, two cases, $1\to 2$ and $1\to 3$ cloners, are studied for different dimensions of states as illustrative examples.

Radio-frequency phase modulation of frequency-entangled photons leads to a two-photon interference pattern in the frequency domain. In recent experiments, the pattern was measured with narrow-band frequency filters which select photons belonging to a given frequency bin. Here we show how photons can be grouped into even and odd frequencies by using periodic frequency filters called interleavers. In our theoretical analysis we show how this reduces the high-dimensional photon state to an effective two-dimensional state. This is of interest for applications such as quantum cryptography or low-dimensional tests of quantum nonlocality. We then report an experimental realization of this proposal. The observed two-photon interference pattern and violation of the CHSH inequality—the simplest binary-outcome Bell inequality—are in good agreement with the theoretical predictions.

Multidimensional covariance analysis and its validity for correlation of processes leading to multiple products are investigated from a theoretical point of view. The need to correct for false correlations induced by experimental parameters which fluctuate from shot to shot, such as the intensity of self-amplified spontaneous emission x-ray free-electron laser pulses, is emphasized. Threefold covariance analysis based on simple extension of the two-variable formulation is shown to be valid for variables exhibiting Poisson statistics. In this case, false correlations arising from fluctuations in an unstable experimental parameter that scale linearly with signals can be eliminated by threefold partial covariance analysis, as defined here. Fourfold covariance based on the same simple extension is found to be invalid in general. Where fluctuations in an unstable parameter induce nonlinear signal variations, a technique of contingent covariance analysis is proposed here to suppress false correlations. In this paper we also show a method to eliminate false correlations associated with fluctuations of several unstable experimental parameters.

The carrier-envelope-phase (CEP) dependence of correlated electron dynamics in molecular nonsequential double ionization by few-cycle laser pulses is investigated with the three-dimensional classical ensemble model. Our results show that the asymmetric longitudinal momentum spectra of the doubly charged ions strongly depend on the CEP of the laser pulses, and the CEP-dependent asymmetry in the ions' momentum spectra varies with varying internuclear distance. By tracing the classical trajectories, it is found that the ionization dynamics of the first electron greatly affects the asymmetry. Back analysis reveals that with increasing internuclear distance, the pathway responsible for energy transfer between the two electrons changes from the recollision process to the collision process. This change causes the shape of the CEP-averaged ion momentum distribution to show a double-single-triple peak structure as the internuclear distance increases.

We demonstrate theoretically that the shaped femtosecond laser pulse with a $\mathsf{V}$-style spectral phase modulation can provide a well-established tool to control the maximal degree and temporal structure of the field-free molecular alignment. By properly designing these controlling parameters characterizing the $\mathsf{V}$-style spectral phase modulation, we can effectively suppress the maximum degree of molecular alignment or reconstruct as that induced by the transform-limited laser pulse while the temporal structure of the molecular alignment keeps unchanged; we also can control the temporal structure of the molecular alignment with a desired shape and switch the molecular alignment and antialignment at any time delay for any temporal structure.

We show that the breaking of integrability in the fundamental one-dimensional model of bosons with contact interactions has consequences on the stationary correlation properties of the system. We calculate the energies and correlation functions of the integrable Lieb-Liniger case, comparing the exact Bethe-ansatz solution with a corresponding Jastrow ansatz. Then we examine the nonintegrable case of different interaction strengths between each pair of atoms by means of a variationally optimized Jastrow ansatz, proposed in analogy to the Laughlin ansatz. We show that properties of the integrable state are more stable close to the Tonks-Girardeau regime than for weak interactions. All energies and correlation functions are given in terms of explicit analytical expressions enabled by the Jastrow ansatz. We finally compare the correlations of the integrable and nonintegrable cases and show that apart from symmetry breaking the behavior changes dramatically, with additional and more pronounced maxima and minima interference peaks appearing.

Three ideas are introduced that when brought together characterize the realistic quasiclassical realms of our quantum universe as particular kinds of sets of alternative coarse-grained histories defined by quasiclassical variables: (i) branch-dependent adaptive coarse grainings that can be close to maximally refined and can simplify calculation, (ii) narrative coarse grainings that describe how features of the universe change over time and allow the construction of an environment, and (iii) a notion of strong decoherence that characterizes realistic mechanisms of decoherence.

In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete generality and we are therefore forced to confront the more general notion of positive-operator valued measures (POVMs), which suffice to describe all measurements that can be implemented in quantum experiments. We study the (in)compatibility of such POVMs and show that quantum theory realizes all possible (in)compatibility relations among sets of POVMs. This is in contrast to the restricted case of projective measurements for which commutativity is essentially equivalent to compatibility. Our result therefore points out a fundamental feature with respect to the (in)compatibility of quantum observables that has no analog in the case of projective measurements.

We present the theoretical basis of a cavity-enhanced polarimetric scheme for the measurement of parity-nonconserving (PNC) optical rotation. We discuss the possibility of detecting PNC optical rotation in accessible transitions in metastable Xe and Hg and ground-state I. In particular, the physics of the PNC optical rotation is presented and we explore the line-shape effects on the expected PNC optical rotation signals. Furthermore, we present an analysis of the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary for understanding the measurement procedure and the ability of employing robust background subtraction procedures using two signal reversals. Using recent atomic structure theoretical calculations, we present simulations of the PNC optical rotation signals for all proposed transitions, assuming a range of experimentally feasible parameters. Finally, the possibility of performing sensitive measurements of the nuclear-spin-dependent PNC effects is investigated for the odd-neutron nuclei ${}^{129}\mathrm{Xe}$ and ${}^{199}\mathrm{Hg}$ and the odd-proton nucleus ${}^{127}\mathrm{I}$.

In the framework of the self-interaction-free time-dependent density-functional theory, we have performed three-dimensional (3D) ab initio calculations of He atoms in near-infrared (NIR) laser fields subject to excitation by a single extreme ultraviolet (XUV) attosecond pulse (SAP). We have explored the dynamical behavior of the subcycle high harmonic generation (HHG) for transitions from the excited states to the ground state and found oscillation structures with respect to the time delay between the SAP and NIR fields. The oscillatory pattern in the photon emission spectra has a period of $\sim$$1.3$ fs which is half of the NIR laser optical cycle, similar to that recently measured in the experiments on transient absorption of He [M. Chini et al., Sci. Rep. 3, 1105 (2013)]. We present the photon emission spectra from $1s2p$, $1s3p$, $1s4p$, $1s5p$, and $1s6p$ excited states as functions of the time delay. We explore the subcycle Stark shift phenomenon in NIR fields and its influence on the photon emission process. Our analysis reveals several interesting features of the subcycle HHG dynamics and we identify the mechanisms responsible for the observed peak splitting in the photon emission spectra.