It is found that stable few-body spin structures, pairs and triplexes in the spin space, may exist as basic constituents in small spin-3 condensates, and they play the role of building blocks when the parameters of interaction fall in particular domains. A specific method is designed to find these constituents.

We present first-principles numerical calculations for few-particle solutions of the attractive Bose-Hubbard model with periodic boundary conditions. We show that the low-energy many-body states found by numerical diagonalization can be written as translational superposition states of compact composite systems of particles. These compact states break the translational symmetry of the problem, and their center-of-mass and internal excitations offer simple explanations of the energy spectrum of the full model.

In this work we investigate a generic method able to extract information on molecular organization in biological samples from polarized second harmonic generation (SHG) microscopy, without the need to infer an a priori model for the molecular orientational distribution. The mean orientation of this distribution, as well as its first and third orders of symmetry, are estimated by monitoring SHG intensity signals under a varying incident polarization. We introduce, in particular, a reduction of the problem to a two-dimensional approach appropriate to the microscopy geometry. This method allows us to retrieve determining information which is not available in the traditional model-oriented methods, as illustrated in molecular-order imaging in collagen fibrils. The precision of the parameters estimation is evaluated by a Monte Carlo analysis, based on the Poisson noise statistics of the measured signal.

In quantum communication and distributed quantum computing, one-dimensional (1D) waveguides provide directional transfer of quantum information. A single-mode waveguide has a density-of-states singularity at the lower cut-off frequency, which resembles sharp resonances of a cavity but with non-Markovian dynamics. Thus we put forward schemes of coupling atomic transitions and a waveguide continuum edge. We first present a scheme of spin-photon quantum interface operating in the non-Markovian regime for a $\Lambda$-type three-level system coupled to a waveguide. Then we show that strong coupling between atomic transitions and a waveguide continuum edge can lead to vacuum Rabi oscillations and bound polariton states.

We develop a Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model which effectively describes both static and dynamic properties of photons evolving in a cubic lattice of cavities, each filled with a two-level atom. To this end we calculate the effective action to first order in the hopping parameter. Within a Landau description of a spatially and temporally constant order parameter we calculate the finite-temperature mean-field quantum phase boundary between a Mott insulating and a superfluid phase of polaritons. Furthermore, within the Ginzburg-Landau description of a spatiotemporal varying order parameter we determine the excitation spectra in both phases and, in particular, the sound velocity of light in the superfluid phase.

We study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on demand by sending coherent states into the proposed system. We calculate the second-order correlation function of the transmitted field and observe bunching and antibunching caused by the bound states. Furthermore, we demonstrate that the proposed system can produce photon pairs with a high degree of spectral entanglement, which have a large capacity for carrying information and are important for large-alphabet quantum communication.

For the last 20 years, the question of what are the fundamental capabilities of quantum precision measurements has sparked a lively debate throughout the scientific community. Typically, the ultimate limits in quantum metrology are associated with the notion of the Heisenberg limit expressed in terms of the physical resources used in the measurement procedure. Over the years, a variety of different physical resources were introduced, leading to a confusion about the meaning of the Heisenberg limit. Here, we review the mainstream definitions of the relevant resources and introduce the universal resource count, that is, the expectation value of the generator (above its ground state) of translations in the parameter we wish to estimate, that applies to all measurement strategies. This leads to the ultimate formulation of the Heisenberg limit for quantum metrology. We prove that this limit holds for the generators of translations with an upper-bounded spectrum.

One-photon intrashell transitions in strongly driven Li ($n=25$) atoms are studied experimentally. The degeneracy of the $n$ shell is lifted by orthogonal dc electric and magnetic fields, which also define the eccentricity of the initial coherent elliptic state. The transitions are driven by a radio frequency pulse linearly polarized parallel to the major axis of the ellipse. A small dc electric field component parallel to the magnetic field splits the one-photon resonance into two, and transitions in between are studied by state-selective field ionization. Unexpected lines in the ionization spectra relating to unknown transitions are found and discussed.

We numerically investigate vortex lattices in rotating two-component Bose-Einstein condensates in which the two components have unequal atomic masses and interact attractively with each other. For sufficiently strong attraction, the system is found to exhibit exotic ground-state structures in a harmonic trap, such as lattices having a square geometry or consisting of two-quantum vortices. The obtained states satisfy the Feynman relation, and they can be realized with current experimental techniques.

The utilization of atom interferometry for gyroscopes is of considerable interest because the detection of inertial rotations via the Sagnac effect has a potential ${10}^{10}$ greater sensitivity than optical gyroscopes. Here we analyze, in the presence of a rotation $\Omega$, phase-coherent transport of atomic matter waves in a one-dimensional chain of $N$ ring interferometers in which the sizes of the rings are chirped symmetrically about the center ring. The gyroscope scale factor of the area-chirped array for $N\lesssim 10$ is several orders of magnitude larger than that for the unchirped array, which itself is larger than the scale factor of a Mach-Zehnder interferometer with the same enclosed area. This enhancement is achieved with total enclosed areas that are larger or smaller than that of the unchirped array by less than 25$\%$. As such, the area chirp achieves rotation sensitivities with $N\lesssim 10$ interferometers that would normally require $N\gg 100$ rings of identical sizes.

The spectrum of two bosons and two fermions in a trap is calculated using a correlated-Gaussian basis throughout the range of a broad Fano-Feshbach resonance. The calculations provide a few-body solution to the magneto-association of fermionic Feshbach molecules. This solution is used to study the time evolution of the system as the scattering length changes, mimicking experiments with Bose-Fermi mixtures near Fano-Feshbach resonances. The structure of avoided crossings in the few-body spectrum enables an interpretation of the dynamics of the system as a sequence of Landau-Zener transitions. The calculated molecule formation rate is compared with experimental observations.

A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments. Their relation to normally ordered moments is derived, which enables us to verify nonclassicality by using well established criteria. Alternatively, nonclassicality criteria are directly formulated in terms of nonclassicality moments. The latter converge in proper limits to the usually used criteria, as is illustrated for squeezing and sub-Poissonian photon statistics. Our theory also yields expectation values of any observable in terms of nonclassicality moments.

We develop a temporal coupled-mode theory to describe the interaction of plane wave with an individual scatterer having an arbitrary shape. The theory involves the expansion of the fields on cylindrical or spherical wave basis for the two-dimensional and three-dimensional cases, respectively, and describes the scattering process in terms of a background scattering matrix and the resonant radiation coefficients into different cylindrical or spherical wave channels. This theory provides a general formula for the scattering and absorption cross sections. We show that for a subwavelength asymmetric scatterer with a single resonance, the scattering and absorption cross sections can exceed the single-resonance limit for some specific incident angles of illumination, but the sum of these cross sections over all angles has an upper limit. We validate the theory with numerical simulations of a metallic scatterer that does not have any rotation symmetry.

It is shown that local distinguishability of orthogonal mixed states can be completely characterized by the local distinguishability of their supports irrespective of entanglement and mixedness of the states. This leads to two kinds of upper bounds on the number of locally distinguishable orthogonal mixed states. The first one depends only on pure-state entanglement within the supports of the states and therefore may be easy to compute in many instances. The second bound is optimal in the sense that it optimizes the bounding quantities, not necessarily the function of entanglement alone, over all orthogonal mixed-state ensembles (satisfying certain conditions) admissible within the supports of the density matrices.

We calculate the thermal Casimir-Polder potential of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ fullerene molecules near gold and silicon nitride surfaces, motivated by their relevance for molecular matter-wave interference experiments. We obtain the coefficients governing the asymptotic power laws of the interaction in the thermal, retarded, and nonretarded distance regimes and evaluate the full potential numerically. The interaction is found to be dominated by electronic transitions and hence independent of the internal temperature of the molecules. The contributions from phonon transitions, which are affected by the molecular temperature, give rise to only a small correction. Moreover, we find that the sizable molecular line widths of thermal fullerenes may modify the nonretarded interaction, depending on the model used. Detailed measurements of the nonretarded potential of fullerene thus allow one to distinguish between different theories of incorporating damping.

We predict feasibility of the photoassociative formation of Sr${}_2$ molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the $c$${}^3{\Pi }_u$, $A$${}^1{\Sigma }_u^{+}$, and $B$${}^1{\Sigma }_u^{+}$ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ${}^{1}S+{}^3{P}_1$ intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground $X$${}^1{\Sigma }_g^{+}$ potential, with $v^{\prime \prime }$ as low as $v^{\prime \prime }=6$. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited-state levels that have the largest bound-to-bound transition moments to deeply bound ground-state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited-state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr${}_2$ molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.

We propose a ringlike three-level model and show that it can be realized using Stark states of highly excited potassium interacting with two-mode microwave fields. We demonstrate this by using both analytical model and numerical simulations to study the problems of multiphoton Rabi oscillations. The results show that the Rabi oscillation patterns of the ringlike three-level system exhibit additional envelope and nodes compared to the oscillatory behavior of a three-level cascade system; in other words, there exist collapse and revival phenomena for Rabi oscillation patterns. The origin of the collapse and revival of the population oscillations is the multiphoton two-color resonances at frequency $\Omega =n{\omega }_1+m{\omega }_2$. Our analytic results are in good agreement with numerical simulations. In addition, all the analytical solutions for the three basic configurations of the three-level system classified as the $\Lambda$, vee, and cascade systems can be deduced from our analytical solution for the ringlike three-level configuration by setting one of the three coupling strengths equal to 0.

We propose that negative absolute temperatures in ultracold atomic clouds in optical lattices can be used to simulate quantum systems in new regions of phase diagrams. First we discuss how the attractive SU(3) Hubbard model in three dimensions can be realized using repulsively interacting ${}^{173}$Yb atoms, then we consider how an antiferromagnetic $S=1$ spin chain could be simulated using spinor ${}^{87}$Rb or ${}^{23}$Na atoms. The general idea to achieve negative absolute temperatures is to reverse the sign of the external harmonic potential. Energy conservation in a deep optical lattice imposes a constraint on the dynamics of the cloud, which can relax toward a $T<0$ state. As the process is strongly nonadiabatic, we estimate the change of the entropy.

The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it is shown that when an object is placed in one of the beam paths the value of the mutual information is strongly dependent on object shape and is closely related to the degree of rotational symmetry present. After analyzing the effect of the object on the OAM correlations, the method of correlated spiral imaging is described. We first present a version using parametric down-conversion, in which entangled pairs of photons with opposite OAM values are produced, placing an object in the path of one beam. We then present a classical (correlated, but nonentangled) version. The relative problems and benefits of the classical versus entangled configurations are discussed. The prospect is raised of carrying out compressive imaging via two-photon OAM detection to reconstruct sparse objects with few measurements.

The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental solitons in the semi-infinite gap and the dipole solitons in the first gap do not exist for negative defects. The influence of the imaginary part of the PT-symmetric potentials on soliton stability is given. When the modulation depth of the PT-symmetric lattices is small, defect solitons can be stable for positive and zero defects, even if the PT-symmetric potential is above the phase transition point.