Interactions of x-ray free-electron laser (XFEL) light with a single cluster target are numerically investigated by using a three-dimensional particle-in-cell code. The plasma dynamics as well as relevant atomic processes are taken into account, such as photoionization, the Auger effect, collisional ionization and relaxation, and field ionization. It is found that as the XFEL intensity increases to as high as $\sim {10}^{21}\left(\text{photons}/\text{pulse}\right)/{\text{mm}}^2$, the field ionization, which is the dominant ionization process over the other atomic processes, leads to rapid target ionization. The target damage due to the irradiation by XFEL light is numerically evaluated, which gives an estimation of the XFEL intensity so as to suppress the target damage within a tolerable range for imaging.

We investigate nonlinear Floquet states and quasienergies of a Bose-Einstein condensate in a double-well potential subject to a high-frequency driving field. A multiple time scale method is used to obtain the nonlinear Floquet states and quasienergies in both weak and strong nonlinearity regimes. It is shown that there are more nonlinear Floquet states without linear counterparts in the strong nonlinearity regime than in the weak nonlinearity regime, and they are phase-locked to an integer multiple of the external driving frequency. The validity of the effective description in the two different regimes is discussed. The stability criterion for these nonlinear Floquet states is found analytically and confirmed numerically.

The high power per mode of a recently developed 10 GHz femtosecond Ti:sapphire frequency comb permits nonlinear Doppler-free saturation spectroscopy in ${}^{87}\text{R}\text{b}$ with a single mode of the comb. We use this access to the natural linewidth of the rubidium $D_2$ line to effectively stabilize the optical frequencies of the comb with an instability of $7\times {10}^{-12}$ in 1 s of averaging. The repetition rate is stabilized to a microwave reference leading to a stabilized and atomically referenced comb. The frequency stability of the 10 GHz comb is characterized using optical heterodyne with an independent self-referenced 1 GHz comb. In addition, we present alternative stabilization approaches for high repetition rate frequency combs and evaluate their expected stabilities.

We demonstrate and theoretically analyze the dressing of several proximate Feshbach resonances in ${}^{87}\text{R}\text{b}$ using radio-frequency (rf) radiation. We present accurate measurements and characterizations of the resonances, and the dramatic changes in scattering properties that can arise through the rf dressing. Our scattering theory analysis yields quantitative agreement with the experimental data. We also present a simple interpretation of our results in terms of rf-coupled bound states interacting with the collision threshold.

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria based on the separability properties of the matrix of moments. In particular, a criterion based on realignment of moments in the matrix is proposed as an analog of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: we obtain various three-mode inseparability criteria, including some previously known ones, which were originally derived from the Cauchy-Schwarz inequality.

The quantum-to-classical transition of a symmetry-breaking coherent control scenario is computationally demonstrated in an optical lattice arrangement. Control is shown to survive in the classical limit and, for small effective $\hslash$, to be comparable in magnitude to quantum control. Moderate decoherence is seen to eliminate structure from the momentum space distribution, but not to cause loss of control. The proposed scenario is designed so as to be demonstrable experimentally in a moving or shaken one-dimensional optical lattice.

We investigate the problem of an ultracold atomic gas in the superfluid phase flowing in the presence of a potential barrier or a periodic potential. We use a hydrodynamic scheme in the local density approximation (LDA) to obtain an analytic expression for the critical current as a function of the barrier height or the lattice intensity, which applies to both Bose and Fermi superfluids. In this scheme, the stationary flow becomes energetically unstable when the local superfluid velocity is equal to the local sound velocity at the point where the external potential is maximum. We compare this prediction with the results of the numerical solutions of the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We discuss the role of long-wavelength excitations in determining the critical velocity. Our results allow one to identify the different regimes of superfluid flow, namely, the LDA hydrodynamic regime, the regime of quantum effects beyond LDA for weak barriers and the regime of tunneling between weakly coupled superfluids for strong barriers. We finally discuss the relevance of these results in the context of current experiments with ultracold gases.

We investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing effect both in the case of a single soliton input and in the regime where dispersive shock waves develop (multisoliton regime). Such conclusions are supported by the linear stability analysis and numerical simulation of the propagation.

Polychromatic propagation-invariant fields (localized waves) with variable spectral coherence properties are considered. A bridge is provided between coherent propagation-invariant pulses, including Bessel pulses, X-waves and focus wave modes, and stationary polychromatic propagation-invariant fields using a difference-frequency spectral-correlation model. In the space-time domain, this assumption leads to a representation of a partially coherent field as a continuum of spectrally fully coherent, mutually independent pulses originating at different instants of time. The influence of partial spectral coherence on temporal coherence and pulse shape as well as intensity distribution and transverse spatial coherence is illustrated by considering fields with propagation-invariant Bessel-mode monochromatic components.

We show that many-body effects in stabilized nanocolloidal suspensions can have a profound effect on their optical nonlinearity. By considering the screened Coulomb repulsions between nanoparticles, we find that the nonlinear optical behavior of these colloids can range from polynomial to exponential depending on their composition and chemistry. The dynamics and stability properties of optical beams propagating in such nonideal gas environments of interacting colloidal particles are investigated. Our analysis provides a theoretical foundation for understanding the recently observed super-Kerr nonlinear optical response of such systems.

Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in arbitrary topologies. Here we present a general construction for the two models for any graph and also for position dependent transition amplitudes. We then prove constructively their unitary equivalence. Defining appropriate projector operators, we moreover show how to obtain the probabilities for one model from the evolution of the other.

We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of $N$ ion qubits that is prepared in a particular Fock state of motion $|m⟩$. The $m$ phonons are removed by applying a laser pulse globally to the $N$ qubits and converting the motional excitation to $m$ flipped spins. The global nature of this pulse ensures that the $m$ flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state $|D_N^{\left(m\right)}⟩$. We calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for $m=1$ and $m=2$. We have demonstrated the basic features of this protocol by preparing the Bell state $|D_2^{\left(1\right)}⟩$ in two ${{}^{25}\text{M}\text{g}}^{+}$ target ions trapped simultaneously with an ${{}^{27}\text{A}\text{l}}^{+}$ ancillary ion.

A systematic investigation of the structures and the dependence of the dipole polarizabilities on the composition of closed and open shell gallium arsenic clusters is presented. Our investigation focuses on nine gallium arsenide (GaAs) clusters with five and six total number of atoms of systematically varying composition. These clusters are the smallest species of small GaAs clusters which have attracted substantial attention due to their strongly oscillating experimental polarizability values. The ground states of those clusters have been determined using a global approach which combines molecular dynamics and an automatic procedure of comparing and selecting cluster structures based on pattern recognition techniques. The polarizabilities have been studied by means of coupled cluster techniques complemented by a semi-empirical hybrid functional which includes corrections from perturbation theory. Our global structural investigation found two different structures for ${\text{Ga}}_4{\text{As}}_2$ and ${\text{Ga}}_1{\text{As}}_5$ which are lower in energy than the previously reported ones. The performed polarizability investigation suggests that open shell GaAs systems composed of five atoms are not more polarizable than closed-shell clusters built by six atoms as is indirectly implied by the reported experimental data. Also, the polarizabilities of those species increase as a function of the number of Ga in a monotonic but not systematic manner. The observed increase type is explained by the large atomic polarizabilities of Ga and in terms of the particular structural and bonding features of a given cluster. Furthermore, the comparison between our theoretical values and earlier experimental polarizability estimations clearly shows that for the five-atomic clusters, the reported experimental polarizability is not largely overestimated as was previously believed. Our results for the six-atomic cluster demonstrate that the polarizability per atom of a six atomic GaAs cluster of any composition is larger than the polarizability of the bulk material, contrary to what has been demonstrated by the experiment.

We develop a complete analytical description of the time evolution of squeezed states of a charged particle under the Fock-Darwin (FD) Hamiltonian and a time-dependent electric field. This result generalizes a relation obtained by Infeld and Plebański for states of the one-dimensional harmonic oscillator. We relate the evolution of a state-vector subjected to squeezing to that of state which is not subjected to squeezing and for which the time evolution under the simple harmonic oscillator dynamics is known (e.g., an eigenstate of the Hamiltonian). A corresponding relation is also established for the Wigner functions of the states, in view of their utility in the analysis of cold-ion experiments. In Appendix A, we compute the response functions of the FD Hamiltonian to an external electric field, using the same techniques as in the main text.

Using a variational approach, we solve the equations of two-fluid hydrodynamics for a uniform and trapped Fermi gas at unitarity. In the uniform case, we find that the first and second sound modes are remarkably similar to those in superfluid helium, a consequence of strong interactions. In the presence of harmonic trapping, first and second sound become degenerate at certain temperatures. At these points, second sound hybridizes with first sound and is strongly coupled with density fluctuations, giving a promising way of observing second sound. We also discuss the possibility of exciting second sound by generating local heat perturbations.

We demonstrated the power noise reduction of a continuous-wave laser field by means of an effective third-order Kerr nonlinear cavity. In contrast to conventional noise reduction schemes relying on linear cavities, a strong noise suppression at Fourier frequencies below the linewidth of the nonlinear cavity was possible. The laser light was reflected off a Kerr nonlinear cavity that had a half width half maximum linewidth of 4.5 MHz. The cavity was operated slightly off-resonance at approximately half of the maximum power buildup, close to its so-called critical state; a power noise reduction of up to 32 dB at Fourier frequencies below 1 MHz was observed after reflection. The effective third-order nonlinearity was a so-called cascaded second-order nonlinearity of $\text{MgO}:{\text{LiNbO}}_3$. The laser had a power of 0.75 W at the wavelength of 1064 nm.

We study theoretically the spontaneous emission rate of a two-level quantum emitter in any nanophotonic system. We derive a general representation of the rate on the orientation of the transition dipole by only invoking symmetry of the Green function. The rate depends quadratically on orientation and is determined by rates along three principal axes, which greatly simplifies visualization: emission rate surfaces provide insight on how preferred orientations for enhancement (or inhibition) depend on emission frequency and location, as shown for a mirror, a plasmonic sphere, and a photonic band-gap crystal. Moreover, insight is provided on means to “switch” the emission rates by actively controlling the orientation of the emitters’ transition dipole.

Let us consider the set of all probabilities generated by local binary measurements on two separated quantum systems of a given local dimension $d$. We address the question of whether the shape of this quantum body is convex or not. We construct a point in the space of probabilities, which is on the convex hull of the local polytope, but still cannot be attained by measuring $d$-dimensional quantum systems if the number of measurement settings is large enough. From this it follows that this body is not convex. We also show that for finite $d$ the quantum body with the generalized measurement associated with positive operator-valued measures allowed may contain points that cannot be achieved with only projective measurements.

A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated $d$-dimensional systems: the multiscale entanglement renormalization ansätze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of $d$-dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case.

High-resolution $K\beta$ x-ray spectra induced by 2 MeV protons in thick Ti, TiO, ${\text{Ti}}_2{\text{O}}_3$, ${\text{TiO}}_2$, ${\text{MgTiO}}_3$, ${\text{FeTiO}}_3$, TiC, TiN, and ${\text{TiB}}_2$ targets were measured using a wavelength dispersive spectrometer combined with a position-sensitive detector. The intensities and energies of the $K{\beta }_{2,5}$ and $K{\beta }^{″}$ lines relative to the $K{\beta }_{1,3}$ line were extracted. The influence of self-absorption in thick targets was investigated using related x-ray-absorption near-edge-structure spectra that are available in the literature to extract mass absorption coefficients close to the $K$ absorption edge. The correlation of the relative position of the $K{\beta }_{2,5}$ line with a titanium formal oxidation state in oxide compounds confirmed that the oxidation state of Ti in ${\text{FeTiO}}_3$ is probably a mixture of Ti III and Ti IV states, which has been recently reported by other authors using different methods. The strengths of the $K{\beta }_{2,5}$ and $K{\beta }^{″}$ transition probabilities per titanium-ligand pair were found to decrease exponentially as the average titanium-ligand bond distance increased, which is similar to results obtained for various compounds with vanadium or manganese as the central $3d$ metal atoms.