A method for calculating partial widths of autoionizing states is proposed. It combines either a complex absorbing potential or exterior complex scaling with the Lindblad equation. The corresponding classical rate equations are reproduced, and the trace conservation inherent in the Lindblad equation ensures that the partial widths sum up to the total width of the initial autoionizing state.

The attainable accuracy of the $X{}^2\Sigma (v,N)=(0,0)\to (v_u,0)$ transition frequencies of optically trapped ${}^{174}$Yb${}^6$Li molecules are analyzed $(v_u=1,2,3,4)$ to test the variation in the proton-to-electron mass ratio. We eliminate the Stark shifts induced by the trap and Raman lasers by choosing appropriate frequencies (magic frequencies). For $v_u=1$ and 2, we obtain more than one experimentally useful magic frequency, thereby leading to more choice in the trap laser. For $v_u=3$ and 4, the choice in the trap laser is limited. The systematic frequency uncertainty is given by the trap laser frequency detuning from the magic frequency and the fluctuation of the power ratio of the two Raman lasers and can be lower than 10${}^{-16}$ for all these transition frequencies. To obtain lower statistical uncertainty, measurement with $v_u=4$ is more advantageous than that with $v_u=1-3$.

We present experimental relative intensity distribution and theoretical radiative probabilities for the spin-allowed $E\left(4\right){}^1{\Sigma }^{+}-X{}^1{\Sigma }^{+}$ and spin-forbidden $E\left(4\right){}^1{\Sigma }^{+}-a{}^3{\Sigma }^{+}$ rovibronic transitions studied in the KCs molecule. The absorbtion and emission Einstein coefficients were predicted in a wide range of vibrational $v$ and rotational $J$ quantum numbers for both singlet-singlet $E-X$ and singlet-triplet $E-a$ rovibronic transitions along with radiative lifetimes of the upper $E$ state and branching ratios of spontaneous emission into the lower-lying electronic states, including both bound-bound and bound-continuum parts of the spectra. The required spin-allowed $E\left(4\right){}^1{\Sigma }^{+}-X;A;C{}^1{\Sigma }^{+};B{}^1\Pi$ transition dipole moments were obtained in the framework of quasirelativistic electronic structure calculations. The regular spin-orbit coupling with the nearest ${}^3\Pi$ states is found to be sufficient to induce the spin-forbidden $E\left(4\right){}^1{\Sigma }^{+}-a;c{}^3{\Sigma }^{+};b{}^3\Pi$ transitions by borrowing probabilities from the relevant $(1-5){}^3\Pi -(a;c){}^3{\Sigma }^{+};b{}^3\Pi$ transitions. Relative intensity distributions in rotationally resolved $E\to X$ and $E\to a$ laser-induced fluorescence (LIF) progressions were determined from Fourier transform spectra. Experimental LIF intensity distributions demonstrated good agreement with their predicted counterparts. The simulations demonstrate that the translationally ultracold KCs molecules could be efficiently produced in their absolute ground state in one stimulated Raman step $X{}^1{\Sigma }^{+};a{}^3{\Sigma }^{+}\left(v^{\prime \prime }\right)\to E\left(4\right){}^1{\Sigma }^{+}(v_E^{\prime }=44,J_E^{\prime }=1)\to X{}^1{\Sigma }^{+}(v_X^{\prime \prime }=0,J_X^{\prime \prime }=0)$ from the weakly bound rovibronic levels $v^{\prime \prime }$ of both singlet $X$ and triplet $a$ states.

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length $l_0$ of the transverse confinement is smaller than the dimer size, $\sim l_0^2/\left|a\right|$, where $a<0$ is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to $a^6$ in the bosonic case and to $a^8$ for the $\uparrow$-$\uparrow \downarrow$ scattering in a two-component fermionic mixture. We show that by tuning $a$ and $l_0$ one can control the “degree of integrability” in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.

Compared to purely atomic collisions, ultracold collisions involving molecules have the potential to support a much larger number of Fano-Feshbach resonances due to the huge amount of ro-vibrational states available. In order to handle such ultracold atom-molecule collisions, we formulate a theory that incorporates the ro-vibrational Fano-Feshbach resonances in a statistical manner while treating the physics of the long-range scattering, which is sensitive to such things as hyperfine states, collision energy, and any applied electromagnetic fields, exactly within multichannel quantum defect theory. Uniting these two techniques, we can assess the influence of highly resonant scattering in the threshold regime, and in particular its dependence on the hyperfine state selected for the collision. This allows us to explore the onset of Ericson fluctuations in the regime of overlapping resonances, which are well known in nuclear physics but completely unexplored in the ultracold domain.

We develop a well-known strong-field approximation in the length gauge for a two-dimensional model atom in a strong circularly polarized laser field. For excited initial states (with the principal quantum number $n=2$) outgoing photoelectrons usually show energy spectra with an envelope having two or three peaks: one always below and one always above the ponderomotive energy $U_P$. In contrast, for the ground state (with $n=1$) there is always a single peak near $U_P$. Our numerical calculations show that the multipeak effect appears for sufficiently high laser intensities $I$ and is more pronounced for higher laser frequencies $\omega$. We believe that the field parameters $\omega$ and $I$, for which the multipeak envelope in the energy spectrum of above-threshold ionization exists, will enable its experimental observation in the near future.

We consider the Bose-Hubbard model with particle losses at one lattice site. For the noninteracting case, we find that half of the bosons of an initially homogeneous particle distribution are not affected by dissipation that only acts on one lattice site in the center of the lattice. A physical interpretation of this result is that the surviving particles interfere destructively when they tunnel to the location of the dissipative defect and therefore never reach it. Furthermore we find for a one-dimensional model that a fraction of the particles can propagate across the dissipative defect even if the rate of tunneling between adjacent lattice sites is much slower than the loss rate at the defect. We analyze the robustness of our findings with respect to small interactions and small deviations from the symmetric setting. A possible experimental realization of our setup is provided by ultracold bosonic atoms in an optical lattice, where an electron beam on a single lattice site ionizes atoms that are then extracted by an electrostatic field.

We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.

We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space, thereby blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.

A perturbation theory for the calculation of optical modes in circular microdisks with a small local boundary deformation of arbitrary shape is introduced. Two examples are studied in detail: a small notch and a localized corrugation at the boundary. In the generic situation where the first moment of the deformation function does not vanish, very good agreement to the full numerical simulations of Maxwell's equations is found in terms of frequencies, decay rates, and light-emission directionality.

Cooling and entanglement in optomechanical systems coupled through radiation pressure and photothermal force are studied. To develop the photothermal model, we derive an expression for deformation constant of the force. By exploiting linearized quantum Langevin equations, we investigate the dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross-correlation effect plays an important role in the dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and then we derive an analytical expression for it at the weak-coupling limit. At the strong-coupling regime, we show that utilizing the photothermal pressure makes the ground-state cooling more approachable. The effect of photothermal force on the optomechanical entanglement is investigated in detail. According to our exact numerical and approximate analytical studies, even though the photothermal force is naturally a dissipative force, it can improve the optomechanical entanglement both quantitatively and qualitatively.

The classical trajectory Monte Carlo (CTMC) method has been used to model fully stripped ions of He, C, Ar, and Kr colliding with aligned elliptic Rydberg hydrogen in various excited initial $n$ states. CTMC cross sections from target eccentricities of −0.99 to 0.99 and reduced ion velocities ranging from 5 to 40 were used to develop an ionization scaling law as a function of reduced velocity $v^{*}$, initial $n$ state, projectile charge $q$, and initial electron eccentricity ε. The nonelliptic part of our scaling law has been compared to other existing ionization models and found to be in very good agreement.

Atomic bosons and fermions in an optical lattice can realize various condensed-matter states that support equilibrium current patterns in the presence of synthetic magnetic fields or non-Abelian gauge fields. As a route to probing such mass currents, we propose a nonequilibrium quantum quench of the Hamiltonian that dynamically converts the current patterns into experimentally measurable real-space density patterns. We illustrate how a specific such “unidirectional” quench of the optical lattice can be used to uncover bulk checkerboard and stripe current orders in lattice Bose superfluids and Fermi gases, as well as chiral edge currents in a quantum Hall state.

We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external vertices, are connected by edges. In the basic star graph, these are the only edges. If we now connect a subset of the external vertices to form a complete subgraph, a quantum walk can be used to find these vertices with a quantum speedup. Thus, under some circumstances, a quantum walk can be used to locate where the connectivity of a network changes. We also look at the case of two stars connected at one of their external vertices. A quantum walk can find the vertex shared by both graphs, again with a quantum speedup. This provides an example of using a quantum walk in order to find where two networks are connected. Finally, we use a quantum walk on a complete bipartite graph to find an extra edge that destroys the bipartite nature of the graph.

We introduce measurement-based quantum repeaters, where small-scale measurement-based quantum processors are used to perform entanglement purification and entanglement swapping in a long-range quantum communication protocol. In the scheme, preprepared entangled states stored at intermediate repeater stations are coupled with incoming photons by simple Bell measurements, without the need of performing additional quantum gates. We show how to construct the required resource states, and how to minimize their size. We analyze the performance of the scheme under noise and imperfections, with focus on small-scale implementations involving entangled states of few qubits. We find measurement-based purification protocols with significantly improved noise thresholds. Furthermore we show that resource states of small size suffice to significantly increase the maximal communication distance. We also discuss possible advantages of our scheme for different setups.

We present a time-dependent density-functional method able to describe the photoelectron spectrum of atoms and molecules when excited by laser pulses. This computationally feasible scheme is based on a geometrical partitioning that efficiently gives access to photoelectron spectroscopy in time-dependent density-functional calculations. By using a geometrical approach, we provide a simple description of momentum-resolved photoemission including multiphoton effects. The approach is validated by comparison with results in the literature and exact calculations. Furthermore, we present numerical photoelectron angular distributions for randomly oriented nitrogen molecules in a short near-infrared intense laser pulse and helium-(I) angular spectra for aligned carbon monoxide and benzene.

We report large-scale $R$-matrix (close-coupling) with pseudostates calculations for electron scattering from Ne atoms. The present calculations were performed in the nonrelativistic $LS$-coupling approximation with a recently developed parallel version of our suite of $B$-spline $R$-matrix codes. The principal goal was to generate converged (with the number of states in the close-coupling expansion) results for angle-integrated elastic, ionization, and total cross sections. The cross sections for excitation, which are also required for the latter, are generated in this nonrelativistic model as the sum for all terms. The close-coupling expansion used in this work includes 679 target states, with the lowest-lying 55 states representing the Ne bound spectrum and the remaining 624 states representing the ionization continuum. Our results are in close agreement with available experimental data for the elastic and total cross sections over the wide range of electron energies between 0.1 and 200 eV. With the pseudostate approach, we also obtain accurate cross sections for ionization from both the ground and the metastable states of neon. Our results confirm the very strong influence of coupling to the target continuum on theoretical predictions for excitation cross sections in Ne at intermediate energies, an effect that was previously reported by Ballance and Griffin [J. Phys. B 37, 2943 (2004)].

We show how the appearance of $d$-wave pairing in fermionic condensates manifests itself in inelastic light scattering. Specifically, we calculate the Bragg scattering intensity from the dynamic structure factor and the spin susceptibility, which can be inferred from spin-flip Raman transitions. This information provides a precise tool with which we can identify nontrivial correlations in the state of the system beyond the information contained in the density profile imaging alone. Due to the lack of Coulomb effects in neutral superfluids, this is also an opportunity to observe the Anderson-Bogoliubov collective mode.