Conditional evolution is crucial for generating non-Gaussian resources for quantum-information tasks in the continuous variable scenario. However, tools are lacking for a convenient representation of heralded processes in terms of quantum maps for continuous variable states, in the same way as Wigner functions are able to give a compact description of the quantum state. Here we propose and study such a representation, based on the introduction of a suitable transfer function to describe the action of a quantum operation on a Wigner function. We also reconstruct the maps of two relevant examples of conditional processes, that is, noiseless amplification and photon addition, by combining experimental data and a detailed physical model. This analysis allows us to fully characterize the effect of experimental imperfections in their implementations.

In a typical quantum circuit, nonlocal quantum gates are applied to nonproximal qubits. If the underlying physical interactions are short-range (e.g., exchange interactions between spins), intermediate swap operations must be introduced, thus increasing the circuit depth. Here we develop a class of “mediated” gates for spin qubits, which act on nonproximal spins via intermediate ancilla qubits. At the end of the operation, the ancillae return to their initial states. We show how these mediated gates can be used (1) to generate arbitrary quantum states and (2) to construct arbitrary quantum gates. We provide some explicit examples of circuits that generate common states [e.g., Bell, Greenberger-Horne-Zeilinger (GHZ), $W$, and cluster states] and gates (e.g., $\sqrt{swap}$, swap, $cnot$, and Toffoli gates). We show that the depths of these circuits are often shorter than those of conventional $swap$-based circuits. We also provide an explicit experimental proposal for implementing a mediated gate in a triple-quantum-dot system.

Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.

Within the hyperspherical framework, the solution of the time-independent Schrödinger equation for a $n$-particle system is divided into two steps: the solution of a Schrödinger-type equation in the hyperangular degrees of freedom and the solution of a set of coupled Schrödinger-type hyperradial equations. The solutions to the former provide effective potentials and coupling matrix elements that enter into the latter set of equations. This paper develops a theoretical framework to determine the effective potentials, as well as the associated coupling matrix elements, for few-body systems with finite angular momentum $L=1$ and negative and positive parity $\Pi$. The hyperangular channel functions are expanded in terms of explicitly correlated Gaussian basis functions, and relatively compact expressions for the matrix elements are derived. The developed formalism is applicable to any $n$; however, for $n\ge 6$, the computational demands are likely beyond present-day computational capabilities. A number of calculations relevant to cold-atom physics are presented, demonstrating that the developed approach provides a computationally efficient means to solving four-body bound and scattering problems with finite angular momentum on powerful desktop computers. Details regarding the implementation are discussed.

Exact analytical expressions of the dipole polarizabilities of the nonrelativistic hydrogen atom in spherical coordinates are derived with the help of the Lagrange-mesh numerical method. This method can provide exact energies and wave functions for well-chosen conditions of calculation. Exact dipole polarizabilities are obtained after an unambiguous rounding up to at least principal quantum numbers around $n=30$. The scalar polarizability of any $nl$ level is given by $n^4[4n^2+14+7l(l+1)]/4$ and its tensor polarizability is given by $-n^4[3n^2-9+11l(l+1)]l/4(2l+3)$, which allows the calculation of the polarizability of any hydrogen state $nlm$.

We estimate rates for the dissociative recombination (DR) of NO${{}_2}^{+}$ $+$ $e^{-}$. Although accurate excited-state potential-energy curves for the excited states of the neutral are not available, we estimate that the 1 ${}^2{\Phi }_g$ and the 1 ${}^2{\Pi }_g$ states of the neutral may intersect the ground-state cation potential-energy surface near its equilibrium geometry. Using fixed nuclei scattering calculations, we estimate the rate for direct DR via these states and find it to be significant. We also perform approximate calculations of DR triggered by the indirect mechanism, which suggest that the indirect DR rate for NO${}_2$ is insignificant compared to the direct rate.

We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of $s$-, $d$-, and $g$-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of $s$-wave resonant scattering.

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients $C_{2k}$ of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density $\rho$ with outer radius $R$ and thickness $t$. The result is $C_{2k}=-c_k(t/R)\sqrt{4\pi \rho }{\left[{\left(2R\right)}^2\right]}^k$. The $c_k$ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation $d$, $-C_6/d^6-C_8/d^8-\cdots$, can be summed analytically, diverging only for $d\le 2R$. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with $R$ fixed by the true static dipole polarizability. Once $t/R$ is fixed, all the higher coefficients are determined by just $C_6$ and $C_8$. Finally, we compare the exact $C_{2k}$ to those from a pair interaction model, which works for solid spheres ($t=R$) but not for fullerenes.

We apply time-dependent $R$-matrix theory to investigate harmonic generation from ground-state Ar${}^{+}$ with $M=0$ at a wavelength of 390 nm. Contributions associated with the different $3s^{2}3p^4$ ionization thresholds are assessed, including the interference between these. The dominant contribution originates from the second ionization threshold, $3s^{2}3p^4{}^{1}D$. Changes to the harmonic yields arising from the higher $3s3p^5$ thresholds are also assessed. We further confirm that Ar${}^{+}$ has a higher harmonic yield than He for the same laser pulse, despite having a higher ionization threshold.

Coherent control of harmonic generation was studied theoretically. A specific harmonic order was targeted. An optimal control theory was employed to find the driving field where restrictions were imposed on the frequency band. Additional restrictions were added to suppress undesired outcomes, such as ionization and dissociation. The method was formulated in the frequency domain. An update procedure for the field based on relaxation was employed. The method was tested on several examples demonstrating the generation of high frequencies from a driving field with a restricted frequency band.

We study Rydberg wave packets produced by pairs of time separated femtosecond laser pulses. The time separation ranges from femtosecond to picosecond time scales. The wave packets consist predominantly of $f$ states of principal quantum numbers $n=22$–32 in Li. With a direct analysis of the field ionization spectra the $n$-level-resolved classical orbit times are displayed. By chirping the second excitation pulse we demonstrate controlled amplitude oscillations of $n$-level amplitudes on femtosecond time scales.

A hybrid ion-neutral trap provides an ideal system to study collisional dynamics between ions and neutral atoms. This system provides a general cooling method that can be applied to species that do not have optically accessible transitions and can also potentially cool internal degrees of freedom. The long-range polarization potentials ($V\propto -\alpha /r^4$) between ions and neutrals result in large scattering cross sections at cold temperatures, making the hybrid trap a favorable system for efficient sympathetic cooling of ions by collisions with neutral atoms. We present experimental evidence of sympathetic cooling of trapped Na${}^{+}$ ions, which are closed shell and therefore do not have a laser-induced atomic transition from the ground state, by equal-mass cold Na atoms in a magneto-optical trap.

Photoassociation, assembling molecules from atoms using laser light, is limited by the low density of atom pairs at sufficiently short interatomic separations. Here we show that nonresonant light with intensities of the order of ${10}^{10}$W/cm${}^2$ modifies the thermal cloud of atoms, enhancing the Boltzmann weight of shape resonances and pushing scattering states below the dissociation limit. This leads to an enhancement of photoassociation rates by several orders of magnitude and opens the way to significantly larger numbers of ground-state molecules in a thermal ensemble than achieved so far.

A model for the simulation of ensembles of laser-driven Rydberg-Rydberg interacting multilevel atoms is discussed. Our hybrid approach combines an exact two-body treatment of nearby atom pairs with an effective approximate treatment for spatially separated pairs. We propose an optimized evolution equation based only on the system steady state, and a time-independent Monte Carlo technique is used to efficiently determine this steady state. The hybrid model predicts features in the pair-correlation function arising from multiatom processes which existing models can only partially reproduce. Our interpretation of these features shows that higher-order correlations are relevant already at low densities. Finally, we analyze the performance of our model in the high-density case.

We investigate the ground state of spin-orbit-coupled Bose-Einstein condensates confined in concentrically coupled annular traps within the full parameter space accounts for all the nonlinear two-body collisions and the spin-orbit coupling. We find that depending on the ratio between interaction parameters and the strength of spin-orbit coupling, this coupled system presents various ground-state phases. Moreover, phase transition between radial phase separation and azimuthal phase separation can be induced by varying the strength of spin-orbit coupling when the system is first in radial phase separation, while phase transition between phase coexistence and azimuthal phase separation can also be realized through spin-orbit coupling when the system is first in phase coexistence. Finally, the spin texture is studied and the results show that the meron-antimeron pair spontaneously appears as the ground state of this coupled system. We also give an experimental protocol to observe these phenomena in future experiments.

The ground state of Bose-Einstein condensates with attractive particle interactions is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as a solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction, the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and is simulated numerically exact within the mean-field approach on a spacetime lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.

In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of interparticle interaction to interwell tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, that is, which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.

We consider spin transport in a two-component ultracold Fermi gas with attractive interspecies interactions close to the BCS pairing transition. In particular, we consider the spin-transport relaxation rate and the spin-diffusion constant. Upon approaching the transition, the scattering amplitude is enhanced by pairing fluctuations. However, as the system approaches the transition, the spectral weight for excitations close to the Fermi level is decreased by the formation of a pseudogap. To study the consequence of these two competing effects, we determine the spin-transport relaxation rate and the spin-diffusion constant using both a Boltzmann approach and a diagrammatic approach. The former ignores pseudogap physics and finite lifetime effects. In the latter, we incorporate the full pseudogap physics and lifetime effects, but we ignore vertex corrections, so that we effectively calculate single-particle relaxation rates instead of transport relaxation rates. We find that there is qualitative agreement between these two approaches, although the results for the transport coefficients differ quantitatively.

Bosons and fermions, in the presence of frustration or background gauge fields, can form many-body ground states that support equilibrium charge or spin currents. Motivated by the experimental creation of frustration or synthetic gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge-invariant route to probing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge modes in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

Motivated by a recent experiment on the nonequilibrium dynamics of interacting bosons in ladder-shaped optical lattices, we report exact calculations on the sweep dynamics of Bose-Hubbard systems in finite two-leg ladders. The sweep changes the energy bias between the legs linearly over a finite time. As in the experiment, we study the cases of (a) the bosons initially all in the lower-energy leg (ground-state sweep) and (b) the bosons initially all in the higher-energy leg (inverse sweep). The approach to adiabaticity in the inverse sweep is intricate, as the transfer of bosons is nonmonotonic as a function of both sweep time and intraleg tunnel coupling. Our exact study provides explanations for these nonmonotonicities based on features of the full spectrum, without appealing to concepts (e.g., gapless excitation spectrum) that are more appropriate for the thermodynamic limit. We also demonstrate and study Stückelberg oscillations in the finite-size ladders.