The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time behavior of the survival probability $S\left(t\right)$ has a dependence on the initial state and may behave as either $S\left(t\right)=1-O\left(t^{3/2}\right)$ or $1-O\left(t^2\right)$. These cases are illustrated by solvable models. The experiment reported by Wilkinson et al. [Nature (London) 387, 575 (1997)] does not distinguish between the above short-time behaviors.

We present a quasiprobability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function provides clear and intuitive graphical representation of a wide variety of states, including Fock states, spin-coherent states, squeezed states, superpositions, and statistical mixtures. The distribution is capable of simultaneously representing several angular momentum shells.

We consider an exact analytical solution to the time-dependent Schrödinger equation with cutoff initial conditions (quantum shutter setup) to show that in such a case the delay time in the dynamics of resonant tunneling near resonance arises from an interference effect of the quantum transients of the problem in the asymptotic limit of large distances and long times.

We examine the evaluation of entanglement measures in weakly correlated Gaussian states. It is shown that they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables us to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also with pairs of arbitrary subsystems. As illustration, we consider different types of contiguous and noncontiguous blocks in two-dimensional lattices. Exact asymptotic expressions are provided for both first-neighbor and full-range couplings, which lead in the first case to area laws depending on the orientation and separation of the blocks.

Reliable and well-characterized quantum resources are indispensable ingredients in quantum information processing. Typically, in a realistic characterization of these resources, apparatuses come with intrinsic uncertainties that can manifest themselves in the form of systematic errors. While systematic errors are generally accounted for through careful calibration, the effect of remaining imperfections on the characterization of quantum resources has been largely overlooked in the literature. In this paper, we investigate the effect of systematic errors that arise from imperfect alignment of measurement bases—an error that can conceivably take place due to the limited controllability of measurement devices. We show that characterization of quantum resources using quantum state tomography or entanglement witnesses can be undermined with an amount of such imprecision that is not uncommon in laboratories. Curiously, for quantum state tomography, we find that having entanglement can help to reduce the susceptibility to this kind of error. We also briefly discuss how a given entanglement witness can be modified to incorporate the effect of such errors.

Device-independent quantum key distribution is the task of using uncharacterized quantum devices to establish a shared key between two users. If a protocol is secure, regardless of the device behavior, it can be used to generate a shared key even if the supplier of the devices is malicious. To date, all device-independent quantum key distribution protocols that are known to be secure require separate isolated devices for each entangled pair, which is a significant practical limitation. We introduce a protocol that requires Alice and Bob to have only one device each. Although inefficient and unable to tolerate reasonable levels of noise, our protocol is unconditionally secure against an adversarial supplier limited only by locally enforced signaling constraints.

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.