We describe a simple measure of fidelity for mixed state postselecting devices. The measure is most appropriate for postselection where the task performed by the output is only effected by a specific state.

We consider complementarity in a bipartite quantum system of arbitrary dimensions. Single-partite and bipartite properties turn out as mutually exclusive quantities. The single-partite properties can be related to a generalized predictability and visibility which compose two complementary realities for themselves. These properties combined become mutually exclusive to the genuine quantum mechanical bipartite correlations of the system which can be quantified with the generalized $I$ concurrence that defines a proper entanglement measure. Consequently, the complementary relation quantifies entanglement in the bipartite system. The concept of complementarity determines entanglement as a property which mutually excludes any single-partite reality. As an application, we provide a proper definition of distinguishability in an $n$-port interferometer.

Tomographic measurements of Bell states of a single-neutron system in an interferometer were carried out. The spin-path joint measurements exhibit clear evidence of entanglement. Reconstructions of the density matrices of, practically complete, Bell states were accomplished. The fidelities as well as the concurrences of the generated states are determined by 0.79 and 0.75 as well as 0.59 and 0.52, respectively, which are again clear evidence of the spin-path entanglement in a single-neutron system.

In this paper, we investigate how quantum architectures affect the efficiency of the execution of the quantum Fourier transform (QFT) and linear transformations, which are essential parts of the stabilizer and Clifford group circuits. In particular, we show that in most common and realistic physical architectures including the linear nearest neighbor, two-dimensional lattice, and bounded degree graph (containing a chain of length $n$), $n$-qubit QFT and $n$-qubit stabilizer circuits can be parallelized to linear depth using no auxiliary qubits. We construct lower bounds that show the efficiency of our approach.

We show there are at least 28 distinct true stochastic local operations and classical communication (SLOCC) entanglement classes for four qubits by means of SLOCC invariant and semi-invariants and derive the number of degenerate SLOCC classes for $n$ qubits.

The path-integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born-Oppenheimer and nonadiabatic simulations, and inspecting projections of the full three-body dynamics onto the adiabatic Born-Oppenheimer approximation. Coupling of the electron and nuclear quantum dynamics is clearly seen. The nuclear pair correlation function is found to broaden by $0.040a_0$, and the average bond length is larger by $0.056a_0$. Also, a nonadiabatic correction to the binding energy is found. The electronic distribution is affected less than the nuclear one upon inclusion of nonadiabatic effects.

Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest $ns$, $n{p}_{1∕2}$, $n{p}_{3∕2}$ states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find “magic” wavelengths in alkali-metal atoms for which the $ns$ and $n{p}_{1∕2}$ and $n{p}_{3∕2}$ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

A general ab initio and nonperturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or quasi-two-electron targets, is described. The field-free Hamiltonian and the dipole matrices are generated using a flexible $B$-spline $R$-matrix method. This numerical implementation enables us to construct term-dependent, nonorthogonal sets of one-electron orbitals for the bound and continuum electrons. The solution of the TDSE is propagated in time using the Arnoldi-Lanczos method, which does not require the diagonalization of any large matrices. The method is illustrated by an application to the multiphoton excitation and ionization of Ne atoms. Good agreement with $R$-matrix Floquet calculations for the generalized cross sections for two-photon ionization is achieved.

We determine the energetically lowest-lying states in the BEC-BCS crossover regime of $s$-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schrödinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with $N=4$ fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to $N=20$ fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the $s$-wave scattering length $a_s$ for $N=2–20$ fermions and different mass ratios $\kappa$ of the two species. On the Bose-Einstein condensate (BEC) and BCS sides, our energies agree with analytically determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to $\kappa =20$. Our energies for the strongly interacting trapped system in the unitarity regime show essentially no shell structure, and are well described by a simple expression whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter $\xi$ for the trapped system for various $\kappa$ is determined, and comparisons with results for the homogeneous system are presented.

We have studied the temporal compression of laser pulses occurring in a scheme based on the coherent control peculiarities of electromagnetically induced transparency. This work extends earlier model studies, including the effect of Doppler broadening in a real hot medium. For definiteness and consistency of the atomic parameters employed, we have treated a scheme in argon. In this way, we establish a realistic model that enables us to predict quantitatively the performance of laser pulse compression experiments.

We consider a two-level atom interacting with a single mode of the electromagnetic field in a cavity within the Jaynes-Cummings model. Initially, the atom is thermal while the cavity is in a coherent state. The atom interacts with the cavity field for a fixed time. After removing the atom from the cavity and applying a laser pulse the atom will be in a thermal state again. Depending on the interaction time with the cavity field the final temperature can be varied over a large range. We discuss how this method can be used to cool the internal degrees of freedom of atoms and create heat baths suitable for studying thermodynamics at the nanoscale.

We provide a detailed theoretical analysis of multiple-copy purification and distillation protocols for phase-diffused squeezed states of light. The standard iterative distillation protocol is generalized to a collective purification of an arbitrary number of $N$ copies. We also derive a semianalytical expression for the asymptotic limit of the iterative distillation and purification protocol and discuss its properties.

An ab initio, three-dimensional quantum mechanical calculation has been performed for the time evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in the continuum wave function is identified and removed analytically. As a result, the continuum components of the regularized wave function are slowly varying with time. Therefore, one can propagate continuum electrons to asymptotically large times and obtain numerically stable, well-converged ejected electron momentum spectra with very low numerical noise. As a consequence, our approach resolves outstanding controversies concerning structures in electron momentum distributions. The main conclusions are general and are illustrated here for ionization of atomic hydrogen by proton impact. Our results show that in order to obtain the correct long-time free-particle propagation, the essential singularity identified here should be removed from the continuum components of solutions to the time-dependent Schrödinger equation.

We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.

Very accurate quantum mechanical calculations of the first five vibrational states of the ${}^4\mathrm{He}{}^3\mathrm{He}^{+}$ molecular ion are reported. The calculations have been performed explicitly including the coupling of the electronic and nuclear motions [i.e., without assuming the Born-Oppenheimer (BO) approximation]. The nonrelativistic non-BO wave functions were used to calculate the ${\alpha }^2$ relativistic mass velocity, Darwin, and spin-spin interaction corrections. For the lowest vibrational transition, whose experimental energy is established with high precision, the calculated and the experimental results differ by only $0.16{\mathrm{cm}}^{-1}$.

Transition frequencies of Fe II ion are known to be very sensitive to variation of the fine-structure constant $\alpha$. The resonance absorption lines of Fe II from objects at cosmological distances are used in a search for the possible variation of $\alpha$ in the course of cosmic time. In this paper we calculated the dependence of the transition frequencies on ${\alpha }^2$ ($q$ factors) for Fe II ion. We found corrections to these coefficients from valence-valence and core-valence correlations and from the Breit interaction. Both the core-valence correlation and Breit corrections to the $q$ factors appeared to be larger than had been anticipated previously. Nevertheless our calculation confirms that the Fe II absorption lines seen in quasar spectra have large $q$ factors of both signs and thus the ion Fe II alone can be used in the search for the $\alpha$ variation at different cosmological epochs.

The radiative cooling of isolated, negatively charged four-atom aluminum clusters has been measured using an electrostatic ion beam trap. Stored $\mathrm{Al}_4{}^{-}$ ions were irradiated by a short laser pulse at different times after their production in a hot ion source, and delayed electron emission was observed up to hundreds of microseconds after the laser pulse. The decay curves could be well reproduced using an Arrhenius decay law and allowed us to deduce the cluster temperatures at the time of the laser pulse. Using this sensitive molecular thermometer, the cluster temperature could be determined as a function of storage time. The radiation intensity is found to decrease from $40\mathrm{eV}∕\mathrm{s}$ at $T=1400\mathrm{K}\text{to}1\mathrm{eV}∕\mathrm{s}$ at $500\mathrm{K}$ with a temperature dependence as given by $T^b$ with $b=3.5\pm 0.2$—i.e., similar to what would be expected from a blackbody. This cooling behavior requires the presence of either electronic transitions or very collective infrared-active vibrations at transition energies around $\sim 200\mathrm{meV}$.

The very pronounced intensity-dependent enhancements of groups of peaks of high-order above-threshold-ionization spectra of rare-gas atoms are investigated using an improved version of the strong-field approximation, which realistically models the respective atom. Two types of enhancements are found and explained in terms of constructive interference of the contributions of a large number of long quantum orbits. The first type is observed for intensities slightly below channel closings. Its intensity dependence is comparatively smooth and it is generated by comparatively few (of the order of 20) orbits. The second type occurs precisely at channel closings and exhibits an extremely sharp intensity dependence. It requires constructive interference of a very large number of long orbits (several hundreds) and generates cusps in the electron spectrum at integer multiples of the laser-photon energy. An interpretation of these enhancements as a threshold phenomenon is also given. An interplay of different types of the threshold anomalies is observed. The position of both types of enhancements, in the photoelectron-energy—laser-intensity plane, shifts to the next channel closing intensity with the change of the ground-state parity. The enhancements gradually disappear with decreasing laser pulse duration. This confirms the interpretation of enhancements as a consequence of the interference of long strong-laser-field-induced quantum orbits.

In a basic physical model where two-dimensional (2D) matter-wave solitons may be stable, namely, the Gross-Pitaevskii equation with the self-attractive nonlinearity and quasi-one-dimensional (1D) optical-lattice (OL) potential, we test robustness of the solitons against periodic time modulation of the OL strength. Stability diagrams for the 2D solitons are presented in the plane of the modulation depth and frequency. Basic features of the diagrams are explained with the help of the variational approximation for the stationary counterpart of the model. In the Bose-Einstein condensate of ${}^7\text{L}\text{i}$ atoms, the stable 2D solitons may contain the number of atoms in the range of ${10}^4–{10}^5$, relevant values of the OL strength and modulation frequency being, respectively, $\lesssim 5$ recoil energies and $\lesssim 10\text{kHZ}$. Head-on collisions between stable 2D solitons moving in the unconfined direction are studied in detail too, for velocities up to $\sim 5\text{cm}∕\text{s}$. A border between quasi-elastic collisions and merger of the solitons into a single localized state is identified. In some cases, the soliton produced by the merger is stable against collapse, which was not observed before in the static OL potential either.