We describe an implementation of a magnetic collider for investigating cold collisions between ultracold atomic clouds in different spin states, and we use this to study scattering involving both even- and odd-order partial waves. Our method relies on the axial asymmetry of a double-well magnetic trap to selectively prepare the spin state in each cloud. We measure the energy dependence of $s$, $p$, and $d$ partial-wave phase shifts in collisions up to $300\mu \mathrm{K}$ between ${}^{87}\mathrm{Rb}$ atoms in the $5S_{1∕2},F=1,m_F=-1$ and $5S_{1∕2},F=2,m_F=1$ states.

We propose a method to generate a single-attosecond soft-x-ray or extreme ultraviolet pulse by use of two infrared (IR) laser pulses of different wavelengths, neither of which alone is sufficiently short for single-pulse generation. Our simulations based on the time-dependent Schrödinger equation show that, when a harmonic pulse train generated by one IR laser field is superposed with the other driving laser and applied to a target atom, only one pulse in the train significantly boosts harmonic generation and acts as an attosecond enhancement gate for isolated pulse generation.

The simplest decomposition of a Toffoli gate acting on 3 qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to 6. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just 3 if one of the three quantum systems has a third state that is accessible during the computation—i.e., is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (e.g., atoms, photonic polarization plus spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.

We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator $G_{\tau }$. For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in $G_{\tau }$. When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one- and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length $\tau$; measurement of this information has critical implications for assessing the scalability of fault-tolerant quantum computation in any physical setup.

Elementary quantum mechanical principles are applied to bipartite or multipartite systems to test the nonseparability of subsystems (or nonadditivity in the system Hamiltonian) through interchanging the ordering of subsystem (local) operators that cause transitions between energy eigenstates, whether applied to pure or mixed states. A tentative measure for quantifying nonseparability is proposed, based on complete sets of subsystem transition operators. This serves as an upper bound for experimental determinations of the intersubsystem coupling. Two- and three-qubit systems are numerically tested to establish criteria for the noninvariance of transition probabilities in them with respect to the sequence of excitations, and it is conjectured that sequence noninvariance can be used as a probe for subsystems’ nonseparability.

We present an investigation of the effects of constant but random shifts of the ground hyperfine qubit states in the setting of quantum computing with ion doped crystals. Complex hyperbolic secant pulses can be used to transfer ions reliably to electronically excited states, and a perturbative approach is used to analyze the effect of ground-state hyperfine shifts. This analysis shows that the errors due to the hyperfine shift are dynamically supressed during gate operation, a fact we attribute to the ac Stark shift. Furthermore we present an implementation of a controlled phase gate which is resilient to the effects of the hyperfine shift. Decoherence and decay effects are included in simulations in order to show that a demonstration of quantum gates is feasible over the relevant range of system parameters.

One of the most fundamental problems in studying general Hamiltonian systems with many degrees of freedom is to extract a low-dimensional subsystem including the essential dynamics. In this paper, a new partial normal form (PNF) method is developed to reduce the number of coupling terms in the Hamiltonian and to simplify the dynamics analyses. The PNF method allows one to decouple many unimportant bath modes as well as the reactive mode from the system by assessing the significance of the coupling terms. The method is applied to the chemical reaction $\mathrm{O}\left({}^{1}D\right)+{\mathrm{N}}_2\mathrm{O}\to \mathrm{NO}+\mathrm{NO}$, which was found to exhibit efficient energy exchange between the two $\mathrm{NO}$ stretching modes despite the short lifetime of the reaction intermediate [S. Kawai et al., J. Chem. Phys. 124, 184315 (2006)]. Through the analysis of the two-dimensional PNF Hamiltonian subsystem, it is found that the motion of the subsystem preserves the “normal mode picture” of the symmetric and antisymmetric $\mathrm{NO}$ stretching modes despite its high energy. Then the vibrational energy, initially localized in the newly formed $\mathrm{NO}$ bond, is transferred to the reactants’ $\mathrm{NO}$ bond through the beating between the symmetric and antisymmetric stretching modes. The preservation of the normal mode picture and the short period of the beating explain the fast energy exchange between the two $\mathrm{NO}$ bonds. This successful application proves that the PNF method can extract the essential small subspace from many-degrees-of-freedom Hamiltonian systems.

We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov–de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov–de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov–de Gennes equations, is a finite-size effect. We find that a bimodal structure emerges in the density profile of the minority-spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.

We investigate Ramsey interferometry for two separated fields oscillating with different frequencies. It is shown that the interplay between average and relative detuning leads to interference effects not present in the standard, single-frequency setup. For a large free-flight time of ground-state atoms before entering the first field region, the Ramsey fringes with respect to the relative detuning become much narrower than the usual ones. The stability of these effects with respect to phase or velocity fluctuations is discussed.

We describe an experiment where the phase and amplitude of the interference pattern of light going through an interferometer was varied by doing operations on quantum-correlated light that did not go through the interferometer. This was accomplished by sending a pair of polarization-entangled photons in separate directions, one to an interferometer and the other one to a phase shifter, in principle in a remote location. The interferometer was set up to put the state of the pair in a superposition of maximally entangled states. The phase shifter inserted a phase between the product-state components that made up each entangled state. Polarizers located before the detectors projected the quantum state of the light. As a result, the phase and amplitude of the interference pattern were varied by changing the settings of the phase shifter and polarizer in the path of the photon in the remote location.

A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.

Photodetachment cross sections and the angular distributions of photoelectrons produced by the single-photon detachment of the transition metal negative ions ${\mathrm{Fe}}^{-}$ and ${\mathrm{Cu}}^{-}$ have been measured at four discrete photon wavelengths ranging from 457.9 to $647.1\mathrm{nm}$ $(2.71–1.92\mathrm{eV})$ using a crossed-beams laser photodetachment electron spectrometry (LPES) apparatus. Photodetachment cross sections were determined by comparing the photoelectron yields from the photodetachment of ${\mathrm{Fe}}^{-}$ to those of ${\mathrm{Cu}}^{-}$ and ${\mathrm{C}}^{-}$, which have known absolute photodetachment cross sections. Using the measured photodetachment cross sections, radiative electron attachment cross sections were calculated using the principle of detailed balance. Angular distributions were determined by measurements of laboratory frame, angle-, and energy-resolved photoelectrons as a function of the angle between the linear laser polarization vector and the momentum vector of the collected photoelectrons. Values of the asymmetry parameter have been determined by nonlinear least-squares fits to these angular distributions. The measured asymmetry parameters are compared to predictions of photodetachment models including Cooper and Zare’s dipole approximation theory [J. Cooper and R. N. Zare, J. Chem. Phys. 48, 942 (1968)], and the angular momentum transfer theory developed by Fano and Dill [Phys. Rev. A 6, 185 (1972)].

In the triple ionization of the Li ground state by single photon absorption the three electrons escape to the continuum mainly through two collision sequences with individual collisions separated by time intervals on the attosecond scale. We investigate the traces of these two collision sequences in the classical probability densities. We show that each collision sequence has characteristic phase space properties which distinguish it from the other. Classical probability densities are the closest analog to quantum mechanical densities allowing our results to be directly compared to quantum mechanical results.

The ionization process in collisions of ${\mathrm{He}}^{2+}$ with ${\mathrm{C}}^{q+}$ $(q=0–5)$ is investigated using a continuum-distorted-wave eikonal-initial-state approximation. Total and single- and double-differential cross sections for $1s$ and $2s$ electrons are calculated for projectile energies from $30\mathrm{keV}∕\mathrm{u}\text{to}10\mathrm{MeV}∕\mathrm{u}$. From the double-differential cross sections at an electron-ejection angle of $\theta =0°$, the variation of ionization mechanisms with $q$ has been studied and their dependences on the projectile energies and the electron subshells are also discussed. It is found that in the whole energy range considered, the absolute values of soft collision (SC) and binary encounter (BE) peaks decrease with increasing $q$. For the lower incident energies, the electron capture to the projectile continuum (ECC) peak, as well as SC and BE peaks, decreases with increasing $q$. For the higher incident energies $(>1\mathrm{MeV}∕\mathrm{u})$, the absolute value of the ECC peak increases with increasing $q$, so that the crossings of cross sections appear for ${\mathrm{C}}^{q+}$ with different $q$. This can be explained by the matching of velocities between the projectile and the initially bound active electron in the target. Finally, by comparing the ionization rate coefficients for $K$-shell electrons of ${\mathrm{C}}^{q+}$ by ion and electron impacts in an environment of inertial controlled fusion (ICF), the possibility to diagnose the ${\mathrm{He}}^{2+}$ distribution in ICF by the characteristic $K\alpha$ spectrum of ${\mathrm{C}}^{q+}$ is investigated.

We studied the two-dimensional electron momentum spectra of Ar by femtosecond intense laser pulses with mean wavelength from $400\mathrm{nm}\text{to}800\mathrm{nm}$, to compare with experimental results of Maharjan et al. [J. Phys. B 39, 1955 (2006)]. At the higher intensities we found that the effects of ground-state depletion and laser-focus volume are very important such that the peak laser field strength is not reached in experiment. The ubiquitous fanlike stripes in the low-energy electron momentum spectra and the evidence of Freeman resonances in the experimental data are well reproduced in the theoretical calculations. We emphasize that depletion of the initial state should be carefully evaluated for ionization of atoms in the tunneling region.

With Girardeau’s Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one-dimensional periodic potential. The analysis of these ground states shows that when the number of bosons $N$ is commensurate with the number of wells $M$ in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when $N$ is not commensurate with $M$, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau’s criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.

In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.

Geometric phase, for a two-level atom in an electromagnetic field interacting with a squeezed-vacuum reservoir, is calculated by establishing connecting density matrices, describing an evolution of a quantum open system, with a nonunit vector ray in a complex projective Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. The results show that the geometric phase for the squeezed-vacuum reservoir has fully different behavior in comparison with one for the normal vacuum reservoir.

We introduce a relativistic version of the quantum encryption protocol by considering two inertial observers who wish to securely transmit quantum information encoded in a free scalar quantum field state forming Minkowski particles. In a nonrelativistic setting a certain amount of shared classical resources is necessary to perfectly encrypt the state. We show that in the case of a uniformly accelerated eavesdropper the communicating parties need to share (asymptotically in the limit of infinite acceleration) just half of the classical resources.