Excitation energies of the $ns$, $n{p}_j$, $n{d}_j$, $n{f}_j$, and $n{g}_j$ states with $n⩽7$ in neutral potassium are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for levels up to $n=9–12$. Electric-dipole ($4s_{1∕2}\text{−}n{p}_j$, $n=4–26$), electric-quadrupole ($4s_{1∕2}\text{−}n{d}_j$, $n=3–26$), and electric-octupole ($4s_{1∕2}\text{−}n{f}_j$, $n=4–26$) matrix elements are calculated to obtain the ground state $E_1$, $E_2$, and $E_3$ static polarizabilities. Scalar and tensor polarizabilities for the $4p_j$ excited state in $\mathrm{K}\mathrm{I}$ are also calculated. All the above-mentioned matrix elements are determined using the all-order method. We also investigate the hyperfine structure in ${}^{39}\mathrm{K}$. The hyperfine $A$ values are determined for the first low-lying levels up to $n=7$. The quadratic Stark effect on hyperfine structure levels of the ${}^{39}\mathrm{K}$ ground state is investigated. The calculated shift for the $(F=2,M=0)\leftrightarrow (F=1,M=0)$ transition is found to be $-0.0746\mathrm{Hz}∕{(\mathrm{kV}∕\mathrm{cm})}^2$, in agreement with the experimental value $-0.071\pm 0.002\mathrm{Hz}∕{(\mathrm{kV}∕\mathrm{cm})}^2$. These calculations provide a theoretical benchmark for comparison with experiment and theory.

We study experimentally and theoretically the production of characteristic $K\alpha$ x-rays during the interaction of intense infrared laser pulse with large ($N\sim {10}^4–{10}^6$ atoms) argon clusters. We focus on the influence of laser intensity and pulse length on both the total x-ray yields and the charge-state distributions of the emitting cluster argon ions. An experimental optimization of the x-ray yield based on the setup geometry is presented and the role of the effective focal volume is investigated. Our theoretical model is based on a mean-field Monte-Carlo simulation and allows identifying the effective heating of a subensemble of electrons in strong fields as the origin of the observed x-ray emission. Well-controlled experimental conditions allow a quantitative bench marking of absolute x-ray yields as well as charge state distributions of ions having a $K$-shell vacancy. The presence of an optimum pulse duration that maximizes the x-ray yield at constant laser energy is found to be the result of the competition between the single cluster dynamics and the number of clusters participating in the emission.

Phase and amplitude modulation of small frequency ranges within broadband femtosecond pulses reshape these pulses providing transients before, before and after, or after the main femtosecond pulse. The absorbed or phase-modulated frequencies appear as transients. We present experimental observations and calculations showing to what extent these transients can be used to drive population changes in the three-level $5s\text{‐}5p\text{‐}5d$ rubidium system in the perturbative limit. We also show computationally that these transients can assist to create complete inversion with nearly 98% population in the upper $5d$ state of rubidium at realistic intensities.

We simulate the growth of a dual species Bose-Einstein condensate using a Gross-Pitaevskii equation with an additional gain term giving rise to the growth. Such growth occurs during simultaneous evaporative cooling of a mixture of two gases. The ground state of a dual condensate is normally either a miscible mixture, or an immiscible phase with two spatially separated components. In a cigar trap the ground state typically consists of one component in the center, and the other component flanking it. Our simulations show that when the condensates are formed in a cigar trap and the mixture is phase separated, then the final state upon the end of the growth is generally far from the true ground state of the system. Instead it consists of multiple, interleaved bubbles of the two species. Such a pattern was observed recently in an experiment by Wieman’s group at JILA [Papp, Pino, and Wieman, Phys. Rev. Lett. 101, 040402 (2008)], and our simulations are in good qualitative agreement with the experiment. We explain the pattern formation as due to the onset of modulation instability during growth, and study the dependence of the final state pattern on various parameters of the system.

By utilizing the interference between an absorptive resonance and an amplifying resonance, one can achieve an enhanced refractive index without an increase in absorption to the beam. We analyze noise added to the beam due to spontaneous emission while propagating through such an index enhanced medium. We find that, for a medium with a refractive index of $n$ and of length $L$, $\approx (n-1)(2\pi ∕{\lambda }_0)L$ noise photons are added to the beam.

We report on a theoretical analysis of the suitability of the $7s{}^{2}S_{1∕2}\leftrightarrow 6d{}^{2}D_{3∕2}$ transition in singly ionized radium to measure parity nonconservation, in the light of an experiment planned at the KVI of the University of Groningen. Relativistic coupled-cluster theory has been employed to perform an ab initio calculation of the parity-nonconserving electric dipole amplitude of this transition, including single, double, and leading triple excitations. We discuss the prospects for a sub-1% precision test of the electroweak theory of particle physics.

We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high-dimensional systems. The generalization to aribitrary prime-dimensional systems is discussed.

Entanglement plays a fundamental role in the brachistochrone evolution of composite quantum systems. In the case of composite systems with distinguishable subsystems quantum brachistochrone evolutions cannot be implemented without entanglement, excepting trivial cases in which only one of the subsystems evolves. Here we explore the connection between entanglement and time-optimal quantum evolution for systems of two identical particles, elucidating its dependence on the type of statistics obeyed by the particles.

Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group $S_N$. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that antisymmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group $B_N$ must also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.

The dipole polarizability tensor components of the tetravalent actinide ions ${\mathrm{Th}}^{4+}$, ${\mathrm{Pa}}^{4+}$, and ${\mathrm{U}}^{4+}$ are computed using the numerical finite-field technique. Four-component correlated calculations have been performed to serve as a reference for establishing the accuracy of two- and one-component relativistic methods. A good agreement within all methods is achieved provided that extended basis sets are used to reach the complete basis set limit. The four-component correlated polarizabilities represent a database of reference values of the dipole polarizability for the early tetravalent actinide ions.

We present the results of calculations determining the cross sections for indirect dissociative recombination of $\mathrm{Li}\mathrm{H}_2{}^{+}+e^{-}$. These calculations employ multichannel quantum defect theory and Fano’s rovibrational frame transformation technique to obtain the indirect dissociative recombination cross section in the manner described by Hamilton and Greene [Phys. Rev. Lett. 89, 263003 (2002)]. We use ab initio electron-molecule scattering codes to calculate quantum defects. In contrast to $\mathrm{H}_3{}^{+}$, the $\mathrm{Li}\mathrm{H}_2{}^{+}$ molecule exhibits considerable mixing between rotation and vibration; however, by incorporating an exact treatment of the rovibrational dynamics of the $\mathrm{Li}\mathrm{H}_2{}^{+}$, we show that this mixing has only a small effect on the observed DR rate. We calculate a large DR rate for this cation, $4.0\times {10}^{-7}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at $1\mathrm{meV}$ incident electron energy.

In this paper we report ionization cross sections of positive ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, neutral He, Ne, Ar, Kr, Xe, and negative ${\mathrm{F}}^{-}$, ${\mathrm{Cl}}^{-}$, ${\mathrm{Br}}^{-}$, ${\mathrm{I}}^{-}$ ions by impact of protons with energies ranging from $25\text{to}1000\mathrm{keV}$. Cross sections of singly charged ions are relevant to the calculation of electron yields in collisions with insulator surfaces. Calculations were performed within the continuum distorted wave–eikonal initial state method using an angular expansion in spherical harmonics and a numerical evaluation of the radial functions corresponding to both the initial (bound) and the final (continuum) states. The first Born approximation was used on an equal footing. We find that this first-order theory holds for proton energies larger than $300\mathrm{keV}$. For comparison, we also calculate the shellwise local plasma approximation. Our results show that it gives a good account of the cross sections for neutral targets.

We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.

Quasibound states in an open system do not in general form an orthogonal and complete basis. It is, however, expected that the nonorthogonality is weak in the case of well-confined states, except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the nonorthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly nonorthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.

In this paper, we experimentally demonstrate that the photon pairs generated via spontaneous four-wave mixing in a hot atomic ensemble are in entangled orbital angular momentum (OAM) states. The density matrix of the OAM states of the photon pair is reconstructed, from which the fidelity to the maximal entangled state and the concurrence are estimated to be about 0.89 and 0.81, respectively. The experimental result also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.

Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.

It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure states. We show that, by contrast, there are two-qubit mixed states for which the REE for some range of a fixed negativity is higher than that for pure states. Moreover, we demonstrate that a mixture of a pure entangled state and pure separable state orthogonal to it is likely to give the maximal REE. By noting that the negativity is a measure of entanglement cost under operations preserving positivity of partial transpose, our results provide an explicit example of operations such that, even though the entanglement cost for an exact preparation is the same, the entanglement of distillation of a mixed state can exceed that of pure states. This means that the entanglement manipulation via a pure state can result in a larger entanglement loss than that via a mixed state.

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation $U_C$. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.

A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum or classical information. RAMs and qRAMs with $n$-bit addresses can access $2^n$ memory sites. Any design for a RAM or qRAM then requires $O\left(2^n\right)$ two-bit logic gates. At first sight this requirement might seem to make large scale quantum versions of such devices impractical, due to the difficulty of constructing and operating coherent devices with large numbers of quantum logic gates. Here we analyze two different RAM architectures (the conventional fanout and the “bucket brigade”) and propose some proof-of-principle implementations, which show that, in principle, only $O\left(n\right)$ two-qubit physical interactions need take place during each qRAM call. That is, although a qRAM needs $O\left(2^n\right)$ quantum logic gates, only $O\left(n\right)$ need to be activated during a memory call. The resulting decrease in resources could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.

We present an efficient computational method for calculating the binding energies of the bound states of ultracold alkali-metal dimers in the presence of magnetic fields. The method is based on propagation of coupled differential equations and does not use a basis set for the interatomic distance coordinate. It is much more efficient than the previous method based on a radial basis set and allows many more spin channels to be included. This is particularly important in the vicinity of avoided crossings between bound states. We characterize a number of different avoided crossings in ${\mathrm{Cs}}_2$ and compare our converged calculations with experimental results. Small but significant discrepancies are observed in both crossing strengths and level positions, especially for levels with $l$ symmetry (rotational angular momentum $L=8$). The discrepancies should allow the development of improved potential models in the future.