We present a protocol to simulate the quantum correlations of an arbitrary bipartite state, when the parties perform a measurement according to two traceless binary observables. We show that ${\log }_2\left(d\right)$ bits of classical communication is enough on average, where $d$ is the dimension of both systems. To obtain this result, we use the sampling approach for simulating the quantum correlations.

We present a simple scheme to realize a highly controlled and selective atom-field interaction in cavity quantum electrodynamics system. It is shown that, based on such a selective interaction, nontrivial Dicke states of $N$ trapped neutral atoms can be produced step by step in an optical cavity with a very high fidelity in the presence of the cavity decay. The scheme does not need a single-photon source and its injection into an optical cavity, and the atomic spontaneous emission is strongly suppressed due to a large atom-field detuning.

Although good progress has been made in the calculation of correlation energies from total energy expressions which are implicit functionals of the one-particle reduced density matrix, and explicit functionals of the natural orbitals (NOs) and their occupation numbers, a formulation of the calculation of excitation energies in this so-called density-matrix-functional theory (DMFT) is still lacking. In this paper we propose a time-dependent density-matrix-functional theory (TDDMFT). It is based on the equation of motion (EOM) for the 1-matrix ${\mathbf{P}}_{\left(s\right)}\left(t\right)$ in the representation of the stationary NOs. In the final form of the EOM, the rate of change of the ${\mathbf{P}}_{\left(s\right)}\left(t\right)$, $\partial {\mathbf{P}}_{\left(s\right)}\left(t\right)∕\partial t$, is determined by the commutator of the generalized time-dependent Fock matrix ${\mathbf{F}}_{\left(s\right)}\left(t\right)$ with ${\mathbf{P}}_{\left(s\right)}\left(t\right)$ plus an additional term ${\mathbf{D}}_{\left(s\right)}\left(t\right)$. The matrix ${\mathbf{F}}_{\left(s\right)}\left(t\right)$ determines the evolution of the NOs in the time-dependent one-electron Schrödinger equations, while ${\mathbf{D}}_{\left(s\right)}\left(t\right)$ determines the time evolution of the NO occupations. With the neglect of the electron Coulomb correlation, the time-dependent one-electron equations for the NOs reduce to those for the Hartree-Fock (HF) orbitals of time-dependent HF (TDHF) theory. The coupled-perturbed equations of TDDMF response theory (TDDMFRT) are derived for the linear response of the 1-matrix $\delta {\mathbf{P}}_{\left(s\right)}\left(t\right)$ to a time-dependent perturbation $\delta v_{\mathrm{ext}}\left(t\right)$ of the external potential. The frequency-dependent changes $\delta P_{\left(s\right),ij}\left(\omega \right)$ and $\delta P_{\left(s\right),kl}\left(\omega \right)$ are coupled through the coupling matrix $K_{ijkl}\left(\omega \right)$, which is produced with the derivatives of ${\mathbf{F}}_{\left(s\right)}\left(t\right)$ and ${\mathbf{D}}_{\left(s\right)}\left(t\right)$ with respect to $P_{kl}\left(t^{\prime }\right)$. Based on the response equations, TDDMFRT eigenvalue equations are derived for the electron excitations ${\omega }_q$.

The relative size of the elastic cross sections between $\mathrm{NH}$ molecules colliding with Cs and Rb atoms on the lowest potential energy surfaces of spin-stretched quartet symmetry are computed using the full quantum treatment and taking the target molecule to be in its ground rotational state. Results are compared between the two systems under similar dynamics and the Rb atom is found to yield larger cross sections at ultralow energies. The process is seen to be dominated by dispersion interaction and an analysis of the effects on the cross sections induced by changes on the $C_6$ coefficients is carried out in detail for both systems.

We construct soliton solutions for a self-attractive Bose-Einstein condensate trapped in a rotating optical lattice. The rotation pivot is set at a local maximum of the lattice potential. We demonstrate that fully localized stable solitons, containing $N\sim \mathrm{10,000}$ atoms, may be supported by the lattice, rotating along with it, if the angular velocity $\omega$ is taken below a critical value ${\omega }_c$ (which is $\lesssim 10\mathrm{kHz}$). A monotonously increasing dependence of ${\omega }_c$ on $N$ is found. In the regime of rapid rotation, the lattice potential is nearly tantamount to the axisymmetric Bessel potential, with a maximum at the center. The latter potential supports fundamental ring-shaped solitons, and also dipole states, which have a bipolar form of two adjacent ring solitons with opposite signs. Stability regions are found for both species (which is the first example of stable azimuthally uniform solitons in a self-focusing model with a radial potential). Unstable solitons of these types evolve into strongly localized nonrotating states. At smaller $\omega$, they start to drift slowly, following the rotating lattice. The second critical value, $\omega ={\omega }_c^{\left(2\right)}$, is found, below which the drifting solitons are destroyed. The rotating lattice supports no stable states in the interval of ${\omega }_c<\omega <{\omega }_c^{\left(2\right)}$.

A millimeter-scale Ioffe-Pritchard trap is used to achieve quantum degeneracy in ${}^7\mathrm{Li}$. The trap employs freestanding copper coils integrated onto a direct-bond copper surface-electrode structure. The trap achieves a radial magnetic gradient of $420\mathrm{G}∕\mathrm{cm}$, an axial oscillation frequency of $50\mathrm{Hz}$, and a trap depth of $66\mathrm{G}$ with a $100\mathrm{A}$ drive current and $7\mathrm{W}$ total power dissipation.

We explore the physics of three-dimensional shell-shaped condensates, relevant to cold atoms in “bubble traps.” We study the ground state of the condensate wave function, spherically symmetric collective modes, and expansion properties of such a shell using a combination of analytical and numerical techniques. We find two breathing-type modes with frequencies that are distinct from that of the filled spherical condensate. Upon trap release and subsequent expansion, we find that the system displays self-interference fringes. We estimate characteristic time scales, degree of mass accumulation, three-body loss, and kinetic energy release during expansion for a typical system of ${}^{87}\mathrm{Rb}$.

We study the quantum phase diagrams of Bose-Fermi mixtures of ultracold atoms confined to one dimension in an optical lattice. For systems with incommensurate densities, various quantum phases, e.g., spin- or charge-density waves, pairing, phase separation, and the Wigner crystal, are found to be dominant in different parameter regimes within a bosonization approach. The structure of the phase diagram leads us to propose that the system is best understood as a Luttinger liquid of polarons (i.e., atoms of one species surrounded by screening clouds of the other species). Special fillings, half filling for fermions, and unit filling for bosons, and the resulting gapped phases are also discussed, as well as the properties of the polarons and the experimental realization of these phases.

We formulate a method for studying the quantum field dynamics of ultracold Bose gases confined within optical lattice potentials, within the lowest Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of Vardi and Anglin [Phys. Rev. Lett. 86, 568 (2001)] to the general case of $M$ lattice sites. The methodology is based on mapping the Bose-Hubbard Hamiltonian to an $\mathrm{SU}\left(M\right)$ pseudospin problem and truncating the resulting hierarchy of dynamical equations for correlation functions, up to pair correlations between $\mathrm{SU}\left(M\right)$ generators. Agreement with few-site exact many-particle calculations is consistently better than the corresponding Hartree-Fock-Bogoliubov approximation. Moreover, our approximation compares favorably with a more elaborate two-particle irreducible effective action formalism, at a fraction of the analytic and numerical effort.

Some nonideal effects as nonunit quantum efficiency, dark counts, dead time, and cavity losses that occur in experiments are incorporated within the continuous photodetection model by using the analytical quantum trajectories approach. We show that in standard photocounting experiments the validity of the model can be verified and the formal expression for the quantum jump superoperator can also be checked.

An optical cavity is designed and implemented that is insensitive to vibration in all directions. The cavity is mounted with its optical axis in the horizontal plane. A minimum response of 0.1 $\left(3.7\right)\mathrm{kHz}∕{\mathrm{ms}}^{-2}$ is achieved for low-frequency vertical (horizontal) vibrations.

What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a ten-local finite-range interaction among qubits on a two-dimensional (2D) lattice having this property. Here we show that pair-interactions among qutrits on a 2D lattice are sufficient, too, and can also implement an ergodic computer where the result can be read out from the time average state after some postselection with high success probability. Two of the three qutrit states are given by the two levels of a spin-$1∕2$ particle located at a specific lattice site, the third state is its absence. Usual hopping terms together with an attractive force among adjacent particles induce a coupled quantum walk where the particle spins are subjected to spatially inhomogeneous interactions implementing holonomic quantum computing. The holonomic method ensures that the implemented circuit does not depend on the time needed for the walk. Even though the implementation of the required type of spin-spin interactions is currently unclear, the model shows that quite simple Hamiltonians are powerful enough to allow for universal quantum computing in a closed physical system.

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.

The many-electron Schrödinger equation allows one to make predictions for the nonrelativistic ionization potentials of both highly charged positive atomic ions and neutral atoms in the limit of large atomic number $Z$. Beginning with theoretical configuration interaction data on both Li- and Be-like positive atomic ions by K.T. Chung et al. [Phys. Rev. A 45, 7766 (1992); Phys. Rev. A 47, 1740 (1993)], their nonrelativistic first ionization potentials $I$ are plotted in the form of $I∕Z^2$ versus $1∕Z$. In these two sequences, it is then clear that ${\lim }_{Z\to \infty }(I∕Z^2)$ remains finite and that this limit is approached essentially linearly. Interpretation is afforded by means of the so-called $1∕Z$ expansion of atomic theory. The question of the behavior of the nonrelativistic ionization potentials for large $Z$ is then addressed for neutral atoms. We perform density functional theory (DFT) calculations using the local density approximation with Dirac exchange and neglecting Coulomb correlation for the heavy actinides as well as for the rare gas and alkali atoms from $Z=10$ up to $Z=291$. Our results suggest that there is a nonzero value for ${\lim }_{Z\to \infty }I$ for both the noble gases and the alkalis, the second one implying that there is a lower bound of about $2.56\mathrm{eV}$ to the ionization potential of any nonrelativistic neutral atom. We also explore an alternative approach via the one-body potential $V\left(r\right)$ of DFT by calculating the eigenenergies of the highest occupied atomic orbital in neutral atoms. Finally, relativistic corrections needed to compare measured ionization potentials to the predictions from the Schrödinger equation are briefly considered.

Generalized oscillator strengths (GOS) for the dipole forbidden quadrupole allowed Lyman-Birge-Hopfield (LBH) valence transition of ${\mathrm{N}}_2$ have been calculated. Complete active space self-consistent-field (CAS) and multireference configuration interaction (MRCI) wave functions of several types have been used and their effects on the computed GOS profiles discussed. Orthogonal and nonorthogonal molecular orbitals have been employed. The latter allows the explicit inclusion of relaxation effects in the excited state leading to a clear spectra interpretation. Hartree-Fock (HF) and CAS wave functions have been compared as a previous step before the MRCI calculations. Differences between the respective GOS profiles were found, with the CAS MRCI GOS curve being slightly closer to experiment than the HF MRCI one. Agreement between the present theoretical CAS MRCI GOS profile employing nonorthogonal orbitals and recent experimental results are very favorable, being the best one among available theoretical calculations in the literature.

We report an exhaustive joint theoretical/experimental collision-induced Raman scattering (CIRS) study of the Raman-forbidden ${\nu }_3$ band of $\mathrm{C}{\mathrm{O}}_2$. Original zeroth and second anisotropic spectral moment formulas for $\mathrm{C}{\mathrm{O}}_2\text{−}\mathrm{Ar}$ are derived, in which complete expressions of Raman amplitudes (derived by the authors with a recently reported universal method [Phys. Rev. A 74, 012723 (2006)]) are input. The method, applicable to any kind of spectroscopy and whatever the number of photons, molecules, or interaction involved, uses the irreducible spherical tensor formalism in conjunction with a Feynman-like diagrammatic technique to describe any long-range induced property mechanism. Experimentally, spectral moments are deduced from careful, absolute-scale, frequency-resolved $\mathrm{C}{\mathrm{O}}_2\text{−}\mathrm{Ar}$ depolarized CIRS measurements of unprecedented accuracy. From comparison between theory and experiment, we provide quantitative evidence of a substantial contribution of a nonlinear dipole polarization mechanism, predicted theoretically in the preceding paper. In this mechanism, both photons are shown to interact with Ar (which then couples to $\mathrm{C}{\mathrm{O}}_2$ via intermolecular interactions), rather than with both colliders that is the case in the standard dipole-induced quadrupole (DIQ) interaction. The effect had thus far escaped notice possibly because of the reduced accuracy of the earlier self-consistent field dipole-quadrupole polarizablity computations along with a lack of CIRS measurements. In light of recent extensive computations by Haskopoulos and Maroulis [Chem. Phys. Lett. 417, 235 (2006)], the improved ab initio data of these properties are found to corroborate our predictions, and confirm that the Raman amplitude owing to the dipole-dipole-quadrupole hyperpolarizability of the atomic perturber strongly and destructively interferes with the (otherwise dominant) DIQ Raman amplitude.

We use a simulation code to study the interaction of swift boron clusters ($\mathrm{B}_n{}^{+}$, $n=2–6$, 14) with amorphous carbon foils. We analyze different aspects of this interaction, such as the evolution of the cluster structure inside the target, the energy and angle distributions at the detector or the stopping power ratio. Our simulation code follows in detail the motion of the cluster fragments through the target and in the vacuum until reaching a detector, taking into account the following interactions: (i) wake force, (ii) Coulomb repulsion among cluster fragments, (iii) stopping force, and (iv) elastic scattering with the target nuclei. Electron capture and loss by each fragment is also included in the code, affecting the above-mentioned interactions. The clusters size grows inside the foil due mainly to the Coulomb explosion but this increase is less pronounced in the plane transversal to the beam direction because of the alignment effect of the wake forces. We obtain an enhancement of the stopping power ratio that increases with the projectile energy and with the number of molecular constituents. Our results agree very well with the available experimental data for the thicker foils $(\gtrsim 10\mu \mathrm{g}∕{\mathrm{cm}}^2)$ and are compatible (within the experimental error bars) for the thinner foils.

We have investigated the nonlinear effects in the stopping power of carbon cluster ions propagating through a thin carbon foil at some velocities lower than the Bohr velocity. We measured the energy loss of slow $\mathrm{C}_n{}^{+}$ $(2⩽n⩽21)$ cluster ions passing through carbon foils of $1.0–10.0\mu \mathrm{g}∕{\mathrm{cm}}^2$ in thickness at energies of $1.5–40\mathrm{keV}$/atom. For all incidents of $\mathrm{C}_n{}^{+}$ $(2⩽n⩽21)$ cluster ions, we observed few but rigid amount of intact cluster ions with 3.3%–19.5% reduced in energy but with no atomic loss after passing through a thin $1.0\mu \mathrm{g}∕{\mathrm{cm}}^2$ carbon foil. The stopping power ratios defined as the stopping power per atom of cluster ions divided by the stopping power of isolated atomic ions at the same velocity were evaluated using a simplified united-atom model as well as an experimental approach. The stopping power ratios of the intact cluster ions in all cluster sizes were much smaller than unity. The authors found the remarkable nonlinear effects in the low-energy region to be contrary to those predicted previously for the stopping power of the cluster ions.

We produce quantitatively accurate data for the energy- and time-dependent formation of the profile of the differential ionization probability of the He $1s^2{}^{1}S$ ground state from the coherent excitation and decay of the doubly excited He $2s2p{}^{1}P^o$ resonance state induced by a pulse of duration of $450\mathrm{a.u.}$ and field strength in the range $F=0.4\times {10}^{-3}\mathrm{a.u.}\text{to}F=0.4\times {10}^{-1}\mathrm{a.u.}$ Two general methods were applied. One is analytic, using Fano’s configuration interaction in the continuum in the framework of first order time-dependent perturbation theory. The other is numerical, using the state-specific expansion approach for the nonperturbative solution of the time-dependent Schrödinger equation. Electronic structures and electron correlation are incorporated via the use of state-specific wave functions for the initial state, the resonance state, and the continuum of scattering states. The results from the two methods are in perfect agreement, with a small discrepancy starting at $F=0.4\times {10}^{-1}\mathrm{a.u.}$ The weak field analytic formulas show explicitly the dependence of the profile formation on the pulse characteristics. In the limit of large times, the system becomes stationary and the computed resonance state profile yields the Fano asymmetry parameter of $q=-2.8$, with energy $E_r=60.20\mathrm{eV}$ and width $\Gamma =0.038\mathrm{eV}$. These values agree with previously published ones obtained from time-independent calculations and from photoabsorption measurements of the type initiated by Madden and Codling in 1963.

We report calculations for excitation and ionization of the hydrogen molecule by using ultrashort vuv laser pulses. The theoretical method is based on the solution of the time-dependent Schrödinger equation in a basis of stationary molecular states that includes all electronic and vibrational degrees of freedom. We show that the use of femtosecond vuv pulses, i.e., of pulses with a duration comparable to that of the molecular vibrational period, can be used to efficiently manipulate the molecular response by constraining the nuclear motion to a desired time interval. Thus it is possible to control the ratio of dissociative to nondissociative ionization and the final $\mathrm{H}_2{}^{+}$ vibrational distribution and, by increasing the laser intensity, to induce stepladder Rabi oscillations that can populate excited electronic states not accessible by direct photon absorption. A precise theoretical description of all these effects can only be achieved by including the vibrational motion during the time evolution.