We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of the complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between either of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger type.

A time-independent many-body Rayleigh-Schrödinger perturbation theory is developed for total energy functionals, which depend simultaneously on a wave function and on the associated electron density. The most prominent example of such functionals is the Kohn-Sham energy functional, but similar situations occur as well in quantum chemical solvent effect theories. In contrast to previous density-functional perturbation theories, formulated in terms of one-electron orbitals, the present approach provides energy and eigenvector corrections for a many-electron wave function that satisfies a nonlinear effective Schrödinger equation. While the perturbed eigenvalues of order $n$ depend on the eigenvector corrections up to the $n\text{th}$ order, perturbational corrections of the total energy functional satisfy Wigner’s $(2n+1)$ rule by virtue of nontrivial cancelations between eigenvalue and double count corrections up to order $n$. As a direct consequence of the nonlinearity of the effective Schrödinger equation, the wave-function corrections of any order are obtained by the solution of a self-consistent equation involving the second functional derivative of the density functional. Explicit total energy corrections are elaborated up to the fourth order. It is shown that the present approach reproduces standard results of the density-functional perturbation theory for static one-electron perturbations. Furthermore, two variants of the long-range Møller-Plesset correlation energy corrections in the range-separated hybrid density-functional framework are derived and discussed.

A set of displaced squeezed number states is proposed as trial wave functions in variational calculations of ro-vibrational energy levels of diatomic molecules. By employing the ladder-operator formalism, we construct such states as well as an algebraic Hamiltonian expressed in terms of normal-ordered boson operators. We also show that this algebraic Hamiltonian can be expanded in terms of pseudoladder operators $\tilde{a}(\lambda ,\kappa )$ and ${\tilde{a}}^{†}(\lambda ,\kappa )$ obtained via a generalized Bogoliubov transformation. In this case, the Hamiltonian matrix is built using the usual Fock basis set and the coherence and squeezing parameters $\lambda$ and $\kappa$ are optimized variationally. The convergence of the variational calculations is largely improved when using the displaced squeezed number states instead of the usual Fock ones. A class of generalized displaced squeezed number states is also considered, and some numerical applications are given.

State selection of molecular oxygen $\left({}^3\Sigma _g^{-}\right)$ by a hexapole magnet and the inversion of population for the ${\mathrm{O}}_2$ spin-rotational states by a two-coil spin flipper are reported. The Stern-Gerlach magnetic deflection spectra of a supersonic ${\mathrm{O}}_2$ beam which is passed through the hexapole magnet show peaks associated with the ${\mathrm{O}}_2$ spin-rotational states with the magnetic quantum number $M_J⩾0$. Peaks corresponding to the states with $M_J⩽0$ appear when the beam is passed through an opposing magnetic field formed in the two-coil spin flipper. The present results indicate that a hexapole magnet can select the spin-rotational states of ${\mathrm{O}}_2$ and the polarity of $M_J$ can be reversed by the diabatic passage through an opposing magnetic field.

We describe an approach for studying molecular photoionization with a hybrid basis that combines the functionality of analytic basis sets to represent electronic coordinates near the nuclei of a molecule with numerically defined grid-based functions. We discuss the evaluation of the various classes of two-electron integrals that occur in a hybrid basis consisting of Gaussian-type orbitals and discrete-variable representation functions. This combined basis is applied to calculate single photoionization cross sections for molecular $\mathrm{Li}_2{}^{+}$, which has a large equilibrium bond distance $(R=5.86a_0)$. The highly nonspherical nature of $\mathrm{Li}_2{}^{+}$ molecules causes higher angular momentum components to contribute significantly to the cross section even at low photoelectron energies, resulting in angular distributions that appear to be $f$-wave dominated near the photoionization threshold. At higher energies, where the de Broglie wavelength of the photoelectron becomes comparable with the bond distance, interference effects appear in the photoionization cross section. These interference phenomena appear at much lower energies than would be expected for diatomic targets with shorter internuclear separations.

We make a detailed study on the dynamics of gain-assisted superluminal optical solitons in a three-state active-Raman-gain medium at room temperature. Using a method of multiple-scales we derive a high-order nonlinear Schrödinger equation with correction terms contributed from differential gain, nonlinear dispersion, delay in nonlinear refractive index, and third-order dispersion of the system. We show that for a long pulse with realistic physical parameters the high-order correction terms are small and can be taken as perturbations. However, for a shorter pulse these higher-order correction terms are significant and hence must be treated on equal footing as the terms in the nonlinear Schrödinger equation. We provide exact soliton solutions of the higher-order nonlinear Schrödinger equation and demonstrate that such solitons have still superluminal propagating velocity and can be generated at very low light intensity.

We present an optical characterization of photonic glasses, composed of randomly arranged, monodisperse dielectric spheres packed at high filling fractions. We provide a detailed optical study of the resonant behavior of diffuse light transport through such systems. By means of independent static and dynamic measurements, we show resonances in the transport mean free path, diffusion constant, and also energy velocity of light. We also show that the main transport parameters can be controlled by varying the sphere diameter.

The phase space is the natural ground to smoothly extrapolate between local and nonlocal correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: Free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.

We determine the feasibility of detecting analog Hawking radiation in a Bose-Einstein condensate in the presence of atom-loss-induced heating. We find that phonons created by three-body losses overshadow those due to analog Hawking radiation. To overcome this problem, three-body losses may have to be suppressed, for example, as proposed by Search et al. [Phys. Rev. Lett. 92, 140401 (2004)]. The reduction of losses to a few percent of their normal rate is typically sufficient to suppress the creation of loss phonons on the time scale of fast analog Hawking phonon detection.

We report on the observation of Bragg diffraction of a spin-polarized ultracold ${}^6\mathrm{Li}$ Fermi gas and demonstrate a Ramsey-type matter-wave interferometer. Suppression of $s$-wave collisions by the Pauli principle allows for unperturbed dynamics of the atoms in the trap for longer than $2\mathrm{s}$. Employing an echo pulse sequence, we observe coherent superpositions of momentum states which do not show any sign of decoherence during the experimentally limited observation time of $100\mu \mathrm{s}$. In contrast, significant decoherence is observed in the presence of a cold cloud of ${}^{87}\mathrm{Rb}$ atoms. The experiment demonstrates the feasibility of high-resolution atomic interferometry with applications for precision measurements in small volumes and near surfaces.

We compute an analog Casimir effect in a one-dimensional spinless Luttinger liquid confined to a segment in the presence of a nearly impenetrable partition dividing the segment into two compartments. The Casimir interaction is found to be a bounded piecewise-continuous oscillatory function whose maxima are points of force discontinuity and correspond to resonant tunneling across the partition. The well-known regularization-based results are reproduced by the lower envelope of this function, which corresponds to an approximation that ignores the rather large oscillations due to particle discreteness. These macroscopic conclusions are tested and confirmed via a rigorous analysis of the Casimir effect in an exactly-solvable model of a one-dimensional nonrelativistic spinless gas of free fermions. Additionally we confirm the result of a recent calculation which employed an effective low-energy theory with a cutoff to find the Casimir interaction between two strong well-separated impurities placed in a Luttinger liquid.

An experimental implementation of an ensemble quantum algorithm is presented in which the thermal state is used as an initial state of the algorithm. More specifically, we use four active qubits to demonstrate the solution of the Deutsch-Jozsa problem using a nuclear magnetic resonance quantum computer. For the implemented algorithm the number of molecules in the NMR sample is irrelevant to the number of qubits available to an NMR quantum computer, and the initial state is chosen to be the state of thermal equilibrium, thereby avoiding the preparation of pseudopure states and the resulting exponential loss of signal as the number of qubits increases. As expected, measured spectra demonstrate a clear distinction between constant and balanced functions.

We prove that rank-three bipartite entangled states are distillable. So there are no bound rank-three bipartite entangled states. By using this fact, we present some families of rank-four states that are distillable. We also analyze the relation between the rank-three state and the Werner state.

In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast a four-dimensional Yang-Baxter equation into its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the degrees of freedom of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into a combination of actions of basic optical elements.

High-precision calculations of the energy levels of the superheavy elements $Z=119$ and $Z={120}^{+}$ are presented. Dominating correlation corrections beyond the relativistic Hartree-Fock method are included to all orders in the Coulomb interaction using the Feynman diagram technique and the correlation potential method. The Breit interaction and quantum electrodynamics radiative corrections are considered. Also, the volume isotope shift is determined. A similar treatment for Cs, Fr, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Ra}}^{+}$ is used to gauge the accuracy of the calculations and to refine the ab initio results.

The direct mechanism of dissociative recombination of $\mathrm{H}{\mathrm{F}}^{+}$ is studied using both time-dependent and time-independent methods, where the dynamics on 30 resonant states is explored. The relevant electronic states are calculated ab initio by combining electron scattering calculations with multireference configuration interaction structure calculations. For collision energies between 0.04 and $10\mathrm{eV}$, we obtain qualitative agreement with experiment. At $1.9\mathrm{eV}$ there is a sharp threshold in both the experimental and theoretical cross sections that can be explained by the opening of new asymptotic limits. The measured cross section below $0.04\mathrm{eV}$ is not reproduced due to the neglect of the electronic couplings between the neutral states. We examine the validity of the local approximation for treating autoionization from the resonant states included in this study.

Synchrotron radiation is used to excite Ar to the intermediate states $3p_{1∕2}^5$ ($3d^{\prime }{[3∕2]}_1$, $5d^{\prime }{[3∕2]}_1$, $5s^{\prime }{[1∕2]}_1$, $7s^{\prime }{[1∕2]}_1$) and $3p_{3∕2}^5$ ($6d{[1∕2]}_1$, $6d{[3∕2]}_1$, $8s{[3∕2]}_1$), then excited by lasers to the autoionizing Rydberg series $3p_{1∕2}^5$ $n{p}^{\prime }$ (${[1∕2]}_{0,1}$, ${[3∕2]}_{1,2}$) and $n{f}^{\prime }{[5∕2]}_2$. For the intermediate states of $5s^{\prime }$, $7s^{\prime }$, and $8s$, the $n{p}^{\prime }$ (${[1∕2]}_0$ and ${[3∕2]}_2$) series are observed with high intensity but not the $n{p}^{\prime }$ (${[1∕2]}_1$ and ${[3∕2]}_1$) series when the polarization vectors of two light beams are in parallel; but when they are in orthogonal, the $n{p}^{\prime }{[1∕2]}_0$ series disappears, the $n{p}^{\prime }{[3∕2]}_2$ intensity remains, and the $n{p}^{\prime }$ (${[1∕2]}_1$ and ${[3∕2]}_1$) series show up strongly. The intensity distribution of the $n{p}^{\prime }$ series strongly depends on the intermediate state. The spectra of the $n{p}^{\prime }$ series are assigned according to their intensity variation with the polarization vectors. The quantum defects determined for the series $n{p}^{\prime }{[1∕2]}_0(n=11–57)$, $n{p}^{\prime }{[3∕2]}_2(n=11–65)$, $n{p}^{\prime }{[3∕2]}_1(n=11–31)$, and $n{f}^{\prime }{[5∕2]}_2(n=9–74)$ are $1.611\pm 0.011$, $1.683\pm 0.013$, $1.688\pm 0.010$, and $0.016\pm 0.005$, respectively. Our values are in excellent agreement with theoretical prediction. The spectral line shapes of autoionizing Rydberg states are analyzed with a Beutler-Fano profile. Reduced autoionization linewidths for the $n{p}^{\prime }{[1∕2]}_0(n=11–16)$ series vary in the range $2549–4145{\mathrm{cm}}^{-1}$, and the $n{f}^{\prime }{[5∕2]}_2(n=9–11)$ series in $186–247{\mathrm{cm}}^{-1}$ in reasonable agreement with theoretical prediction.

We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali-metal atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the application of techniques for robust control developed for NMR spectroscopy. We establish the conditions under which the system is controllable in the sense that one can generate an arbitrary unitary map on the system. We apply this to the case of ${}^{133}\mathrm{Cs}$ with its $d=16$ dimensional Hilbert space of magnetic sublevels in the $6S_{1∕2}$ state, and design control wave forms that generate an arbitrary target state from an initial fiducial state. We develop a generalized Wigner function representation for this space consisting of the direct sum of two irreducible representations of SU(2), allowing us to visualize these states. The performance of different control scenarios is evaluated based on the ability to generate a high-fidelity operation in an allotted time with the available resources. We find good operating points commensurate with modest laboratory requirements.

Quantum-state conversion among different information-carrying media is essential in a quantum network. It is found that the many schemes of quantum-state conversion can be unified under one simple process—that is, the parametric process of three-wave mixing. These schemes include quantum-state storage in atomic media, where a photonic state is converted to an atomic Raman state and vice versa, the frequency up- and down-conversion in photonic states, and photonic-state conversion to Brillouin phononic states and vice versa. The efficiency of conversion can in principle reach 100%, and the conversion process is noiseless. When the same idea is applied to a four-wave mixing process, unit conversion efficiency between a two-photon state and a single-photon state can be achieved. When applied to a two-photon entangled state in parametric down-conversion, entangled states of multiple photons can be generated.

The multiphoton wave function after Kerr interaction is obtained analytically for an arbitrary photon number. The wave function is composed of two fundamental functions: the input mode function and the linear response function. The nonlinear effects appearing in this wave function are evaluated quantitatively, revealing the limitations of nonlinear quantum optics theories based on single-mode approximations.