We propose a quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of a noninteracting Hamiltonian onto a ground state of an interacting Hamiltonian and the phase estimation algorithm to retrieve the ground-state energy. The expectation value of an observable for the ground state is obtained with the help of the Hellmann-Feynman theorem. As an illustration of our method, we consider a displaced harmonic oscillator, a quartic anharmonic oscillator, and a potential scattering model. The results obtained by this method are in good agreement with the known results.

In 1959, Bopp developed a lower bound to atomic and molecular ground-state energies by summing the lowest eigenvalues of the two-particle reduced Hamiltonian, ${}^2\widehat{K}$. His approximation is accurate only for very small systems (fewer than about four electrons), with the results degenerating rapidly for larger problems. In this paper, we extend and improve Bopp’s work by introducing a flexible distribution function, guided by familiar Fermi-Dirac statistics, in order to generate occupation numbers for the energy levels of ${}^2\widehat{K}$. The distribution function and the resulting energy are parametrized by a correlation temperature $T$. For a given system, characteristic temperatures may be identified that yield the true energy or any other benchmark energy of the system. Using a geometric argument and the empirical properties of the energy vs temperature curve, the two-electron statistics are investigated as a predictive tool for a variety of small atoms and molecules.

Deactivation of broad quasi-one-dimensional dibosonic molecules is analyzed. Within the integrable Lieb-Liniger-McGuire (LLMG) model an exact expression does not demonstrate suppression of the deactivation at low collision energies. The solution of Faddeev equations demonstrates that when a Feshbach resonance lifts the symmetry of the LLMG model the deactivation becomes suppressed. This effect shows a way for formation of a stable gas of dibosonic Feshbach molecules.

Ionization of neutral ${\text{D}}_2$ molecules by a short and intense pump laser pulse may create a vibrational wave packet on the lowest $\left(1s{\sigma }_g^{+}\right)$ adiabatic potential curve of the $\text{D}_2{}^{+}$ molecular ion. We investigate the possibility of manipulating the bound motion, dissociation, and vibrational-state composition of $\text{D}_2{}^{+}$ nuclear wave packets with ultrashort, intense, near infrared control laser pulses. We show numerically that a single control pulse with an appropriate time delay can quench the vibrational state distribution of the nuclear wave packet by increasing the contribution of a selected stationary vibrational state of $\text{D}_2{}^{+}$ to more than 50%. We also demonstrate that a second control pulse with a carefully adjusted delay can further squeeze the vibrational-state distribution, thereby suggesting a multipulse control protocol for preparing almost stationary excited nuclear wave functions. The subsequent fragmentation of the molecular ion with a probe pulse provides a tool for assessing the degree at which the nuclear motion in small molecules can be controlled.

We report on the observation of interference of a series of atom lasers. A comblike array of atomic beams is generated by outcoupling atoms from distinct Bose-Einstein condensates confined in the different sites of a mesoscopic optical lattice. The observed interference signal arises from the spatial beating of the overlapped atom laser beams, which is monitored over a range corresponding to $2\mathrm{ms}$ of freefall time. The relative de Broglie frequencies and phases of the atom lasers were measured.

Mixed-type (bright-dark) soliton solutions of the integrable $N$-coupled nonlinear Schrödinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients are obtained by using Hirota’s bilinearization method. Generally, for the mixed $N$-CNLS equations the bright and dark solitons can be split up in $\left(N-1\right)$ ways. By analyzing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N>2$, if the bright solitons appear in at least two components, nontrivial effects, such as onset of intensity redistribution, amplitude-dependent phase shift, and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude-dependent phase shift as that of bright solitons. Thus, in the mixed CNLS system, there is a coexisting shape-changing collision of bright solitons and elastic collision of dark solitons with amplitude-dependent phase shift, thereby influencing each other mutually in an intricate way.

The interaction of a quantized field with three-level atoms in $\Lambda$ configuration inside a two-mode cavity is analyzed in the small-noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency. The effect of the atoms’ base level decoherence in the cavity output field is also studied. It is found that the output field is very sensitive to two-photon detuning.

We propose a potential scheme to generate cluster states with one-step operation based on cavity quantum electrodynamics in a multiatom and microwave cavity system with an additional driven classical field. The proposed quantum operation avoids cavity-field induced decay and may achieve the cluster states with ideal success probability.

In the present work, we have carried out an investigation on the $S$-wave resonances of $e^{+}\text{−}\mathrm{H}$ in plasma environments based on the Debye model for weakly coupled plasmas. We employ the complex-coordinate-rotation method with highly correlated Hylleraas-type wave functions. For resonant states below the respective $\mathrm{H}(n=2s)$ and $\mathrm{Ps}(n=2s)$ thresholds, good agreement has been found with an earlier calculation using the stabilization method. Results for the other five $S$-wave autoionization states up to and below the $\mathrm{H}(n=4s)$ threshold of the $e^{+}\text{−}\mathrm{H}$ system immersed in a Debye plasma are reported here.

We examine the transformation of noise under a quantum-error-correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are optimally adapted to use error syndrome information from the previous levels of the code. We use the Shannon entropy of these channels to estimate the thresholds of correctable noise for QECCs and find considerable improvements under this adaptive concatenation. Similar methods could be used to increase quantum-fault-tolerant thresholds.

A method of laser-assisted field-free dynamic molecular orientation employing a short, moderately intense three-color phase-locked laser pulse is proposed. Numerical simulations show that it provides an exceedingly effective control of orientation in molecular gases even at room temperatures. The underlying mechanism is based on the specific laser-induced orientation-dependent selective excitation of molecules and subsequent self-transformation of the induced geometrical orientation into a dynamical one. It is shown that this mechanism is significantly more powerful than the widely investigated kick mechanism.

We consider the low-energy spectrum of spin-$\frac{1}{2}$ two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one-dimensional ladder systems of various geometries. Analytical results are derived that yield the behavior of the ground states, their energies, and the transition points. The entanglement properties of the ground state of these models are examined and we find that the entanglement depends on the lattice geometry due to frustration effects. To this end, the chirality of a given quantum state is used as a witness of tripartite entanglement. Finally, the two-dimensional model is investigated numerically by means of exact diagonalization and indications are presented that the low energy sector is a chiral spin liquid.

We propose an experiment for the observation of the quantum Zeno effect (QZE) in a bipartite system. The setup involves two microwave cavities and a “tunneling” photon, which is observed by the passage of Rydberg atoms. Our proposal allows for the consideration of two types of measurements, namely, sequential observations of the atomic state and its inclusive measurement. In the present system the two processes are shown to lead to the same result in the ideal case. We consider realistic atom-field interaction times, cavity dissipation, and limited detection efficiency. Analytical expressions for the “tunneling” probability are obtained exhibiting a competition between the environment induced exponential decay and the characteristic $t^2$ (for short times) dependence of the QZE. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.

For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback $\left(E_B\right)$, and we show that this quantity lies between two other well-studied quantities. These two quantities—namely the quantum capacity assisted by two-way classical communication $\left(Q_2\right)$ and the quantum capacity with classical feedback $\left(Q_B\right)$—are widely conjectured to be different: There exists a quantum discrete memoryless channel for which $Q_2>Q_B$. We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly defined quantity of the quantum depolarizing channel, and illustrate with the repetition code and Shor code. We contrast the present notion with entanglement purification protocols by showing that, whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned repetition code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any $E_B$ protocols. We then apply this formula to the $E_B$ protocols that we discuss to obtain lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel.

We present a quantum multimodal treatment describing electromagnetically induced transparency (EIT) as a mechanism for storing continuous-variable quantum information in light fields. Taking into account the atomic noise and decoherences of realistic experiments, we numerically model the propagation, storage, and readout of signals contained in the sideband amplitude and phase quadratures of a light pulse using phase space methods. An analytical treatment of the effects predicted by this model is then presented. Finally, we use quantum information benchmarks to examine the properties of the EIT-based memory and show the parameters needed to operate beyond the quantum limit.

We present a joint theoretical and experimental study of the dynamical instability of a Bose—Einstein condensate at the band edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and undertake a thorough theoretical study of the dynamical instability in systems of different dimensionality. We find spontaneous scattering is an important part of this process, and thus the Gross-Pitaevskii equation is unable to accurately predict the dynamics in this system. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and heating that are observed in the laboratory, and we find good agreement with the experimental results.

We report differential cross-section measurements for electron-impact excitation of the $C{}^1\Sigma ^{+}+c{}^3\Pi$ and $E{}^1\Pi$ electronic states in carbon monoxide. The energy range of this work is $30–200\mathrm{eV}$. Where a comparison is possible, reasonable agreement is found with the earlier $20–50\mathrm{eV}$ results from Middleton et al. [J. Phys. B 26, 1743 (1993)]. A generalized oscillator strength analysis of the present differential cross-section data enables us to determine estimates of the corresponding integral cross sections, which are compared to results from the $\mathrm{BE}f$-scaling approach [Y.-K. Kim, J. Chem. Phys. 126, 064305 (2007)] calculated as a part of this study. Very good agreement between them is in general found. Finally our $100\text{−}\mathrm{eV}$ and $200\text{−}\mathrm{eV}$ generalized oscillator strength data are also employed to determine values of the respective $C{}^1\Sigma ^{+}$ and $E{}^1\Pi$ optical oscillator strengths, with excellent agreement being found between them and the previous dipole $(e,e)$ results from Chan et al. [Chem. Phys. 170, 123 (1993)].

Resonant vibrational excitation (RVE) cross sections have been calculated for the electron-${\text{H}}_2$ molecule collisions in the energy range 11–14 eV involving the ${{}^2\Sigma }_g^{+}$ excited electronic state of the molecular hydrogen ion $\text{H}_2{}^{-}$. This state, whose threshold is located around 14 eV, gives rise to the so-called series $a$ of the observed peaks in electron-impact differential cross-section measurements. The calculations have been performed within the local complex potential approximation by using the available theoretical potential energy and width for the ${{}^2\Sigma }_g^{+}$ resonant state. The cross sections for all $v_i=0\to v_f=1–14$ RVE transitions have been calculated. A satisfactory agreement of calculated cross sections with the available experimental data is obtained.

We calculate the photoionization-with-excitation to photoionization ratios $R_{nl}$ and $R_n={\Sigma }_l{R}_{nl}$ for atomic helium and positive heliumlike ions at intermediate values of the photon energies. The final-state interactions between the electrons are included in the lowest order of their Sommerfeld parameter. This enables us, in contrast to purely numerical calculations, to investigate the roles of various mechanisms contributing beyond the high-energy limit. The system of two bound electrons is described by the functions obtained by the correlation function hyperspherical harmonic method. For the case of heliumlike ions we present the high-energy limits as a power expansion in the inverse charge of the nucleus. We analyze the contribution of excitation of states with nonzero orbital momenta to the ratios $R_n$. In the case of helium our results for $R_n$ are in good agreement with those of experiments and of previous calculations.

Equilibrium geometries and electronic and magnetic properties of small ${\mathrm{Sc}}_n\mathrm{Al}$ $(n=1–8,12)$ clusters have been studied based on the density-functional theory with all-electron spin-polarized generalized gradient approximation. The calculated results show that the Al atom remains on the surface for $n=1–8$, but at the center of the ${\mathrm{Sc}}_{12}\mathrm{Al}$ cluster with a variable icosahedral structure $\left(C_{3v}\right)$. Doping of the Al atom enhances the stability of the scandium clusters. Maximum peaks are observed for clusters of $n=3,6$ on the size dependence of the second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. This study also reveals that the Al atom is seen to induce significant changes in the magnetic property of the host cluster. Especially, the magnetic moment of the ${\mathrm{Sc}}_n\mathrm{Al}$ cluster is quenched for $n=3$, 5, and 7, and the total magnetic moment of the ${\mathrm{Sc}}_{12}\mathrm{Al}$ cluster is only $7{\mu }_B$ (but $19{\mu }_B$ for ${\mathrm{Sc}}_{13}$).