Composite quantum states can be classified by how they behave under local unitary transformations. Each quantum state has a stabilizer subgroup and a corresponding Lie algebra, the structure of which is a local unitary invariant. In this paper, we study the structure of the stabilizer subalgebra for $n$-qubit pure states, and find its maximum dimension to be $n-1$ for nonproduct states of three qubits and higher. The $n$-qubit Greenberger-Horne-Zeilinger state has a stabilizer subalgebra that achieves the maximum possible dimension for pure nonproduct states. The converse, however, is not true: We show examples of pure 4-qubit states that achieve the maximum nonproduct stabilizer dimension, but have stabilizer subalgebra structures different from that of the $n$-qubit GHZ state.

The energy dependencies of the intensities and angular distribution parameters $\beta$ of the resonant Auger final states $4p^4\left({}^{1}D\right)np$ $(n=5,6)$ of Kr were determined experimentally in the excitation-energy region of the overlapping $3d_{3∕2}^{-1}5p$ and $3d_{5∕2}^{-1}6p$ resonances. The experimental results were compared with the outcome of multiconfiguration Dirac-Fock calculations. Combining experimental and calculated results allowed us to study interference effects between the direct and several resonant channels that populate the $4p^4\left({}^{1}D\right)np$ states. The inclusion of the direct channel was crucial in order to reproduce the observed energy behavior of the angular distribution parameters. It was also important to take into account experimentally observed shake transitions.

The formation of heteronuclear molecules in their electronic ground states from a mixture of two ultracold atomic species via a one-photon stimulated emission process is investigated. The presence of an additional external homogeneous and static electric field is shown to severely influence the induced emission process. Using the LiCs molecule as a prototype, we study the corresponding cross section and its dependence on the continuum energy, final rovibrational state, and static electric field strength. The possibility of controlling the single-photon association process via an additional static electric field is demonstrated.

We present an ab initio calculation of small numbers of trapped, strongly interacting fermions using the Green’s function Monte Carlo method. The ground-state energy, density profile, and pairing gap are calculated for particle numbers $N=2–22$ using the parameter-free “unitary” interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression $a_{\mathit{TF}}{E}_{\mathit{TF}}+\Delta \mathrm{mod}(N,2)$ where $E_{\mathit{TF}}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\Delta$ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\Delta =0.7\pm 0.2\omega$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.

We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity.

We present a model of an $N$-qubit channel where consecutive qubits experience correlated random rotations. Our model is an extension to the standard decoherence-free subsystems approach which assumes that all qubits experience the same disturbance. The variation of rotations acting on consecutive qubits is modeled as diffusion on the SU(2) group. The model may be applied to spins traveling in a varying magnetic field or to photons passing through a fiber whose birefringence fluctuates over the time separation between photons. We derive an explicit formula describing the action of the channel on an arbitrary $N$-qubit state. For $N=3$ we investigate the effects of diffusion on both the classical and quantum capacities of the channel. We observe that nonorthogonal states are necessary to achieve optimal classical capacity. Furthermore, we find the threshold for the diffusion parameter above which coherent information of the channel vanishes.

The emission characteristics of a vertical-cavity surface-emitting laser (VCSEL) coupled to an external cavity with a diffraction grating as a frequency-selective element are theoretically analyzed. We introduce envelope functions for the set of external-cavity modes based on the loci of modes with extremal gain or frequency in the proper parameter space. Replacing the set of discrete stationary solutions by these envelope functions, simple analytical expressions are derived for the existence of bistability between a lasing state strongly affected by the feedback and a state close to the solitary laser emission (in particular the nonlasing state) and for the frequency of the VCSEL in the grating-controlled regime. It is shown how the initial jump of the laser intensity during abrupt turn-on can be maximized. By a control of the feedback change, the width of the hysteresis loop can be increased significantly. The scheme under consideration can be useful in all-optical photonic switching applications.

We calculate level densities and pairing gaps for an ultracold dilute gas of fermionic atoms in harmonic traps under the influence of mean field and anharmonic quartic trap potentials. Supershell nodes, which were found in Hartree-Fock calculations, are calculated analytically within periodic orbit theory as well as from WKB calculations. For attractive interactions, the underlying level densities are crucial for pairing and supershell structures in gaps are predicted.

The functional renormalization group is used for the BCS-BEC crossover in gases of ultracold fermionic atoms. In a simple truncation, we see how universality and an effective theory with composite bosonic diatom states emerge. We obtain a unified picture of the whole phase diagram. The flow reflects different effective physics at different scales. In the BEC limit as well as near the critical temperature, it describes an interacting bosonic theory.

An investigation of charge transfer in collisions of ground-state ${\text{Cl}}^{7+}$ with H has been conducted based on a fully quantum-mechanical molecular-orbital close-coupling (QMOCC) approach. The charge-transfer process ${\text{Cl}}^{7+}\left({}^{1}S\right)+\text{H}\to {\text{Cl}}^{6+}\left(2p^{6}n\ell {}^{2}S,{{}^{2}P}^o,{}^{2}D,{{}^{2}F}^o,{}^{2}G\right)+{\text{H}}^{+}$ with $n=5$ and 6 is taken into account for collision energies between ${10}^{-4}\text{eV}∕\text{u}$ and 1 keV/u. The relevant adiabatic potentials and nonadiabatic coupling matrix elements for the ${\text{ClH}}^{7+}$ system are evaluated with the configuration-interaction method. The investigation shows that electron capture into the $5d$, $5f$, $5g$, and $6p$ states dominates for collision energies less than $\sim 1\text{eV}∕\text{u}$, while above 100 eV/u the $5s$, $5p$, $5d$, and $6p$ are the primary capture channels. Comparison with experimental data for collisions of ${\text{Cl}}^{7+}\left({}^{1}S\right)$ with D reveals a discrepancy over the full range of measured energies (5–430 eV/u), while no significant isotope effect is found for QMOCC calculations with deuterium. Furthermore, comparison with a previous calculation of the one-electron ${\text{N}}^{7+}+\text{H}$ system, as well as measurements of the multielectron ${\text{Al}}^{7+}+\text{H}$ and ${\text{Fe}}^{7+}+\text{H}$ systems, suggests that the electronic structure of the core has a non-negligible effect on the charge-transfer process. A one-electron model for relative $\ell$ distributions is found to agree with the QMOCC results for $n=5$ between 100 and 1000 eV/u, but fails at lower collision energies. Finally, state-selective and total rate coefficients are given for temperatures between 10 and 200 000 K.

Using a semiclassical rescattering model, we investigate the nonsequential double ionization (NSDI) process of diatomic molecules aligned parallel and perpendicular to the intense linearly polarized field. It is shown that a simple hydrogen-molecule-like model can simulate a nitrogen molecule effectively by giving the alignment dependence of the ratio of double to single ionization and the momentum distribution qualitatively consistent with the experimental result of ${\mathrm{N}}_2$. However, the alignment dependence of the momentum correlation of two ejected electrons does not agree with the experimental result, which indicates that the quantum effect needs to be included in the rescattering and the field-ionization process to explain the experimental observation.

We discuss the existence of combined dark and antidark soliton forms or combined solitons in the generalized coupled mode equations of a nonlinear optical Bragg grating. These solitons are not allowed in the conventional coupled mode equations with uniform nonlinearity and exist outside the linear grating band gap. Their related Hamiltonian phase portrait was briefly reported by de Sterke et al. [Phys. Rev. E 54, 1969 (1996)]. The explicit expressions for the corresponding solitons are presented, as well as their bifurcation process. We demonstrate the unstable propagation of perturbed combined solitons with zero velocity by means of direct numerical integration.

Quantization of a random-walk model is performed by giving a qudit (a multicomponent wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the qudit of the walker is mixed according to the quantum coin at each time step, when the walker hops to other sites. As special cases of the quantum walks driven by high-dimensional quantum coins generally studied by Brun, Carteret, and Ambainis, we study the models obtained by choosing rotation as the unitary transformation, whose matrix representations determine quantum coins. We show that Wigner’s $(2j+1)$-dimensional unitary representations of rotations with half-integers $j$’s are useful to analyze the probability laws of quantum walks. For any value of half-integer $j$, convergence of all moments of walker’s pseudovelocity in the long-time limit is proved. It is generally shown for the present models that, if $(2j+1)$ is even, the probability measure of limit distribution is given by a superposition of $(2j+1)∕2$ terms of scaled Konno’s density functions, and if $(2j+1)$ is odd, it is a superposition of $j$ terms of scaled Konno’s density functions and a Dirac’s delta function at the origin. For the two-, three-, and four-component models, the probability densities of limit distributions are explicitly calculated and their dependence on the parameters of quantum coins and on the initial qudit of walker is completely determined. Comparison with computer simulation results is also shown.

We investigate the properties of quantum entanglement of two-mode squeezed states interacting with symmetric linear baths with general gain and loss parameters. By explicitly solving for $\rho$ from the master equation, we determine analytical expressions of eigenvalues and eigenvectors of ${\rho }^{T_A}$ (the partial transposition of density matrix $\rho$). In Fock space, ${\rho }^{T_A}$ is shown to maintain a block diagonal structure as the system evolves. In addition, we discover that the decoherence induced by the baths would break the degeneracy of ${\rho }^{T_A}$, and leads to a set of eigenvectors for the construction of entanglement witness operators. Such eigenvectors are shown to be time independent, which is a signature of robust entanglement of two-mode squeezed states in the presence of noise.

We show that the entanglement witnesses based on local orthogonal observables, which were introduced by Yu and Liu [Phys. Rev. Lett. 95, 150504 (2005)] and Gühne et al. [Phys. Rev. A 74, 010301(R) (2006)] in linear and nonlinear forms, respectively, can be optimized. As applications, we use our method to calculate the optimal nonlinear witnesses of pure bipartite states and to show a lower bound on the $I$ concurrence of bipartite higher-dimensional systems.

We propose a quantum computation architecture of double-dot molecules, where the qubit is encoded in the molecule two-electron spin states. By arranging the two dots inside each molecule perpendicular to the qubit scaling line, the interactions between neighboring qubits are largely simplified and the scaling to the multiqubit system becomes straightforward. As an Ising-model effective interaction can be expediently switched on and off between any two neighboring molecules by adjusting the potential offset between the two dots, universal two-qubit gates can be implemented without requiring time-dependent control of the tunnel coupling between the dots. A Bell-state measurement scheme for qubit encoded in double-dot singlet and triplet states is also proposed for quantum molecules arranged in this way.

We consider a toy model of the interaction of a qubit with an exotic space-time containing a timelike curve. Consistency seems to require that the global evolution of the qubit be nonunitary. Given that quantum mechanics is globally unitary, this then is an example of a quantum gravity information paradox. However, we show that a careful analysis of the problem in the Heisenberg picture reveals an underlying unitarity, thus resolving the paradox.

We study the performance of holonomic quantum gates, driven by lasers, under the effect of a dissipative environment modeled as a thermal bath of oscillators. We show how to enhance the performance of the gates by a suitable choice of the loop in the manifold of the controllable parameters of the laser. For a simplified, albeit realistic model, we find the surprising result that for a long time evolution the performance of the gate (properly estimated in terms of average fidelity) increases. On the basis of this result, we compare holonomic gates with the so-called stimulated raman adiabatic passage (STIRAP) gates.

Solution of many problems of gas kinetics, transport phenomena, and spectroscopy can be significantly simplified using the linearized Boltzmann equation within so called one-dimensional approximation, in which the collision kernel is averaged over the transverse velocities. The error introduced by this approximation is usually considered to be small, however, no quantitative analysis of its value has been done so far. We study the accuracy of the one-dimensional approximation in a particular problem of calculating spectral line shapes in gases. The inaccuracy is shown to be small in the wings of line, in the cases of light buffer molecules or low collision frequency. For arbitrary parameters the error is calculated numerically within the rigid-sphere model. These results outline the area of applicability of computationally economic one-dimensional approach.

We present a $B$-spline-based complex-rotation (BSCR) method with spin-dependent interaction for the study of atomic photoionization leading to multiple ionization channels dominated by doubly excited resonances for two-electron and divalent atoms. The degree of mixing between different spin states and between the bound and continuum components of the state function of the resonance state can be easily identified in the BSCR method. Its application to Mg photoionization gives good agreement with observed singlet-triplet mixed Mg spectra.