The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-$\frac{1}{2}$ is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-$\frac{1}{2}$ magnetic dipole in a time-dependent magnetic field.

We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-$Z$ gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-$Z$ gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

Optimized, necessary, and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

We analyze and review the theory of the hydrogen-deuterium isotope shift for the $1S$-$2S$ transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result $\Delta f_{\mathrm{th}}=670\hspace{0.5em}999\hspace{0.5em}566.90(66)(60)\hspace{0.5em}\text{kHz}$ (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result $\Delta f_{\mathrm{expt}}=670\hspace{0.5em}994\hspace{0.5em}334\hspace{0.5em}605(15)\hspace{0.5em}\mathrm{Hz}$, we infer the deuteron-proton charge-radius difference $\langle r^2\rangle {}_d-\langle r^2\rangle {}_p=3.820\hspace{0.5em}07(65)\hspace{0.5em}{\mathrm{fm}}^2$ and the deuteron structure radius $r_{\mathrm{str}}=1.975\hspace{0.5em}07(78)\hspace{0.5em}\mathrm{fm}$.

The electrostatic interaction between an excited atom and a diatomic ground-state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions competes with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 Bohr radii. Numerical results are given for the long-range interaction between Cs and Cs${}_2$, showing that the photoassociation is probably efficient for any Cs${}_2$ rotational energy.

We model a system of ultracold fermionic dipolar molecules on a two-dimensional square lattice. Assuming that the molecules are in their nondegenerate hyperfine ground state, and that the dipole moment is polarized perpendicular to the plane (as in the recent experiments on ${}^{40}\mathrm{K}$-${}^{87}\mathrm{Rb}$ molecules), we approximate these molecules as spinless fermions with long-range repulsive dipolar interactions. We use mean-field theory to obtain the restricted phase diagram as a function of the filling, the strength of interaction, and the temperature. We find a number of ordered density-wave phases in the system, as well as phase separation between these phases. A Monte Carlo analysis shows that the higher-period phases are usually suppressed in the exact solution.

We have studied the parametric evolution of morphology-dependent resonances according to the change of openness in a two-dimensional dielectric microdisk for transverse-electric polarization. We found that the dynamics exhibit avoided resonance crossings between the inner and outer resonances even though the corresponding billiard is integrable. Due to these recondite avoidances, inner and outer resonances can be exchanged and the quality ($Q)$ factor of inner resonances is strongly affected. We analyze the diverse phenomena arising from these dynamics including the avoided crossings.

It is shown that, in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe an optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a counterintuitive enhancement of transparency of the coupler with an increase of the dissipation and represents an optical analog of the quantum Zeno effect. Experimental realization of the phenomenon based on the use of chalcogenide glasses is proposed. The system allows for observation of the crossover between the linear and nonlinear Zeno effects, as well as the effective manipulation of light transmission through the coupler.

We study the classical and quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the down-converted frequency, under the injection of a resonant TEM${}_{10}$ mode. Unlike the usual single-mode DOPO with injected signal, large levels of squeezing are predicted even for relatively large injections. We interpret these results in connection with the spontaneous symmetry breaking predicted for this system in the absence of injection and with the existence of a bifurcation giving rise to the switching on of the (noninjected) TEM${}_{01}$ mode.

We theoretically propose and numerically investigate an active plasmonic device made up of a nonlinear $\epsilon$-near-zero metamaterial slab of thickness smaller than $100$ nm lying on a linear $\epsilon$-near-zero metamaterial substrate. We predict that in free-space coupling configuration the system operating at low intensity displays plasmon mediated hysteresis behavior. The phase difference between the reflected and the incident optical waves turns out to be multivalued and dependent on the history of the excitation process. Such an hysteresis behavior allows the proposed system to be regarded as a memory device whose state is accessible by measuring either the mentioned phase difference or the power, which is multivalued as well, carried by the nonlinear plasmon wave. Since multiple plasmon powers comprise both positive and negative values, the device also operates as a switch of the plasmon power direction at each jump along an hysteresis loop.

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local-density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations—which includes reproducing subtle signatures of the particle density stages—shows that our density functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, in contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.

In this paper, we consider continuous-variable quantum-key-distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error-correction procedures, hence allowing the protocols to outperform previous protocols in terms of achievable range. In their simplest implementation, these protocols are secure for any linear quantum channels (hence against Gaussian attacks). We also show how the use of decoy states makes the protocols secure against arbitrary collective attacks, which implies their unconditional security in the asymptotic limit.

In a solid-state circuit QED system, we extend the previous study of generating and stabilizing a two-qubit Bell state [Phys. Rev. A 82, 032335 (2010)] to a three-qubit GHZ state. In a dispersive regime, we employ the homodyne joint readout for multiple qubits to infer the state for further processing, and in particular we use it to stabilize the state directly by means of an alternate-flip-interrupted Zeno (AFIZ) scheme. Moreover, the state-of-the-art feedback action based on the filtered current enables not only a deterministic generation of the pre-GHZ state in the initial stage, but also a fast recovery from occasional error in the later stabilization process. We show that the proposed scheme can maintain the state with high fidelity if the efficient quantum measurement and rapid single-qubit rotations are available.

We derive a first-principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is eventually made to vanish, introduced in the structure. This is illustrated by calculating the van der Waals pressure in a thin film with dissipative properties embedded between two semi-infinite media.

We investigated transition strengths from ultracold weakly bound ${}^{41}\mathrm{K}$${}^{87}\mathrm{Rb}$ molecules produced via the photoassociation of laser-cooled atoms. An accurate potential energy curve of the excited state $(3){}^1{\Sigma }^{+}$ was constructed by carrying out direct potential fit analysis of rotational spectra obtained via depletion spectroscopy. Vibrational energies and rotational constants extracted from the depletion spectra of $v^{\text{'}}=41$–50 levels were combined with the results of the previous spectroscopic study and they were used for modifying an ab initio potential. An accuracy of 0.14% in vibrational level spacing and 0.3% in rotational constants was sufficient to predict the large observed variation in transition strengths among the vibrational levels. Our results show that transition strengths from weakly bound molecules are a good measure of the accuracy of an excited state potential.

The explosions of noble gas clusters from argon and xenon irradiated by intense 35-fs infrared laser pulses have been studied. The kinetic energy spectra of ions produced in small clusters (<700 atoms) show a two-mode shell structure that is attributed to originating from a radial charge distribution. With a simple classical particle simulation of Coulomb explosions, the energy structure was reproduced using information on the arrangement of charge in the cluster. It was found that, during the explosion, the inner atoms of the clusters were less ionized than the outer atoms.

We consider a reaction design for table-top nuclear fusion between two distinct nuclei, with high-energy nuclei being produced by a Coulomb explosion (CE) of homonuclear nanodroplets of one reagent reacting with a solid target of a second reagent. This scheme was applied for a theoretical-computational study of the table-top aneutronic $p+{}^{11}\mathrm{B}\to 3\alpha +8.7$ MeV reaction generated by a source of high-energy (0.3–6 MeV) protons produced by a CE of hydrogen nanodroplets driven by ultra-intense, femtosecond, near-infrared laser pulses and which penetrate into a solid ${}^{11}\mathrm{B}$ target. The averaged reaction probability and the yield for ${}^{11}\mathrm{B}(p,\alpha )2\alpha$ fusion were calculated from the energy-dependent reaction probability, which was obtained from the ratio of the large fusion cross sections and the stopping power of the protons, and by the proton kinetic energy distribution function, which was obtained from scaled electron and ion dynamics simulations. The fusion yields were determined in the nanodroplet size range and in the laser intensity domain, satisfying the conditions of weak laser intensity attenuation within a single nanodroplet and within an assembly of exploding nanodroplets in the macroscopic plasma filament. The highest values of the fusion yield of 10${}^8$ per laser pulse were attained for the largest nanodroplets with initial radii of 200 nm at the laser peak intensity of 10${}^{19}$ W cm${}^{-2}$. The ${}^{11}\mathrm{B}(p,\alpha )2\alpha$ fusion yields for the exploding hydrogen nanodroplet source-solid ${}^{11}\mathrm{B}$ cylindrical target are higher by three to four orders of magnitude than the yields of ${10}^4-{10}^5$ per laser pulse from a laser-irradiated mixed boron-hydrocarbon solid and from a CE of boron-hydrogen heteronuclear nanodroplets. The high efficiency for fusion within the exploding nanodroplets source-cylindrical solid target design provides guidelines for the optimization of yields for table-top nuclear fusion.

We have investigated experimentally and theoretically the dynamics of Stark-Zeeman split states in Li($n=25$) Rydberg atoms when they are exposed to a superposition of a slowly varying field and a harmonic RF field. Regular oscillatory structures are observed in the intrashell transitions. By solving the time-dependent Schrödinger equation for the problem it is shown that the dynamics is strongly influenced by the nonhydrogenic core which breaks the dynamical symmetry of the Coulomb problem. It is also shown that the dynamics effectively reduces to that of a two-level atom. The oscillations are remnants of interferences that arise partly due to a phase difference which develops between the two levels when they go through two consecutive one-photon resonances, and partly due to an effective change of the carrier-envelope phase of the coupling field.

Magneto-optical traps on atom chips are usually restricted to small atomic samples due to a limited capture volume caused primarily by distorted field configurations. Here we present a magneto-optical trap based on a millimeter-sized wire structure which generates a magnetic field with minimized distortions. Together with the loading from a high-flux two-dimensional magneto-optical trap, we achieve a loading rate of $8.4\times {10}^{10}$ atoms/s and maximum number of $8.7\times {10}^9$ captured atoms. The wire structure is placed outside of the vacuum to enable a further adaptation to new scientific objectives. Since all magnetic fields are applied locally without the need for external bias fields, the presented setup will facilitate parallel generation of Bose-Einstein condensates on a conveyor belt with a cycle rate above $1$ Hz.

Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role in the design of coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization.