We have numerically investigated the lasing threshold of three-dimensional diffusive random lasers composed of pointlike scatterers. The lasing threshold ${\Gamma }_T$ is determined by the mode with the smallest decay rate. The dependence of ${\Gamma }_T$ on the number of scatterers $N$ (system size) is shown to follow the power law ${\Gamma }_T\propto N^{-2∕3}$. This result, which reflects the diffusion law for the lasing threshold, is shown to apply even when the system is very close to the Anderson localization transition. We suggest that this result corroborates the scenario in which extended modes are at the origin of random lasing in the diffusive regime, as revealed by recent experiments.

We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium $\alpha =(24.33\pm 0.16)\times {10}^{-30}{\mathrm{m}}^3$ with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to $4\times {10}^{-9}$ for our largest field, is measured with a ${10}^{-3}$ accuracy.

This article identifies a series of properties common to all theories that do not allow for superluminal signaling and predict the violation of Bell inequalities. Intrinsic randomness, uncertainty due to the incompatibility of two observables, monogamy of correlations, impossibility of perfect cloning, privacy of correlations, bounds in the shareability of some states; all these phenomena are solely a consequence of the no-signaling principle and nonlocality. In particular, it is shown that for any distribution, the properties of (i) nonlocal, (ii) no arbitrarily shareable, and (iii) positive secrecy content are equivalent.

In recent investigations, Ozawa showed that the angular momentum conservation laws led to a precision limit on quantum computing in single-spin qubit systems and suggested the importance of encoding of a logical qubit by multiple-spin qubits for circumventing this difficulty. Subsequently, Lidar pointed out that the universal encoding on decoherence-free (noiseless) subspaces or subsystems can be used effectively for this purpose. In this paper, we investigate the three-qubit decoherence-free subsystem proposed by Knill, Laflamme, and Viola to construct error-free quantum logic gates in the serial mode satisfying the angular-momentum conservation law. This paper shows that the class of quantum gates defined by the 19-gate sequence with the repetition and correlation symmetries precisely coincides with the class of controlled-$U$ operations up to local equivalence. As a result, any controlled rotation, frequently used in quantum Fourier transforms, can be performed by the 26-gate sequence, the same as the controlled-NOT operation.

The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures.

We consider entanglement detection for quantum-key-distribution systems that use two signal states and continuous-variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.

We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zener pulse, the qubit transition frequency is varied in time so that it passes through the frequency of the radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency.

We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.

We show that Josephson vortices in a quasi-one-dimensional atomic Bose Josephson junction can be controllably manipulated by imposing a difference of chemical potentials on the atomic Bose-Einstein condensate waveguides forming the junction. This effect, which has its origin in the Berry phase structure of a vortex, turns out to be very robust in the whole range of the parameters where such vortices can exist. We also propose that a Josephson vortex can be created by the phase imprinting technique and can be identified by a specific tangential feature in the interference picture produced by expanding clouds released from the waveguides.

The Bose-Hubbard model is extended to include nearest- and far-neighbor interactions and is related to the fractional quantum Hall effect (FQHE). Both models may be studied in optical lattices with quantum gases. The ground state is calculated for the extended Bose-Hubbard model with strong repulsive interactions (weak hopping). Incompressible Mott insulator states are found at rational filling fractions compatible with the principal and secondary FQHE filling fractions of the lowest Landau levels observed experimentally. It is discussed to which extent these states at fractional filling survive or undergoes a Mott insulator transition to a superfluid as hopping terms are included.

In this paper I study the dynamics of a two-level atom interacting with a standing-wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time-dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behavior of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time, and its impact on the atomic motion. Wave-packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.

We discuss an adaptive interferometric approach to quantum estimation of phase shifts. In a first step we find optimized two-mode input states for a generalized Mach-Zehnder interferometer. These two states show a small phase variance at the so-called Heisenberg limit. It turns out that they can be generated by entangling a coherent state and a squeezed vacuum at a beam splitter. Moreover, the interferometric setup allows us to describe an adaptive estimation scheme for arbitrary phase shifts if we assume a fixed mean photon number as a quantum resource.

We study the effect of inhomogeneous coupling between atoms and external light fields on quantum memories that employ electromagnetically induced transparency (EIT). By introducing atomic subensembles to describe the present inhomogeneous coupling case we find that there is a nonsymmetric dark-state subspace that allows the EIT quantum-memory technique to function perfectly. This shows that such a memory scheme can work ideally even if the atomic state is very far from being a symmetric one.

We calculate the entanglement-assisted classical capacity of symmetric and asymmetric Pauli channels where two consecutive uses of the channels are correlated. It is evident from our study that in the presence of memory, a higher amount of classical information is transmitted over quantum channels if there exists prior entanglement as compared to product and entangled state coding.

We have investigated photoassociation (PA) spectra of ultracold ${}^{88}\mathrm{Sr}$ atoms near the $5s^2{}^{1}S_0+5s5p{}^{1}P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be $r_0=3.78\left(18\right)\mathrm{nm}$. The PA lines also determined a precise lifetime of the ${}^{1}P_1$ state to be $5.263\left(4\right)\mathrm{ns}$.

Recent experimental results of Milne-Brownlie et al. on the ionization of the water molecule by low-energy electron (250 eV) have been compared to theoretical predictions performed in the distorted-wave first Born model [Phys. Rev. A 69, 032701 (2004)]. It was found that this theory was unable to predict the very large recoil scattering observed experimentally. In this work, more sophisticated theoretical models are investigated in order to better understand the water ionization process at the multidifferential level and to reproduce the experimental observations.

Electron-impact excitation cross sections for the $2p^6\to 2p^{5}3l$ transitions in ${\mathrm{Fe}}^{16+}$ are calculated in a configuration-average distorted-wave approximation. Resonant-excitation contributions from the $2p^{5}3pn{l}^{\prime }$, $2p^{5}3dn{l}^{\prime }$, and $2p^{5}4ln{l}^{\prime }$ series are included in the isolated resonance approximation. The accuracy of the distorted-wave calculations is determined by comparison with previous 139 level resolved $(n⩽5)$ fully relativistic $R$-matrix calculations. Excellent agreement is found between the configuration-average distorted-wave and $R$-matrix total rate coefficients for the strong $2p^6\to 2p^{5}3p$ and $2p^6\to 2p^{5}3d$ transitions, while differences found for the relatively weak $2p^6\to 2p^{5}3s$ transition are mainly attributed to close-coupling effects.

We investigate the scattering of an evanescent light field by a single cesium atom outside a nanofiber. We show that the confinement of the field, the presence of the longitudinal field component and the tangential Poynting vector component, the enhancement of spontaneous emission, and the degeneracy of the atomic ground state substantially affect the scattering process. We find that, in the close vicinity of the fiber surface, the transmittance of the field in the stationary regime can be substantially reduced to 48% due to scattering into radiation modes (with the efficiency as high as 44%) and backward guided modes (with the efficiency as high as 8%).

We propose an optical readout scheme allowing a proof of principle of information extraction below the diffraction limit. This technique, which could lead to improvement in data readout density onto optical disks, is independent from the wavelength and numerical aperture of the reading apparatus, and involves a multipixel array detector. Furthermore, we show how to use nonclassical light in order to perform a bit discrimination beyond the quantum noise limit.

The emission from a radiating source embedded in a photonic lattice is calculated. The analysis considers the photonic lattice and free space as a combined system. Furthermore, the radiating source and electromagnetic field are quantized. Results show the deviation of the photonic lattice spectrum from the blackbody distribution, with intracavity emission suppressed at certain frequencies and enhanced at others. In the presence of rapid population relaxation, where the photonic lattice and blackbody populations are described by the same equilibrium distribution, it is found that the enhancement does not result in output intensity exceeding that of the blackbody at the same frequency. However, for slow population relaxation, the photonic lattice population has a greater tendency to deviate from thermal equilibrium, resulting in output intensities exceeding those of the blackbody, even for identically pumped structures.