Representing an ensemble of random lasers with an ensemble of random matrices, we compute the average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to the environment are considered. In the latter case, contrary to an earlier claim in the literature, we do not find a power-law dependence of the average mode number on the pump strength. For the relative fluctuations, however, a power law can be established. It is shown that, due to the mode competition, the distribution of the number of excited modes over an ensemble of lasers is not binomial.

We show how the entanglement in a wide range of continuous variable non-Gaussian states can be preserved against decoherence for long-range quantum communication through an optical fiber. We apply protection via decoherence-free subspaces and quantum dynamical decoupling to this end. The latter is implemented by inserting phase shifters at regular intervals $\Delta$ inside the fiber, where $\Delta$ is roughly the ratio of the speed of light in the fiber to the bath high-frequency cutoff. Detailed estimates of relevant parameters are provided using the boson-boson model of system-bath interaction for silica fibers and $\Delta$ is found to be on the order of a millimeter.

We formulate an effective-range theory for the near-threshold behavior of the amplitudes describing quantum reflection in attractive potential tails by adapting the effective-range theory of ordinary elastic scattering to the case of incoming boundary conditions at small distances. For homogeneous attractive potentials proportional to $-1∕r^{\alpha }$ with $\alpha >5$, the effective range turns out to be a real multiple (with known coefficient) of the complex scattering length which defines the leading, linear momentum dependence of phase and modulus of the quantum reflection amplitude. Analytical expressions are also given for the leading and next-to-leading terms in the near-threshold behavior of the quantum reflection amplitudes for homogeneous attractive potentials proportional to $-1∕r^3$, $-1∕r^4$, and $-1∕r^5$.

We demonstrate a new type of a cavity-enhanced optical trap whose standing-wave potential well can be transformed by using phase modulation. When the modulation frequency is matched to the free spectral range of the cavity, the potential well can be changed continuously from a corrugated form of a standing wave to a flattened form of a traveling wave depending on the modulation index. With the phase modulation, more atoms are trapped due to the increase in the trap volume, and there is a pronounced increase by a factor of 1.9 when an optimal modulation is applied. From the increase in number of trapped atoms we also infer that the temperature associated with longitudinal motion is strongly affected by the transformation of the potential well. This technique can be used to study collective behavior of trapped atoms and to manipulate atomic distribution for quantum information processing.

We report on the dynamics of ultracold collisions induced by near-resonant frequency-chirped light. A series of identical chirped pulses, separated by a variable delay, is applied to an ultracold sample of ${}^{85}\mathrm{Rb}$, and the rate of inelastic trap-loss collisions is measured. For small detunings of the chirped light below the atomic resonance, we observe that the rate of collisions induced by a given pulse can be increased by the presence of an earlier pulse. We attribute this to the enhancement of short-range collisional flux by the long-range excitation of atom pairs to an attractive molecular potential. For larger detunings and short delays, we find that a leading pulse can suppress the rate of collisions caused by a following pulse. This is due to a depletion of short-range atom pairs by the earlier pulse. Comparison of our data to classical Monte Carlo simulations of the collisions yields reasonable agreement.

We present a variational method to study the ground state of the newly realized ${}^{52}\mathrm{Cr}$ dipolar Bose-Einstein condensate. Besides the usual contact potential term in the mean-field equation, there is an additional long-range and anisotropic dipole-dipole interaction potential. We develop an efficient Newton-Raphson’s scheme to solve the condensate state. The solution shows a double-peak feature in the loosely confined dimension. Compared to the existing single-peak calculations, the double-peak solution has lower energy and reflects the distinct property of the dipole-dipole interaction. Our method is easy and efficient to use for future investigations of the dipolar systems.

Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second-order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap $\Delta$ (at fixed chemical potentials) is demonstrated to be equivalent to the positive definiteness of the particle number susceptibility matrix. In addition, we show the positivity of the effective pair mass constitutes another nontrivial stability condition. These conditions determine the (local) stability of the system towards phase separation (or other ordered phases). We also study systematically the effects of finite temperature and the related pseudogap on the phase diagrams defined by our stability conditions.

We calculate the weak-driving transmission of a linearly polarized cavity mode strongly coupled to the $D2$ transition of a single cesium atom. Results are relevant to future experiments with microtoroid cavities, where the single-photon Rabi frequency $g$ exceeds the excited-state hyperfine splittings, and photonic band-gap resonators, where $g$ is greater than both the excited- and ground-state splitting.

We describe a qualitatively different regime of cavity quantum electrodynamics, the superstrong coupling regime. This regime is characterized by atom-field coupling strengths of the order of the free spectral range of the cavity, resulting in a significant change in the spatial mode functions of the light field. It can be reached in practice for cold atoms trapped in an optical dipole potential inside the resonator. We present a nonperturbative scheme that allows us to calculate the frequencies and linewidths of the modified field modes, thereby providing a good starting point for a quantization of the theory.

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam’s geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.

We have found that for a wide range of two-qubit Hamiltonians the canonical-ensemble thermal state is entangled in two distinct temperature regions. In most cases the ground state is entangled; however we have also found an example where the ground state is separable and there are still two regions. This demonstrates that the qualitative behavior of entanglement with temperature can be much more complicated than might otherwise have been expected; it is not simply determined by the entanglement of the ground state, even for the simple case of two qubits. Furthermore, we prove a finite bound on the number of possible entangled regions for two qubits, thus showing that arbitrarily many transitions from entanglement to separability are not possible. We also show that only one entangled region is possible for the special case of Hamiltonians without magnetic fields.

The superconducting charge-phase “quantronium” qubit is considered in order to develop a model for the measurement process used in the experiment of Vion et al. [Science 296, 886 (2002)]. For this model we propose a method for including the bias current in the readout process in a fundamentally irreversible way, which to first order is approximated by the Josephson junction tilted-washboard potential phenomenology. The decohering bias current is introduced in the form of a Lindblad operator and the Wigner function for the current-biased readout Josephson junction is derived and analyzed. During the readout current pulse used in the quantronium experiment we find that the coherence of the qubit initially prepared in a symmetric superposition state is lost at a time of $0.2\mathrm{ns}$ after the bias current pulse has been applied, a time scale that is much shorter than the experimental readout time. Additionally we look at the effect of Johnson-Nyquist noise with zero mean from the current source during the qubit manipulation and show that the decoherence due to the irreversible bias current description is an order of magnitude smaller than that found through adding noise to the reversible tilted-washboard potential model. Our irreversible bias current model is also applicable to persistent-current-based qubits where the state is measured according to its flux via a small-inductance direct-current superconducting quantum interference device.

$K\beta$ x-ray spectra of metallic vanadium and its compounds (${\mathrm{V}}_2{\mathrm{O}}_3$, $\mathrm{V}{\mathrm{O}}_2$, ${\mathrm{V}}_2{\mathrm{O}}_5$, VC, VN, $\mathrm{V}{\mathrm{Cl}}_2$, $\mathrm{N}{\mathrm{H}}_4\mathrm{V}{\mathrm{O}}_3$, and $\mathrm{V}\mathrm{O}\mathrm{S}{\mathrm{O}}_4\times 5{\mathrm{H}}_2\mathrm{O}$) induced in thick targets by $3\mathrm{MeV}$ proton beams were measured by using wavelength dispersive (WD) x-ray spectrometer. In addition to the main $K{\beta }_{1,3}$ x-ray line, “satellites” or second order contributions like $K{\beta }^{\prime }$, $K{\beta }^{″}$, $K{\beta }^{‴}$, and $K{\beta }_{2,5}$ were clearly resolved. Intensities and positions of these lines relative to the $K{\beta }_{1,3}$ x-ray line have been extracted by fitting the spectra and corrected for x-ray sample self-absorption. The influence of the oxidation states and vanadium-ligand bond distances in studied compounds on relative intensities and positions of $K{\beta }^{″}$, $K{\beta }_{2,5}$, and $(K{\beta }^{″}+K{\beta }_{2,5})$ x-ray lines (relative to $K{\beta }_{1,3}+K{\beta }^{\prime }$) has been studied and discussed. The obtained results indicate that the strength of the $K{\beta }^{″}$ and $K{\beta }_{2,5}$ transition probability per vanadium-ligand pair decreases exponentially with increasing vanadium-ligand distance, in agreement with the observation reported by Bergman et al. for $K{\beta }^{″}$ relative intensity in a number of Mn oxide compounds [U. Bergmann, C. R. Horne, T. J. Collins, J. M. Workman, and S. P. Cramer, Chem. Phys. Letters 302, 119 (1999)].

Absolute photoionization cross sections for ${\mathrm{Kr}}^{3+}$ were measured in the energy range $39.05–143.2\mathrm{eV}$ for single ionization and $120.6–137.7\mathrm{eV}$ for double ionization. For comparison, an electron-impact single-ionization measurement was made in the energy range $43.1–179.1\mathrm{eV}$ and normalized to previously published absolute measurements. The Flexible Atomic Code and Cowan atomic structure codes were used to calculate energy levels, excitation energies and oscillator strengths for $3d\to np$, $3d\to nf$, and $4s\to np$ autoionizing transitions from the ground and metastable states. From the single-photoionization measurements, ionization thresholds of the ${}^{2}P^o{}_{3∕2}$, ${}^{2}D^o{}_{5∕2}$ metastable states and ${}^{4}S^o{}_{3∕2}$ ground state were measured to be $46.62\pm 0.02$, $48.59\pm 0.01$, and $50.70\pm 0.02\mathrm{eV}$, nearly $2\mathrm{eV}$ lower than National Institute of Standards and Technology tabulated values. Within the experimental uncertainty, oscillator strengths determined from the photoionization measurements are in agreement with both calculations. Excitation-autoionization and resonant-excitation double-autoionization features are evident in the electron-impact ionization cross section.

Slow, multiply charged ions interacting with surfaces provide a tool for accessing surface properties on a very short length scale. Using characteristic KLL Auger electron emission from ${\mathrm{He}}^{**}$ atoms formed in front of a ferromagnetic surface, the local spin polarization of the surface can be linked to the population probability of different spin states in doubly excited He. An atomic model is developed to describe the population of the ${\mathrm{He}}^{**}$ states and their decay. The influences of the surface electronic response and the projectile parameters on the shape of the Auger spectra are discussed. Subsequently, the model is applied to ${\mathrm{He}}^{2+}$ on Ni(110) to extract the surface spin polarization dependence on the crystal temperature from the changes in the relative intensities of Auger peaks corresponding to different spin states. By choosing different scattering conditions, magnetic information on nanometer scale can be obtained.

In this paper, we explore a scheme to tackle a challenging problem of stable Bose-Einstein condensates (BECs) with attractive atom interactions. In this scheme, the $s$-wave scattering length is tuned in space, rather than in time as previously studied, by a far-off-resonant Gaussian optical field, from negative to positive in the center region of the potential well. We find that this tuning leads to coexisting repulsive and attractive interactions within a single atomic gas and consequently a stable BEC in the repulsive region. We investigate the ground-state properties of the tuned BECs and show them to exhibit a strikingly different spatial density distribution from a conventional one with a positive $s$-wave scattering length. The tuned BEC is formed only when the condensed number is less than a critical number. We derive a formula for the critical number.

The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below the solitary laser threshold where low-frequency fluctuations (LFF’s) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a vertical cavity surface emitting laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK model can be considered as realistic. In particular, it clearly demonstrates that the deterministic LK model, for realistic values of the linewidth enhancement factor $\alpha$, reproduces the LFF’s only as a transient dynamics towards one of the stationary modes with maximal gain. A reasonable reproduction of real data from VCSEL’s can be obtained only by considering the noisy LK or alternatively deterministic LK model for extremely high $\alpha$ values.

We show how high-fidelity quantum teleportation of light to atoms can be achieved in the same setup as was used in the recent experiment [J. Sherson et al., Nature443, 557, 2006], where such an interspecies quantum state transfer was demonstrated for the first time. Our improved protocol takes advantage of the rich multimode entangled structure of the state of atoms and scattered light and requires simple postprocessing of homodyne detection signals and squeezed light in order to achieve fidelities up to 90% (85%) for teleportation of coherent (qubit) states under realistic experimental conditions. The remaining limitation is due to atomic decoherence and light losses.

We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case.

The search for particle electric dipole moments (EDM’s) represents a most promising way to search for physics beyond the standard model. A number of groups are planning a new generation of experiments using stored gases of various kinds. In order to achieve the target sensitivities it will be necessary to deal with the systematic error resulting from the interaction of the well-known $\vec{v}\times \vec{E}$ field with magnetic field gradients which is often referred to as the geometric phase effect [E. D. Commins, Am. J. Phys. 59, 1077 (1991); J. M. Pendlebury et al., Phys. Rev. A 70, 032102 (2004)]. This interaction produces a frequency shift linear in the electric field, mimicking an EDM. In this work we introduce an analytic form for the velocity autocorrelation function which determines the velocity-position correlation function which in turn determines the behavior of the frequency shift [S. K. Lamoreaux and R. Golub, Phys. Rev A 71, 032104 (2005)] and show how it depends on the operating conditions of the experiment. We also discuss some additional issues.