Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg model are discussed. The adiabatic processes are assumed to consist in the slow variation of the strength of the magnetic field that environs the spin systems. These processes are of current interest in the treatment of cold atoms in optical lattices and in adiabatic quantum computation. We determine the probability that, during an adiabatic passage starting from the ground state, states with higher energy are excited.

Quantum key distribution with the Bennett-Brassard 1984 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g., loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.

The periodically kicked Rydberg atom displays quantum localization, features of which depend on the orientation and strength of the unidirectional kicks. They include scarring of the wave function, localization by cantori, and exponential localization in the regime of strong perturbation resembling dynamical localization. Using the semiclassical Herman-Kluk propagator we investigate the degree to which semiclassical dynamics can mimic quantum localization. While the semiclassical approximation has difficulties to reproduce the scarred wave functions, the exponential tail which is a typical signature of the dynamical localization is well represented in the case of strong classical diffusion. Also the localization by broken tori is observed in the semiclassical recurrence probability for short times but the deviation from the corresponding quantum dynamics becomes more pronounced for the long-time evolution.

We report experimental generation of nonclassically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons is separated by a controllable time delay up to $2\mu \mathrm{s}$. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.

We extend the collective atomic recoil lasing (CARL) model including the effects of friction and diffusion forces acting on the atoms due to the presence of optical molasses fields. The results from this model are consistent with those from a recent experiment by Kruse et al. [Phys. Rev. Lett. 91, 183601 (2003)]. In particular, we obtain a threshold condition above which collective backscattering occurs. Using a nonlinear analysis we show that the backscattered field and the bunching evolve to a steady state, in contrast to the nonstationary behavior of the standard CARL model. For a proper choice of the parameters, this steady state can be superfluorescent.

We present a scheme to perform an all optical simulation of quantum algorithms and maps. The main components are lenses to efficiently implement the Fourier transform and programmable liquid-crystal displays to introduce space dependent phase changes on a classical optical beam. We show how to simulate Deutsch-Jozsa and Grover’s quantum algorithms using essentially the same optical array programmed in two different ways.

After delineating the physical regimes that vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate $\Omega$ increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $⩾2\Omega$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where $\Omega$ is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacements and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long-range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long-wavelength single-particle Green’s function in the rotating system and calculate the condensate depletion as a function of temperature.

We develop an approach for calculating stationary states of rotating Bose-Einstein condensates in harmonic traps which is applicable for arbitrary ratios of the rotation frequency to the transverse frequency of the trap ${\omega }_{\perp }$. Assuming the number of vortices to be large, we write the condensate wave function as the product of a function that describes the structure of individual vortices times an envelope function varying slowly on the scale of the vortex spacing. By minimizing the energy, we derive Gross-Pitaevskii equations that determine the properties of individual vortices and the global structure of the cloud. For low rotation rates, the structure of a vortex is that of an isolated vortex in a uniform medium, while for rotation rates approaching the frequency of the trap (the mean-field lowest-Landau-level regime), the structure is that of the lowest $p$-wave state of a particle in a harmonic trap with frequency ${\omega }_{\perp }$. The global structure of the cloud is determined by minimizing the energy with respect to variations of the envelope function; for conditions appropriate to most experimental investigations to date, we predict that the transverse density profile of the cloud will be of the Thomas-Fermi form, rather than the Gaussian structure predicted on the assumption that the wave function consists only of components in the lowest Landau level for a regular array of vortices.

A simple method is presented to analyze the stability of static solitonic excitations of two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. First, a quick assessment can be made for the values of interspecies scattering length $a_{12}$ allowing existence of static solitons independent of the particle numbers $N_1$ and $N_2$. If the true value of $a_{12}$ falls into that acceptable interval, then a fine tuning is performed to get the ratio $N_2∕N_1$ at which the static solitons may be created. The technique is illustrated for the lithium-rubidium and sodium-rubidium condensates.

Dispersion relations and sum rules for nonlinear susceptibilities are derived using complex analysis and especially the concept of a meromorphic function. The dispersion relations and sum rules provide frames to investigate the consistency between the theory and experiments.

High-accuracy helium wave functions based on exponentials with random coefficients are transformed into momentum space. The utility of the wave functions is demonstrated through calculation of the expectation value of various operators needed to evaluate relativistic and QED corrections.

We propose and demonstrate an echo method to reduce the inhomogeneous linewidth of Bogoliubov excitations, in a harmonically-trapped Bose-Einstein condensate. Our proposal includes the transfer of excitations with momentum $+q$ to $-q$ using a double two photon Bragg process, in which a substantial reduction of the inhomogeneous broadening is calculated. Furthermore, we predict an enhancement in the method’s efficiency for low momentum due to many-body effects. As a proof of principle, the echo can also be implemented by using a four photon process, as is demonstrated experimentally.

We show that the density matrix of a spin-$l$ system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of $4l+1$ different spin directions. It is thus possible to represent the complete quantum statistics of any $N$-level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin-$l$ systems is discussed.

We develop a spectral representation formalism to calculate the nonretarded Casimir force between a spherical particle and a substrate, both with arbitrary local dielectric properties. The spectral formalism allows us to study systematically such force as a function of its geometrical properties separately from its dielectric properties. The calculated force is attractive, and at a small separations it is orders of magnitude larger for nanometric-size spheres than for micrometer particles. We also found that the force depends more on the dielectric properties of the sphere than of the substrate.

The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.

The triple-photoionization cross section of neon and argon near threshold has been investigated by ion time-of-flight spectrometry. We applied the Wannier power law to our data and confirmed the theoretical Wannier exponent in the cases of Ne and Ar. Our data also agree with previous findings regarding the Wannier exponent and its range of validity for Ne. However, the Wannier power law exhibits a much smaller range of validity of $2\text{eV}$ for Ar compared to $5\text{eV}$ for Ne. Also, in contrast to a previous experiment, we do not find a “second” power law but a gradual decrease of the exponent above the range of validity of the Wannier power law.

In a uniform fluid, a quantized vortex line with circulation $h∕M$ can support long-wavelength helical traveling waves $\propto e^{i(kz-{\omega }_{k}t)}$ with the well-known Kelvin dispersion relation ${\omega }_k\approx (\hslash k^2∕2M)\ln (1∕\mid k\mid \xi )$, where $\xi$ is the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity $\mathbf{V}$ of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the line’s curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wave number $k\left(z\right)$ upward near the trap center, and $k\left(z\right)$ then increases still more toward the ends.

Electric dipole matrix elements for , , , , transitions in cesium are calculated using a relativistic all-order method. The resulting matrix elements are used to evaluate lifetimes and polarizabilities. The data are compared with experimental lifetime and polarizability measurements made by different groups. Domination of the scalar polarizabilities by dipole matrix elements facilitates an exacting consistency check of lifetime and polarizability data. Values of matrix elements obtained from experimental lifetime data are found to be inconsistent with those inferred from polarizabilities derived from experimental Stark shift data. Our calculated polarizabilities agree well with experimental determinations.

We observed superradiant Raman scattering from a Bose-Einstein condensate irradiated by a single off-resonant light beam. Spontaneous mode selection of the scattered radiation turns probabilistic optical pumping into a stimulated Raman process, whereby the atoms are coherently transferred into a different hyperfine state. The population in the pumped state grew exponentially in time, demonstrating the emergence of bosonic stimulation in the optical pumping process.