We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.

We have studied dissipation in a Bose-Einstein condensed gas by moving a blue detuned laser beam through the condensate at different velocities. Strong heating was observed only above a critical velocity.

A Comment on the Letter by D. M. Barnett, et al., Phys. Rev. Lett. 76, 1812 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by A. Torcini, Ch. Dellago, and H. A. Posch.

We present the first measurement of the longitudinal density matrix of a matter-wave beam. Using a unique interferometric scheme, both the amplitude and phase of off-diagonal density matrix elements were determined directly, without the use of traditional tomographic techniques. The measured density matrix of a doubly amplitude modulated atomic sodium beam compares well with theoretical predictions.

The scaling properties of pair correlations at criticality are reproduced through an equivalence between random walk distributions and order parameter correlations. The shift from Gaussian to fractal walks with self-similar clusters corresponds to the changeover from a Gaussian to a nontrivial fixed point with nonvanishing dimensional anomaly. We show that the renormalization group trajectories lead to fixed points of minimum entropy, and use the Tsallis entropy index $q$ to measure nonextensivity as behavior departs from Gaussian.

The dynamical correlation spectra of the Toda chain are obtained by a molecular dynamics simulation and analyzed in terms of Bethe-ansatz-based soliton phenomenology. The spectrum of local temperature fluctuations exhibits a feature which can be unambiguously assigned to solitons. Detailed linewidth analysis demonstrates the phenomenon of nondissipative soliton diffusion, i.e., the stochastic sequence of spatial shifts experienced by the soliton as it moves through the lattice and interacts with other excitations without momentum exchange. Our results provide strong support for the dynamical predictions of the finite-temperature Bethe ansatz excitation spectrum.

We investigate the efficacy with which polarization entanglement can be teleported using a continuous measurement scheme. We show that by using the correct gain for the classical channel the degree of violation of locality that can be demonstrated (using a CH-type inequality) is not a function of the level of entanglement squeezing used in the teleportation. This is possible because a gain condition can always be chosen such that passage through the teleporter is equivalent to pure attenuation of the input field.

The formation of quasicondensate droplets in ultracold atomic gases is investigated as a first-order phase transition. Physical parameters and size distribution of metastable condensate droplets are derived from conditions of local equilibrium between quasicondensate and normal gas phases. Droplet characteristics are used for the quantitative description of recent measurements of enormous frequency shifts in the $1S-2S$ two-photon absorption in spin-polarized hydrogen in the normal gas phase. Theoretical evaluation of the line shape is in good agreement with experimental data.

We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical $N$-body Hamiltonian system with long-range interaction showing a second-order phase transition in the canonical ensemble. Anomalous diffusion is observed only in a transient out-of-equilibrium regime and for a small range of energy, below the critical one. Superdiffusion is due to Lévy walks of single particles and is checked independently through the second moment of the distribution, power spectra, trapping, and walking time probabilities. Diffusion becomes normal at equilibrium, after a relaxation time which diverges with $N$.

A Comment on the Letter by Apoorva Wagh et al., Phys. Rev. Lett. 81, 1992 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by Rajendra Bhandari.

We show that the critical temperature of a uniform dilute Bose gas increases linearly with the $s$-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

A second order phase transition induced by a rapid quench can inject far more topological defects into the ordered phase than would appear in equilibrium. We use quantum kinetic theory to show that this mechanism, originally postulated in the cosmological context, and analyzed so far only on the mean field classical level, should allow spontaneous generation of vortex lines in trapped Bose-Einstein condensates of simple topology, or of winding number in toroidal condensates.

The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive entropies. This limits the range of the nonextensivity parameter $q$ to $\left(0,1\right)$ so as to preserve the concavity of the entropies. The Tsallis entropy is thereby found to be appropriately renormalized.

We study an example of exact parametric resonance in an extended system ruled by nonlinear partial differential equations of nonlinear Schrödinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in nonlinear optics.

The ground state of a rotating Bose-Einstein condensate with attractive interaction in a quasi-one-dimensional torus is studied in terms of the ratio $\gamma$ of the mean-field interaction energy per particle to the single-particle energy-level spacing. The plateaus of quantized circulation are found to appear if and only if $\gamma <1\mathrm{}$ with the lengths of the plateaus reduced due to hybridization of the condensate over different angular-momentum states.

A 1D Bose gas interacting through $\delta ,{\delta }^{\prime }$ and double $\delta$ function potentials is shown to be equivalent to a $\delta$ anyon gas, allowing an exact Bethe ansatz solution. In the noninteracting limit, it describes an ideal gas with generalized exclusion statistics and solves some recent controversies.

The activationless escape of a free Brownian particle from a unit interval is analyzed over the entire range of friction coefficient $\gamma$. Approximate analytic expressions that compare favorably with simulations are derived for the effective and asymptotic rate constants $k$ and $\Gamma$ that describe the escape kinetics. Both rate constants show a turnover behavior as functions of $\gamma$, qualitatively similar to the rate constant in the Kramers theory of activated rate processes. It is found that $k\sim 1/\ln \left(1/\gamma \right)$ and $\Gamma \sim {\gamma }^{1/3}$ as $\gamma \to 0$ while both rate constants vanish as ${\gamma }^{-1\mathrm{}}$ as $\gamma \to \infty$.

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and noncompact groups are found to play a role.