We analyze the extraction from a trapped Bose-Einstein condensate to a nontrapping state of a coherent atomic beam and its subsequent fall, at $T=0\mathrm{}\mathrm{K}$. Our treatment fully takes gravity into account but neglects the mean-field potential exerted on the free falling beam by the trapped atoms. We derive analytical expressions for the output rate and the output mode of the quasicontinuous “atom laser.” Comparison with experimental data of Bloch et al. [Phys. Rev. Lett. 82, 3008 (1999)] is satisfactory.

The relative phase of two initially independent Bose-Einstein condensates can be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we show that this phase cooling process already appears within a semiclassical model. We calculate the stationary states, find regions of bistable behavior, and suggest a Ramsey-type experiment to measure the buildup of phase coherence between the condensates. We also study quantum effects and imperfections of the system.

Existing works on coherence resonance, i.e., the phenomenon of noise-enhanced temporal regularity, focus on excitable dynamical systems such as those described by the FitzHugh-Nagumo equations. We extend the scope of coherence resonance to an important class of dynamical systems: coupled chaotic oscillators. In particular, we show that, when a system of coupled chaotic oscillators is under the influence of noise, the degree of temporal regularity of dynamical variables characterizing the difference among the oscillators can increase and reach a maximum value at some optimal noise level. We present numerical results illustrating the phenomenon and give a physical theory to explain it.

We show a new approach for solving the $N$-body problems based on neural networks. Without loss of generality, we derived a network solution for the time-dependent positions of $N$ bodies in self-gravitating systems. The simulation is limited to a system of collisionless disks—a case for determining the spatial distributions of dark matter and in reproducing global effects such as formation of spiral galaxies. Our approach yields a solution that is analytic with time-reversed path-tracing capabilities that could lead to new findings in the study of the collective behavior of $N$-body systems.

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state, where each of the photons carries (partial) information of the initial state, was used to perform such a measurement.

It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable theorems that apply to real experiments, so that noncontextual hidden variables can indeed be experimentally disproved. The essential point is that for the derivation of hidden-variable theorems one does not have to know which observables are really measured by the apparatus. Predictions can be derived for observables that are defined in an entirely operational way.

For any mean value of a Cartesian component of a spin vector we identify the smallest possible uncertainty in any of the orthogonal components. The corresponding states are optimal for spectroscopy and atomic clocks. We show that the results for different spin $J$ can be used to identify entanglement and to quantify the depth of entanglement in systems with many particles. With the procedure developed in this Letter, collective spin measurements on an ensemble of particles can be used as an experimental proof of multiparticle entanglement.

We experimentally demonstrate observation of highly pure four-photon GHZ entanglement produced by parametric down-conversion and a projective measurement. At the same time this also demonstrates teleportation of entanglement with very high purity. Not only does the achieved high visibility enable various novel tests of quantum nonlocality, it also opens the possibility to experimentally investigate various quantum computation and communication schemes with linear optics. Our technique can, in principle, be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.

An effective boson Hamiltonian applicable to atomic beam splitters, coupled Bose-Einstein condensates, and optical lattices can be made exactly solvable by including all $n$-body interactions. The model can include an arbitrary number of boson components. In the strong interaction limit the model becomes a quantum phase model, which also describes a tight-binding lattice particle. Through exact results for dynamic correlation functions, it is shown how the previous weak interaction dynamics of these systems are extended to strong interactions, now becoming relevant in the experiments. The effect of the number of boson components is also analyzed.

Using a focused laser beam we stir a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate confined in a magnetic trap. We observe that the steady states of the condensate correspond to an elliptic cloud, stationary in the rotating frame. These steady states depend nonlinearly on the stirring parameters (amplitude and frequency), and various solutions can be reached experimentally depending on the path followed in this parameter space. These states can be dynamically unstable and we observe that such instabilities lead to vortex nucleation in the condensate.

We create Bose-Einstein condensates of ${}^{87}\mathrm{Rb}$ in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the Bose-Einstein condensate and accounts for the main features of the observed behavior.

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam.

We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as “Bose enhancement.”

We discuss the relationship between bosonic stimulation, density fluctuations, and matter wave gratings. It is shown that enhanced stimulated scattering, matter wave amplification, and atomic four-wave mixing do not require macroscopic occupation of a single quantum state. These processes are in principle possible for fermionic or nondegenerate samples, if they are prepared in a cooperative state. In practice, there are limitations due to short coherence times.

Based on Richardson's exact solution of the multilevel pairing model we derive a new class of exactly solvable models for the finite boson system. As an example we solve a particular Hamiltonian which displays a transition to a fragmented condensate for repulsive pairing interaction.

The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable ${}^{85}\mathrm{Rb}$ BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be $\frac{N|a|}{a_{\mathrm{ho}}}=0.459\mathrm{}\pm 0.012\pm 0.054$, slightly lower than the predicted value of 0.574.

We consider pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum ( $c$) or even becomes negative. A signal velocity is defined operationally based on the optical signal-to-noise ratio, and is computed for cases appropriate to the recent experiment where such a negative group velocity was observed. It is found that quantum fluctuations limit the signal velocity to values less than $c$.

We demonstrate that Bragg scattering from a condensate can be sensitive to the spatial phase distribution of the initial state. This allows preferential scattering from a selected spatial region, and provides a robust signature for a vortex state. We develop an analytic model which accurately describes this phenomenon, and we give quantitative predictions for current experimental conditions.

We propose a method of generating a vortex ring in a Bose-Einstein condensate by means of electromagnetically induced atomic transitions. Some remnant population of atoms in a second internal state remains within the toroidal trap formed by the mean-field repulsion of the vortex ring. This population can be removed, or it can be made to flow around the torus (i.e., within the vortex ring). If this flow has a unit topological winding number, the entire structure formed by the two condensates is an example of a three-dimensional Skyrmion texture.

We have studied the properties of the scissors mode of a trapped Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms at finite temperature. We measured a significant shift in the frequency of the mode below the hydrodynamic limit and a strong dependence of the damping rate as the temperature increased. We compared our damping rate results to recent theoretical calculations for other observed collective modes, finding a fair agreement. From the frequency measurements we deduce the moment of inertia of the gas and show that it is quenched below the transition point, because of the superfluid nature of the condensed gas.