We show that with a suitable modification of the model proposed by Yurke, Schleich, and Walls [Phys. Rev. A 42, 1703 (1990)] for the generation of linear superpositions of macroscopically distinct quantum states, it is possible to arrange a scheme for generating and detecting optical Schrödinger catlike states which is experimentally feasible with current technologies.

Bose-Einstein condensation of sodium atoms has been observed in a novel “cloverleaf” trap. This trap combines tight confinement with excellent optical access, using only dc electromagnets. Evaporative cooling in this trap produced condensates of $5\times {10}^6$ atoms, a tenfold improvement over previous results. We measured the condensate fraction and the repulsive mean-field energy, finding agreement with theoretical predictions.

We observe phononlike excitations of a Bose-Einstein condensate (BEC) in a dilute atomic gas. ${}^{87}$Rb atoms are optically trapped and precooled, loaded into a magnetic trap, and then evaporatively cooled through the BEC phase transition to form a condensate. We excite the condensate by applying an inhomogeneous oscillatory force with adjustable frequency and symmetry. We have observed modes with different angular momenta and different energies and have studied how their characteristics depend on interaction energy. We find that the condensate excitations persist longer than their counterparts in uncondensed clouds.

A Comment on the Letter by A. L. Sukstanskii and K. I. Primak, Phys. Rev. Lett. 75, 3029 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by Yuri S. Kivshar and Angel Sánchez.

We construct a generally applicable short-time perturbative expansion for coherence loss. Successive terms of this expansion yield characteristic times for decorrelation processes involving successive powers of the Hamiltonian. The second order results are sufficient to precisely reproduce expressions for “decoherence times” obtained in the literature by much more involved and indirect methods. Examples illustrating the influence of initial conditions and the need to evaluate higher order terms are given in the context of the Jaynes-Cummings model. It is shown that, in this case, the short-time decoherence behavior can probe the importance of antiresonant contributions.

The study of spin Hamiltonians is facilitated by the use of the Bethe equations. Up to now, these equations were primarily used for the study of the energy of the lowest state of a given symmetry. In this paper, we would like to show that there is a technique by which these equations for finite cycles can be transformed into an algebraic equation for the energy in which the coefficients are polynomials in the coupling constant, or just numbers. From this algebraic equation, we can get all energies of a given symmetry in a straightforward way.

It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $\mathrm{nm}$ is in a random pure state then the average entropy of a subsystem of dimension $m$ where $m\le n$ is $S_{m,n}=\left(\Sigma {k=n+1\mathrm{}}^{\mathrm{mn}}1/k\right)-(m-1\mathrm{})/2n$. In this Letter a simple proof of this conjecture is given.

We measure the energy distribution of a slow Cesium atomic beam when it is chopped into a short pulse and we find results which agree well with the time-energy uncertainty principle. The chopper consists in an atomic mirror formed by a laser evanescent wave whose intensity is pulsed. We use the temporally diffracted beam to design a Young-slit-type interferometer, in which the interfering paths consist of atomic trajectories bouncing at two different times on the mirror. By changing the mirror intensity, we can scan the atomic phase difference between the two arms.

Using a histogram Monte Carlo method and nonuniversal metric factors of a recent Letter [Phys. Rev. Lett. 75, 193 (1995)], we find that the probability for the appearance of $n$, $n=1,2,\dots ,$ top to bottom percolating clusters on finite square, planar triangular, and honeycomb lattices falls on the same universal scaling functions, which show interesting behavior as the aspect ratio of the lattice increases. Our results suggest many interesting problems for further research.

We study the WKB method away from the short-wave limit. Incorporating the correct phase loss due to reflection at a classical turning point, in place of the usual choice $\pi /2\mathrm{}$, can greatly improve the accuracy of the WKB wave function in the classically allowed region. For a repulsive ${1/x}^2$ potential this leads to far more accurate WKB wave functions that the usual Langer modification of the potential.

The diffusion properties of overdamped particles moving in spatially symmetrical periodic potentials subject to both symmetrical time-periodic driving and stochastic forcing are investigated [the typical model formally reads $\dot{x}{=-V}^{\prime }\left(x\right)+U\left(t\right)+\gamma \left(t\right)$, $V(L\pm x)=V\left(x\right)$, $U(T+t)=U\left(t\right)$, $〈\gamma \left(t\right)〉=0\mathrm{}$, $〈\gamma \left(t\right)\gamma \left(\tau \right)〉=2D\delta (t-\tau )$]. It is found that the diffusion rate can be greatly enhanced if the various forcings are chosen in an optimal matching. In particular, we may get a diffusion rate larger than the rate of free diffusion.

A new strategy for finding optimal solutions to complex problems with many competing requirements is proposed. It consists in an alternating optimization of the energy, cost, or fitness function of the system itself, and of subsystems of all sizes with an appropriate weight function. For various spin glasses (the $N-k$ model, the low autocorrelation binary sequence model, and the Coulomb glass), and for traveling salesman problems, the corresponding Monte Carlo algorithm is shown to yield results superior to those obtained by previous optimization techniques.

Classically, sending more than one bit of information requires manipulation of more than one two-state particle. We demonstrate experimentally that one can transmit one of three messages, i.e., 1 “trit” $\approx 1.58\mathrm{bit}$, by manipulating only one of two entangled particles. The increased channel capacity is proven by transmitting ASCII characters in five trits instead of the usual 8 bits.

The time evolution of a closed system of mean fields and fluctuations is Hamiltonian, with the canonical variables parametrizing the general time-dependent Gaussian density matrix of the system. Yet, the evolution manifests both quantum decoherence and apparent irreversibility of energy flow from the coherent mean fields to fluctuating quantum modes. Using scalar QED as an example, we show how this collisionless damping and decoherence may be understood as the result of dephasing of the rapidly varying fluctuations and particle production in the time varying mean field.

Statistical mechanics is useful to introduce generalizations of standard thermodynamics through the generalization of the entropy and other state functions. Along these lines the Tsallis nonextensive and the Bergmann group symmetric generalizations have proven to be very useful. We combine both formalisms to describe the nonextensive thermostatistics in a relativistic setting. We obtain the generalized forms of the first and second laws of thermodynamics for reversible processes, and apply the resulting theory to the cosmic blackbody radiation in a Robertson-Walker model of the Universe. We show that the temperature of the cosmic blackbody radiation varies as the inverse of the scale factor of the Universe, and is independent of the degree of nonextensivity.

It is shown theoretically and by analog electronic experiment that, in dissipative oscillatory systems for which the frequency of eigenoscillation displays an extremum as a function of energy, the dynamics of nonlinear resonance can differ markedly from the conventional case. Transitions between the conventional and novel types of nonlinear resonance, as parameters vary, correspond to changes in the topology of basins of attraction. With added noise, they can result in drastic changes in fluctuational transition rates between small- and large-amplitude regimes.

Quantum estimation of a phase shift is formulated within quantum mechanics and information theory. Using Bayes' estimation, the phase can be attributed even to a single interfering particle. The method is demonstrated for neutron interferometry operating near the quantum limit.

We calculate dynamical entropies from experimental data produced by a Schmitt trigger subjected to noise and a periodic forcing. Both input and output signals are converted to binary sequences. Conditional and Kullback entropies exhibit extrema for certain values of noise intensity. These extrema can be interpreted and will be related to the synchronization effect of switching events induced by external periodic bias.

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring.