We consider a weakly interacting, harmonically trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.

We have analyzed the interplay between an externally added noise and the intrinsic noise of systems that relax fast towards a stationary state, and found that increasing the intensity of the external noise can reduce the total noise of the system. We have established a general criterion for the appearance of this phenomenon and discussed two examples in detail.

We have scattered photons from an interfering path of a multiple beam Ramsey interference experiment realized with a cesium atomic beam. It is demonstrated that in multiple beam interference the decoherence from photon scattering cannot only lead to a decrease but, under certain conditions, also to an increase of the Michelson fringe contrast. In all cases, the atomic quantum state loses information with photon scattering, as “which-path” information is carried away by the photon field. We outline an approach to quantify this which-path information from observed fringe signals, which allows for an appropriate measure of decoherence in multiple path interference.

The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. The number of anomalous modes increases for an elongated condensate. The largest mode frequency exceeds the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe both vortex precession and the critical rotation frequency for creation of the first vortex in an elongated condensate.

We propose an experiment to measure the slow $\log \left(N\right)$ convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, ${p=1-e}^{-J/k_{B}T}$, in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred pointer states remain unchanged. This conclusion—reached for a specific class of models—is investigated in a general setting of conditional master equations using suitable generalizations of predictability sieve. We also find indications that the einselected states are easiest to infer from the measurements carried out on the environment.

The rotational motion of an interacting Bose-Einstein condensate confined by a harmonic trap is investigated by solving the hydrodynamic equations of superfluids, with the irrotationality constraint for the velocity field. We point out the occurrence of an overcritical branch where the system can rotate with angular velocity larger than the oscillator frequencies. We show that in the case of isotropic trapping the system exhibits a bifurcation from an axisymmetric to a triaxial configuration, as a consequence of the interatomic forces. The dynamical stability of the rotational motion with respect to the dipole and quadrupole oscillations is explicitly discussed.

We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with parameters different from the classical action. We present numerical results for the harmonic oscillator with weak perturbation, the quartic potential, and the double well potential. The quantum action is relevant for quantum chaos and quantum instantons.

A careful treatment of the discretization errors in the path integral formulation of quantum mechanics leads to a unique prescription for the translation from the Hamiltonian to the action in the functional integral. An example is given by an interaction quadratic in the occupation number, characteristic for many body bosonic systems. As a result, the term linear in the occupation number (chemical potential) receives a correction as compared to the usual formulation based on coherent states. A perturbative calculation supports the relevance of this correction.

We have designed and experimentally studied a simple beam splitter for guided atoms realized with a current carrying Y-shaped wire nanofabricated on a surface (atom chip). Such a Y-configuration beam splitter has many advantages compared to conventional designs based on tunneling, especially that it will enable robust beam splitting. This and other similar designs can be integrated into more sophisticated surface-mounted atom optical devices at the mesoscopic scale.

We present an exact many-body solution for the dynamics of the population difference $N_2{-N}_1$ induced by an rf field in the two-component atomic cloud characterized by equal scattering lengths. We show that no intrinsic decoherence occurs for $N_2{-N}_1$, provided that the exact intrinsic $\mathrm{SU}\left(2\right)$ symmetry holds. Decoherence for $N_2{-N}_1$ arises when deviations from the symmetry exist either in the scattering lengths or in the confining potentials. We suggest testing the evolution of $N_2{-N}_1$ by conducting echo-type experiments.

We study a random bisection problem where an interval of length $x$ is cut into two random fragments at the first stage, then each of these two fragments is cut further, etc. We compute the probability $P_n\left(x\right)$ that at the $n$th stage, each of $2^n$ fragments is shorter than 1. We show that $P_n\left(x\right)$ approaches a traveling wave form, and the front position $x_n$ increases as $x_n\sim n^{\beta }{\rho }^n$ for large $n$ with $\rho =1.261\mathrm{}076\dots$ and $\beta =0.453\mathrm{}025\dots$. We also solve the $m$-section problem where each interval is broken into $m$ fragments and show that ${\rho }_m\approx m/\left(\ln m\right)$ and ${\beta }_m\approx 3/\left(2\ln m\right)$ for large $m$. Our approach establishes an intriguing connection between extreme value statistics and traveling wave propagation in the context of the fragmentation problem.

We derive a new hierarchy of local minimum Heisenberg-uncertainty states by introducing a superposition of “small waves” onto some initial state. Our objective is to increase the resolution in one observable, with the least decrease in the resolution in the conjugate observable. This leads to a constrained minimization which in a well-defined sense yields the best possible way of achieving this goal. The results are relevant to many topics (e.g., quantum optics and control, Bose-Einstein condensation, path integration, etc.).

A Comment on the Letter by Janna Levin, Phys. Rev. Lett. 84, 3515 (2000).

Linearly polarized classical light can be expressed in a vertical and a horizontal component. Geometrically rotating vertically polarized light by 90° will convert it to the orthogonal horizontal polarization. We have experimentally generated a two-photon state of light which evolves into an orthogonal state upon geometrical rotation by 60°. Rotating this state by an additional 60° will yield a state which is mutually orthogonal to the first two states. Generalizing this procedure, one can generate $N+1\mathrm{}$ mutually orthogonal $N$-photon states that cyclicly evolve from one to another upon a geometric rotation by $180/(N+1\mathrm{})$ degrees.

We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of entangled states of the ion and the vibrational mode.

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density $P_t\left(x\right)=|\Psi (x,t){|}^2$ is shown not to change during the time evolution. We prove a universal relation $D_t{=1+D}_x/2$ linking the dimensions of space cross sections $D_x$ and time cross sections $D_t$ of the fractal quantum carpets.

We propose using spontaneous Raman scattering from an optically driven Bose-Einstein condensate as a source of atom-photon pairs whose internal states are maximally entangled. Generating entanglement between a particle which is easily transmitted (the photon) and one which is easily trapped and coherently manipulated (an ultracold atom) will prove useful for a variety of quantum-information related applications. We analyze the type of entangled states generated by spontaneous Raman scattering and construct a geometry which results in maximum entanglement.