The one-dimensional flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau’s approach. Besides, for penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.

We perform numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. [Nature (London) 412, 295 (2001)] on the dynamics of collapsing and exploding Bose-Einstein condensates of ${}^{85}\mathrm{Rb}$ atoms. These authors manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one, and vice versa. In the actual experiment they suddenly changed the scattering length of atomic interaction from a positive to a large negative value on a preformed condensate in an axially symmetric trap. Consequently, the condensate collapsed and ejected atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.

We study the boundary between two interpenetrating Bose-Einstein condensates interacting repulsively in the case of their spatial separation. We show that the analytical expressions for the distribution of the condensate density can be obtained in the limiting cases corresponding to the weak and strong separations. Using these expressions, we consider the excitation spectrum of a particle confined in the vicinity of the boundary and the surface waves at the boundary.

A two-dimensional rotating six-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. The emphasis is placed on the study of the effect of symmetry. The magic numbers are found to originate from the quantum constraints. The energy of an eigenstate and the spatial distribution of its wave function are found to be strongly affected by its inherent ability to get access to symmetric shapes. Some states with special inherent ability are found to be crystal-like, they have explicit geometric structures.

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

We have investigated quantum revivals of wave packets in a one-dimensional infinite square well potential containing a $\delta$ well in the middle. The time-dependent Schrödinger equation for this composite potential admits formally exact solutions. We present analytical results for revival properties in three physically motivated approximations: wave packets containing eigenstates with large numbers in the presence of an arbitrary $\delta$ well, “shallow” and “deep” $\delta$ wells. Analytical results in the case of a “shallow” $\delta$ well have been tested numerically.

In this paper we study the quantum Zeno effect using the irreversible model of the measurement. The detector is modeled as a harmonic oscillator interacting with the environment. The oscillator is subjected to the force, proportional to the energy of the measured system. We use the Lindblad-type master equation to model the interaction with the environment. The influence of the detector’s temperature on the quantum Zeno effect is obtained. It is shown that the quantum Zeno effect becomes stronger (the jump probability decreases) when the detector’s temperature increases.

We study the Braunstein-Kimble setup for teleportation of a quantum state of a single mode of an optical field. We assume that the sender and receiver share a two-mode Gaussian state and we identify optimum local Gaussian operations that maximize the teleportation fidelity. We consider the fidelity of teleportation of pure Gaussian states and we also introduce the fidelity of the teleportation transformation. We show in an explicit example that in some cases the optimum local operation is not a simple unitary symplectic transformation but some more general completely positive map.

We have investigated three identical bosons with very large pairwise scattering lengths. Normally such a situation is associated with Efimov states, where the three-body system has a set of very loosely bound states close to the three-body threshold. In the limit of infinite scattering length, the three-body system has infinitely many bound states. If, however, the two-body subsystems have deep lying two-body bound states, the Efimov states lie over the corresponding thresholds for breakup. We have calculated the positions and widths of these Feshbach resonances for some simple potentials numerically and have extracted the systematics. We explore the possibility of observing such Efimov resonances in atom-diatom scattering experiments with alkali atoms.

We report the production of highly charged ions, ${\mathrm{C}}^{5+}$ and ${\mathrm{O}}^{6+},$ obtained by Coulomb explosion of propane and, respectively, carbon dioxide clusters, exposed to laser pulses of (1–$6)\times {10}^{14}\hspace{0.5em}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ intensity. At such intensities, only triply charged ions were created via tunneling ionization of isolated molecules. Carbon ions with energies of 1.2 keV and oxygen ions with energies of 2 keV have been detected. Some information about the explosion dynamics could be extracted from numerical simulations.

Using the numerical solution to the time-dependent Dirac equation we show that the effect of relativity on the usual Larmor period for an electron in a magnetic field can be enhanced drastically if a suitably scaled and aligned static electric field is added to the interaction. This electric field does not change the electron’s speed but leads to an elliptical spin precession due to relativity. This spin precession is accompanied by a position-dependent spin distribution.

We consider a Bose-Einstein condensate of ${}^7\mathrm{Li}$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double-well potential, obtained by adding a standing-wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation leads, in fact, to a macroscopic quantum superposition or Schrödinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called macroscopic quantum coherence (MQC); we study the effects of losses on MQC.

We calculate the critical temperature of a superfluid phase transition in a polarized Fermi gas of dipolar particles. In this case the order parameter is anisotropic and has a nontrivial energy dependence. Cooper pairs do not have a definite value of the angular momentum and are coherent superpositions of all odd angular momenta. Our results describe prospects for achieving the superfluid transition in single-component gases of fermionic polar molecules.

We discuss the low-energy shape oscillations of a magnetically trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g., as for ${}^{85}\mathrm{Rb}$ atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley et al., Nature (London) 412, 295 (2001)].

The breathing mode collective-excitation frequency of a Bose-Einstein condensate is studied in a highly asymmetric (two- or one-dimensional) trap by using a sum-rule method and a time-dependent variational method. The collective-excitation frequency of the breathing mode in the Thomas-Fermi limit for a purely two- or one-dimensional trap is reproduced by a general result for a three-dimensional trap. In the case of a two- or one-dimensional trap, we obtain the lowest-order correction for the excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction or the finiteness of the number of atoms.

We present a scheme to generate the polarization-entangled two-photon state $1/\sqrt{2}(|H〉|V〉+|V〉|H〉),$ which is of much interest in the field of quantum information processing. Furthermore, we demonstrate the capability of this concept in respect of a generalization to entangle N-photon states for interferometry and lithography. This scheme requires single-photon sources, linear optical elements, and a multifold coincidence detection.

We show that it is possible to demonstrate quantum nonlocality for three particles in a nonmaximally entangled state without using inequality. The nonlocal effect might be much stronger than that which a two-particle nonmaximally entangled state can exhibit, as described by Hardy [Phys. Rev. Lett. 71, 1665 (1993)].

It is impossible to discriminate four Bell states through local operations and classical communication, if only one copy is provided. To complete this task, two copies will suffice and be necessary. When n copies are provided, we show that the distillable entanglement is exactly $n-2.$

We show that an unknown quantum state of a mode of the cavity field that contains no more than N photons can be reversibly transferred into an entangled state of N Rydberg atoms. We utilize this technique to design quantum scissors for the cavity-field state. Encoding the cavity-field state into atoms may also be useful for teleportation or reconstruction of that state.