For nearly fifty years, atomic resonances have been employed to stabilize electromagnetic field frequency. Here, a dynamical Rabi resonance, associated with an alkali atom's ground state hyperfine transition, is used to stabilize electromagnetic field strength: A 7% sinusoidal variation was superimposed on a microwave field's strength, and through atomic stabilization this variation was reduced to 0.1%. Although the method is demonstrated with microwave fields, the technique could also be employed to stabilize optical fields via Rabi resonances associated with electronic transitions in atoms or molecules.

We study the output properties of a pulsed atom laser consisting of an interacting Bose-Einstein condensate in a magnetic trap and an additional rf field transferring atoms to an untrapped Zeeman sublevel. For weak output coupling we calculate the dynamics of the decaying condensate population, of its chemical potential, and the velocity of the output atoms analytically.

Reconsidering the variational procedure for uniaxial systems modeled by continuous free energy functionals, we derive new general conditions for thermodynamic extrema. The utility of these conditions is briefly illustrated on the models for the classes I and II of incommensurate-commensurate systems.

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

The quantum Liouville equation for an $n$-level atomic system driven by external fields has a nontrivial kinematic structure; the quantities $\mathrm{tr}{\rho }^j$, $j=1,2,\dots ,n$ remain constant in time, independent of the Hamiltonian. These invariants are physically significant; the qualitative character of the solution depends on their existence. A generic numerical method will not, in general, preserve these invariants. We present a numerical technique which evolves the density matrix via unitary transformations thus exactly preserving these invariants to all orders in the time step.

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum nonseparability. The possibility that negative (virtual) information can be carried by entangled particles suggests a consistent interpretation of quantum informational processes.

We have observed a sharp and nonmonotonic crossover of the susceptibility (osmotic compressibility) from mean-field to Ising critical behavior in semidilute solutions of polystyrene in deuterocyclohexane as the temperature decreases from the $\Theta$ region down to the critical temperature of the phase separation. We describe this crossover in terms of a competition between the long-range but finite intramolecular correlations of monomers in the polymer chain and the diverging correlation length of concentration fluctuations.

Several systems are exhibited in which the establishment of local realism violation is achieved even when some of the detectors employed are insensitive. The insensitive detectors are homodyne detectors whose task is to determine if the amplitude of a coherent state is $\alpha$ or $-\alpha$. This determination can be achieved with low quantum efficiency detectors when $|\alpha |$ is large. The other detectors employed determine whether there is an even number or an odd number of photons in a state. These detectors are sensitive since they are required to resolve the difference of one photon. For the examples given, the local realism violation is not diminished as $|\alpha |$ is increased.

We study a quantum particle, for which the duration $\tau$ it spends in some region of space is controlled by a meter, e.g., a Larmor clock. The particle is described by a wave function $\Psi (x,t\mid \tau )$, with $|\Psi (x,t\mid \tau ){|}^2$ giving the distribution of the meter's readings at location $x$. The wave function satisfies the “clocked” Schrödinger equation, which we solve numerically for the cases of bound motion and wave packet scattering. The method is shown to be a natural extension of the conventional quantum mechanics.

We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel “macroscopic quantum self-trapping” effect.

It is shown that certain sum rule identities exist which relate correlation functions for n Potts spins on the boundary of a planar lattice for $n\ge 4$. Explicit expressions of the identities are obtained for $n=4\mathrm{}$. It is also shown that the identities provide the missing link needed for a complete determination of the duality relation for the n-point boundary correlation function. The $n=4\mathrm{}$ duality relation is obtained explicitly. More generally we deduce the number of sum rule identities as well as a cyclic inversion relation for any n, and conjecture on the general form of the duality relation.

We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.

A measurement scheme is proposed to determine the state of a bosonic two-mode system completely. Without relying on the existence of a reference field, we reconstruct the quantum state from joint number measurement only, in case $[\mathit{\rho },{\hat{N}}_{\mathrm{tot}}]=0\mathrm{}$. Based on an analogy to angular momentum, we have obtained an explicit inversion procedure for the density matrix of the system and discuss its application.

A coherent coupler is proposed to spin a Bose-Einstein condensate composed of ultracold alkali atoms into a vortex state. The proposal is based on a Raman transition induced by two copropagating ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized Laguerre-Gaussian laser beams with different frequencies. We show that the transfer of angular momentum of photons to the condensed atoms through a Raman transition leads to a coherent coupling of the ground-state condensate to a rotating condensate in a vortex state. The detection of such a vortex state is discussed.

The conflict between Bohr's assertion that the magnetic moment of the electron cannot be measured with experiments based on the concept of classical trajectories, and the measurement of the magnetic moment of electrons in a modified Penning trap by Dehmelt et al. has led us to reevaluate other implications of Bohr's assertion. We show that, contrary to the analysis of Bohr and Pauli, the assumption of classical trajectories in a Stern-Gerlach–like device can result in a high degree of spin separation for an electron beam. This effect may persist within a fully quantum-mechanical analysis. The magnetic fields considered are such that a tabletop Stern-Gerlach electron spin filter is feasible.

An optimization algorithm is presented which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively. It works particularly well when it is applied to an archive of samples instead of to a single one. We demonstrate for the traveling salesman problem that this algorithm is far more efficient than the usual simulated annealing; our implementation can compete concerning speed with recent, very fast genetic local search algorithms.

We present novel stable solutions which are soliton pairs and trains of the 1D complex Ginzburg-Landau equation (CGLE), and analyze them. We propose that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations. We present a two-dimensional phase plane (“interaction plane”) for analyzing the stability properties and general dynamics of two-soliton solutions of the CGLE.

The Euclidean path-integral formalism is studied for the system without any unstable state. While the usual bounce calculation yields a fake complex energy spectrum, proper account of the global structure of the functional space is shown to lead to the real eigenvalues. For this purpose, the valley instanton is constructed by the proper valley method and the dilute-gas approximation is carried out. This establishes a general imaginary-time formalism, unifying the instanton and the bounce method.

We study the damping of low-lying collective excitations of condensates in a weakly interacting Bose gas model within the framework of an imaginary time path integral. A general expression of the damping rate has been obtained for both the very low temperature regime and the higher temperature regime. For the latter, the result is new and applicable to recent experiments. Theoretical predictions for the damping rate are compared with the experimental values.

We present analytical and numerical results suggesting that the optimal path in an energy landscape in the strong disorder limit is in the universality class of the shortest path in invasion percolation with trapping. Our results imply that, in contrast to common belief, invasion percolation with trapping and regular percolation in $d=3\mathrm{}$ are in different universality classes.