We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and we derive a classical sum rule which allows one to predict the chaotic transport velocity from properties of regular phase-space components. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one to resolve the classical phase-space structure. We derive a quantum sum rule analogous to the classical one, based on the relation between quantum transport and band structure.

We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a “quantum Hall” regime where the density profile is a Gaussian in the $\mathrm{xy}$ plane and an inverted parabolic profile along $z$. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.

We present a method for decomposing a wave field, described by a second-order ordinary differential equation, into a radiative component and a nonradiative one, using a biorthonormal system related to the problem under consideration. We show that it is possible to select a special system such that the wave field is purely radiating. We discuss the differences and analogies with approaches which, unlike our approach, start from the corresponding sources of the field.

We propose a scalable procedure to generate superpositions of motional coherent states and also entangled vibronic states in $N$ trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies on decoherence.

We find that in very elongated 3D trapped Bose gases, even at temperatures far below the BEC transition temperature $T_c$, the equilibrium state will be a 3D condensate with fluctuating phase (quasicondensate). At sufficiently low temperatures the phase fluctuations are suppressed and the quasicondensate turns into a true condensate. The presence of the phase fluctuations allows for extending thermometry of Bose-condensed gases well below those established in current experiments.

We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an arbitrarily high temperature. We find the time and temperature variation of a lower bound on the amount of entanglement produced and study the classical correlations quantified by the mutual information.

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state $|1〉$ was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of $(55\pm 1)\%$. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.

Van Hove’s theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.

We report the first observation of the quantum Zeno and anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.

We formulate a dynamical fluctuation theory for stationary nonequilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a nonequilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems.

We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, $W$, and Greenberger-Horne-Zeilinger states. These classes are successively embedded into each other. We show that contrary to pure $W$-type states, the mixed $W$ class is not of measure zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the $W$ class. Finally, we present a new family of PPTES “edge” states with maximal ranks.

We report on the atom optical manipulation of an atom laser beam. Reflection, focusing, and its storage in a resonator are demonstrated. Precise and versatile mechanical control over an atom laser beam propagating in an inhomogeneous magnetic field is achieved by optically inducing spin flips between atomic ground states with different magnetic moment. The magnetic force acting on the atoms can thereby be effectively switched on and off. The surface of the atom optical element is determined by the resonance condition for the spin flip in the inhomogeneous magnetic field. More than $98\%$ of the incident atom laser beam is reflected specularly.

We investigate $\mathrm{U}\left(N\right)$ Chern-Simons theories on the noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized $\kappa =n/2\mathrm{}\pi$ with an integer $n$. This is a surprise for the $\mathrm{U}\left(1\right)$ gauge theory. When uniform background charge density ${\rho }_e$ is present, the quantization rule changes to $\kappa +{\rho }_e\theta =n/2\mathrm{}\pi$ with the noncommutative parameter $\theta$. With the exact expression for the angular momentum, we argue in the $\mathrm{U}\left(1\right)$ theory that charged particles in the symmetric phase carry fractional spin $1/2n$ and vortices in the broken phase carry half-integer or integer spin $-n/2\mathrm{}$.

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.

The ground state and its structure for a rotating, harmonically trapped $N$-boson system with a weak repulsive contact interaction are studied as the angular momentum $L$ increases up to $3N$. We show that the ground state is generally a fragmented condensate due to angular momentum conservation. In response to an (arbitrarily weak) asymmetric perturbation of the trap, however, the fragmented ground state can be transformed into a single condensate state. We manifest this intrinsic instability by calculating the conditional probability distributions, which show patterns analogous to the boson density distributions predicted by mean-field theory.

We study the global phase diagram of the infinite-range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram shows first-order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.

We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions.

We show the impossibility of reflection and refraction phenomena at linear diffusion-wave-field (DWF) interfaces. Instead, interfacial flux expressions are derived which involve coherent accumulation or depletion phenomena subject to an interface flux conservation principle. The conditions for reflectionless and refractionless interfaces are the parabolic nature and the concomitant Fickian constitutive relations satisfied by DWFs. Simulations show that the reflection and Snell's laws can be adequate approximations only under near-normal incidence conditions, in agreement with published experimental evidence in wide areas of biomedical, electronic, and materials physics.