Effects of atomic interactions on Quantum Accelerator Modes

We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.Comment: 4 pages, 6 figure

Quantum Accelerator Modes near Higher-Order Resonances

Quantum Accelerator Modes have been experimentally observed, and theoretically explained, in the dynamics of kicked cold atoms in the presence of gravity, when the kicking period is close to a half-integer multiple of the Talbot time. We generalize the theory to the case when the kicking period is sufficiently close to any rational multiple of the Talbot time, and thus predict new rich families of experimentally observable Quantum Accelerator Modes.Comment: Inaccurate reference [12] has been amende

Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model

We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked Rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to the nonlinear perturbation of the rotor's phase evolution. For an intermittent time regime, the nonlinearity even enhances the resonant quantum transport, leading to superballistic motion.Comment: 8 pages, 10 figures; to appear in Phys. Rev.

Decay of Quantum Accelerator Modes

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/hbar, are identified, depending on the resolution of KAM substructures that is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better resolution are available upon request to the authors); added reference for section

Stable Quantum Resonances in Atom Optics

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system, that are similar to those of solids, allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is {\em not} Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity.Comment: 5 pages, 3 figure

Arnol'd Tongues and Quantum Accelerator Modes

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.Comment: 20 pages, 6 encapsulated postscript figure

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.Comment: 4 pages, 5 figure

Effects of a nonlinear perturbation on dynamical tunneling in cold atoms

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is the driven pendulum, considered in ref.\cite{raiz1}, and the other is a variant of the well-known Kicked Rotator Model. In absence of the nonlinear perturbation, the system is invariant under some discrete symmetries and quantum dynamical tunnelling between symmetric classical islands is found. The presence of nonlinearity destroys tunnelling, breaking the symmetries of the system. Finally, further consequences of nonlinearity in the kicked rotator case are considered.Comment: 10 pages, 15 figure

Evidence of Distinct Tumour-Propagating Cell Populations with Different Properties in Primary Human Hepatocellular Carcinoma

Increasing evidence that a number of malignancies are characterised by tumour cell heterogeneity has recently been published, but there is still a lack of data concerning liver cancers. The aim of this study was to investigate and characterise tumour-propagating cell (TPC) compartments within human hepatocellular carcinoma (HCC).After long-term culture, we identified three morphologically different tumour cell populations in a single HCC specimen, and extensively characterised them by means of flow cytometry, fluorescence microscopy, karyotyping and microarray analyses, single cell cloning, and xenotransplantation in NOD/SCID/IL2Rγ/⁻ mice.The primary cell populations (hcc-1, -2 and -3) and two clones generated by means of limiting dilutions from hcc-1 (clone-1/7 and -1/8) differently expressed a number of tumour-associated stem cell markers, including EpCAM, CD49f, CD44, CD133, CD56, Thy-1, ALDH and CK19, and also showed different doubling times, drug resistance and tumorigenic potential. Moreover, we found that ALDH expression, in combination with CD44 or Thy-1 negativity or CD56 positivity identified subpopulations with a higher clonogenic potential within hcc-1, hcc-2 and hcc-3 primary cell populations, respectively. Karyotyping revealed the clonal evolution of the cell populations and clones within the primary tumour. Importantly, the primary tumour cell population with the greatest tumorigenic potential and drug resistance showed more chromosomal alterations than the others and contained clones with epithelial and mesenchymal features.Individual HCCs can harbor different self-renewing tumorigenic cell types expressing a variety of morphological and phenotypical markers, karyotypic evolution and different gene expression profiles. This suggests that the models of hepatic carcinogenesis should take into account TPC heterogeneity due to intratumour clonal evolution