Shape oscillation of a rotating Bose-Einstein condensate

We present a theoretical and experimental analysis of the transverse monopole mode of a fast rotating Bose-Einstein condensate. The condensate's rotation frequency is similar to the trapping frequency and the effective confinement is only ensured by a weak quartic potential. We show that the non-harmonic character of the potential has a clear influence on the mode frequency, thus making the monopole mode a precise tool for the investigation of the fast rotation regime

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp

Vortex Rings in Fast Rotating Bose-Einstein Condensates

When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex phase appears, that is the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii energy on the unit disc. In particular we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold there are vortices in the condensate. We prove that they gather along a particular circle on which they are evenly distributed. This is done by providing new upper and lower bounds to the GP energy.Comment: to appear in Archive of Rational Mechanics and Analysi

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all figures, in text (especially in Sec III) and in Reference

From Rotating Atomic Rings to Quantum Hall States

Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the emblematic strongly correlated quantum Hall regime. The routes followed so far essentially rely on thermodynamics, i.e. imposing the proper Hamiltonian and cooling the system towards its ground state. In rapidly rotating 2D harmonic traps the role of the transverse magnetic field is played by the angular velocity. For particle numbers significantly larger than unity, the required angular momentum is very large and it can be obtained only for spinning frequencies extremely near to the deconfinement limit; consequently, the required control on experimental parameters turns out to be far too stringent. Here we propose to follow instead a dynamic path starting from the gas confined in a rotating ring. The large moment of inertia of the fluid facilitates the access to states with a large angular momentum, corresponding to a giant vortex. The initial ring-shaped trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum Hall regime. We provide clear numerical evidence that for a relatively broad range of initial angular frequencies, the giant vortex state is adiabatically connected to the bosonic $\nu=1/2$ Laughlin state, and we discuss the scaling to many particles.Comment: 9 pages, 5 figure

Vortices in multicomponent Bose-Einstein condensates

We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on that in two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross-Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose-Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose-Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.Comment: 69 pages, 25 figures, Invited review article for International Journal of Modern Physics

Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R) (2004)] for the vortex distribution, a consequence of which is that the vortex distribution is strongly inhomogeneous close to the critical speed and gradually homogenizes when the rotation speed is increased. From the mathematical point of view, a novelty of our approach is that we do not use any compactness argument in the proof, but instead provide explicit estimates on the difference between the vorticity measure of the GP ground state and the minimizer of a certain renormalized energy functional.Comment: 41 pages, journal ref: Communications in Mathematical Physics: Volume 321, Issue 3 (2013), Page 817-860, DOI : 10.1007/s00220-013-1697-

Identification and structural analysis of C-terminally truncated collapsin response mediator protein-2 in a murine model of prion diseases

<p>Abstract</p> <p>Background</p> <p>Prion diseases are fatal neurodegenerative disorders that accompany an accumulation of the disease-associated form(s) of prion protein (PrP^Sc) in the central nervous system. The neuropathological changes in the brain begin with focal deposits of PrP^Sc, followed by pathomorphological abnormalities of axon terminal degeneration, synaptic loss, atrophy of dendritic trees, and eventual neuronal cell death in the lesions. However, the underlying molecular basis for these neuropathogenic abnormalities is not fully understood.</p> <p>Results</p> <p>In a proteomic analysis of soluble proteins in the brains of mice challenged intracerebrally with scrapie prion (Obihiro I strain), we found that the amount of the full-length form of collapsin response mediator protein-2 (CRMP-2; 61 kDa) decreased in the late stages of the disease, while the amount of its truncated form (56 kDa) increased to comparable levels observed for the full-length form. Detailed analysis by liquid chromatography-electrospray ionization-tandem mass spectrometry showed that the 56-kDa form (named CRMP-2-ΔC) lacked the sequence from serine⁵¹⁸to the C-terminus, including the C-terminal phosphorylation sites important for the regulation of axonal growth and axon-dendrite specification in developing neurons. The invariable size of the mRNA transcript in Northern blot analysis suggested that the truncation was due to post-translational proteolysis. By overexpression of CRMP-2-ΔC in primary cultured neurons, we observed the augmentation of the development of neurite branch tips to the same levels as for CRMP-2^T514A/T555A, a non-phosphorylated mimic of the full-length protein. This suggests that the increased level of CRMP-2-ΔC in the brain modulates the integrity of neurons, and may be involved in the pathogenesis of the neuronal abnormalities observed in the late stages of the disease.</p> <p>Conclusions</p> <p>We identified the presence of CRMP-2-ΔC in the brain of a murine model of prion disease. Of note, C-terminal truncations of CRMP-2 have been recently observed in models for neurodegenerative disorders such as ischemia, traumatic brain injury, and Wallerian degeneration. While the structural identity of CRMP-2-ΔC in those models remains unknown, the present study should provide clues to the molecular pathology of degenerating neurons in prion diseases in connection with other neurodegenerative disorders.</p

CRMP5 Regulates Generation and Survival of Newborn Neurons in Olfactory and Hippocampal Neurogenic Areas of the Adult Mouse Brain

The Collapsin Response Mediator Proteins (CRMPs) are highly expressed in the developing brain, and in adult brain areas that retain neurogenesis, ie: the olfactory bulb (OB) and the dentate gyrus (DG). During brain development, CRMPs are essentially involved in signaling of axon guidance and neurite outgrowth, but their functions in the adult brain remain largely unknown. CRMP5 has been initially identified as the target of auto-antibodies involved in paraneoplasic neurological diseases and further implicated in a neurite outgrowth inhibition mediated by tubulin binding. Interestingly, CRMP5 is also highly expressed in adult brain neurogenic areas where its functions have not yet been elucidated. Here we observed in both neurogenic areas of the adult mouse brain that CRMP5 was present in proliferating and post-mitotic neuroblasts, while they migrate and differentiate into mature neurons. In CRMP5−/− mice, the lack of CRMP5 resulted in a significant increase of proliferation and neurogenesis, but also in an excess of apoptotic death of granule cells in the OB and DG. These findings provide the first evidence that CRMP5 is involved in the generation and survival of newly generated neurons in areas of the adult brain with a high level of activity-dependent neuronal plasticity