A minimisation approach for computing the ground state of Gross\u2013Pitaevskii systems

In this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross\u2013Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation

Cruising through molecular bound state manifolds with radio frequency

The emerging field of ultracold molecules with their rich internal structure is currently attracting a lot of interest. Various methods have been developed to produce ultracold molecules in pre-set quantum states. For future experiments it will be important to efficiently transfer these molecules from their initial quantum state to other quantum states of interest. Optical Raman schemes are excellent tools for transfer, but can be involved in terms of equipment, laser stabilization and finding the right transitions. Here we demonstrate a very general and simple way for transfer of molecules from one quantum state to a neighboring quantum state with better than 99% efficiency. The scheme is based on Zeeman tuning the molecular state to avoided level crossings where radio-frequency transitions can then be carried out. By repeating this process at different crossings, molecules can be successively transported through a large manifold of quantum states. As an important spin-off of our experiments, we demonstrate a high-precision spectroscopy method for investigating level crossings.Comment: 5 pages, 5 figures, submitted for publicatio

Evidence for a GABAergic system in rodent and human testis: Local GABA production and GABA receptors

The major neurotransmitter of the central nervous system, gamma-aminobutyric acid (GABA), exerts its actions through GABA(A), GABA(B) and GABA(C) receptors. GABA and GABA receptors are, however, also present in several non-neural tissues, including the endocrine organs pituitary, pancreas and testis. In the case of the rat testis, GABA appears to be linked to the regulation of steroid synthesis by Leydig cells via GABA(A) receptors, but neither testicular sources of GABA, nor the precise nature of testicular GABA receptors are fully known. We examined these points in rat, mouse, hamster and human testicular samples. RT-PCR followed by sequencing showed that the GABA-synthesizing enzymes glutamate decarboxylase (GAD) 65 and/or GAD67, as well as the vesicular GABA transporter vesicular inhibitory amino acid transporter (VIAAT/VGAT) are expressed. Testicular GAD in the rat was shown to be functionally active by using a GAD assay, and Western blot analysis confirmed the presence of GAD65 and GAD67. Interstitial cells, most of which are Leydig cells according to their location and morphological characteristics, showed positive immunoreaction for GAD and VIAAT/VGAT proteins. In addition, several GABA(A) receptor subunits (alpha1-3, beta1-3, gamma1-3), as well as GABAB receptor subunits R1 and R2, were detected by RT-PCR. Western blot analysis confirmed the results for GABA(A) receptor subunits beta2/3 in the rat, and immunohistochemistry identified interstitial Leydig cells to possess immunoreactive GABA(A) receptor subunits beta2/3 and alpha1. The presence of GABA(A) receptor subunit alpha1 mRNA in interstitial cells of the rat testis was further shown after laser microdissection followed by RT-PCR analysis. In summary, these results describe molecular details of the components of an intratesticular GABAergic system expressed in the endocrine compartment of rodent and human testes. While the physiological significance of this peripheral neuroendocrine system conserved throughout species remains to be elucidated, its mere presence in humans suggests the possibility that clinically used drugs might be able to interfere with testicular function. Copyright (C) 2003 S. Karger AG, Basel

Atom-molecule dark states in a Bose-Einstein condensate

We have created a dark quantum superposition state of a Rb Bose-Einstein condensate (BEC) and a degenerate gas of Rb$_2$ ground state molecules in a specific ro-vibrational state using two-color photoassociation. As a signature for the decoupling of this coherent atom-molecule gas from the light field we observe a striking suppression of photoassociation loss. In our experiment the maximal molecule population in the dark state is limited to about 100 Rb$_2$ molecules due to laser induced decay. The experimental findings can be well described by a simple three mode model.Comment: 4 pages, 6 figure

High spatial resolution and temporally resolved t(2) (*) mapping of normal human myocardium at 7.0 tesla: an ultrahigh field magnetic resonance feasibility study

Myocardial tissue characterization using T(2) (*) relaxation mapping techniques is an emerging application of (pre)clinical cardiovascular magnetic resonance imaging. The increase in microscopic susceptibility at higher magnetic field strengths renders myocardial T(2) (*) mapping at ultrahigh magnetic fields conceptually appealing. This work demonstrates the feasibility of myocardial T(2) (*) imaging at 7.0 T and examines the applicability of temporally-resolved and high spatial resolution myocardial T(2) (*) mapping. In phantom experiments single cardiac phase and dynamic (CINE) gradient echo imaging techniques provided similar T(2) (*) maps. In vivo studies showed that the peak-to-peak B(0) difference following volume selective shimming was reduced to approximately 80 Hz for the four chamber view and mid-ventricular short axis view of the heart and to 65 Hz for the left ventricle. No severe susceptibility artifacts were detected in the septum and in the lateral wall for T(2) (*) weighting ranging from TE = 2.04 ms to TE = 10.2 ms. For TE >7 ms, a susceptibility weighting induced signal void was observed within the anterior and inferior myocardial segments. The longest T(2) (*) values were found for anterior (T(2) (*) = 14.0 ms), anteroseptal (T(2) (*) = 17.2 ms) and inferoseptal (T(2) (*) = 16.5 ms) myocardial segments. Shorter T(2) (*) values were observed for inferior (T(2) (*) = 10.6 ms) and inferolateral (T(2) (*) = 11.4 ms) segments. A significant difference (p = 0.002) in T(2) (*) values was observed between end-diastole and end-systole with T(2) (*) changes of up to approximately 27% over the cardiac cycle which were pronounced in the septum. To conclude, these results underscore the challenges of myocardial T(2) (*) mapping at 7.0 T but demonstrate that these issues can be offset by using tailored shimming techniques and dedicated acquisition schemes

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state $|n=0>$, we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190 ms. We also report on ground state cooling of two ions.Comment: 12 pages, 6 figures. submitted to Journal of Modern Optics, Special Issue on Quantum Optics: Kuehtai 200

Entropy exchange in a mixture of ultracold atoms

We investigate experimentally the entropy transfer between two distinguishable atomic quantum gases at ultralow temperatures. Exploiting a species-selective trapping potential, we are able to control the entropy of one target gas in presence of a second auxiliary gas. With this method, we drive the target gas into the degenerate regime in conditions of controlled temperature by transferring entropy to the auxiliary gas. We envision that our method could be useful both to achieve the low entropies required to realize new quantum phases and to measure the temperature of atoms in deep optical lattices. We verified the thermalization of the two species in a 1D lattice.Comment: 5 pages, 4 figure

Repulsively bound atom pairs in an optical lattice

Throughout physics, stable composite objects are usually formed via attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report on the first observation of such an exotic bound state, comprised of a pair of ultracold atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under collisions with one another. Signatures of the pairs are also recognised in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, due to the presence of strong decay channels. These results exemplify on a new level the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model, a correspondence which is vital for future applications of these systems to the study of strongly correlated condensed matter systems and to quantum information.Comment: 5 pages, 4 figure