Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

We have observed the superfluid phase transition in a strongly interacting Fermi gas via high-precision measurements of the local compressibility, density and pressure down to near-zero entropy. Our data completely determine the universal thermodynamics of strongly interacting fermions without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity. In particular, the heat capacity displays a characteristic lambda-like feature at the critical temperature of $T_c/T_F = 0.167(13)$. This is the first clear thermodynamic signature of the superfluid transition in a spin-balanced atomic Fermi gas. Our measurements provide a benchmark for many-body theories on strongly interacting fermions, relevant for problems ranging from high-temperature superconductivity to the equation of state of neutron stars.Comment: 11 pages, 8 figure

Direct Observation of the Superfluid Phase Transition in Ultracold Fermi Gases

Water freezes into ice, atomic spins spontaneously align in a magnet, liquid helium becomes superfluid: Phase transitions are dramatic phenomena. However, despite the drastic change in the system's behaviour, observing the transition can sometimes be subtle. The hallmark of Bose-Einstein condensation (BEC) and superfluidity in trapped, weakly interacting Bose gases is the sudden appearance of a dense central core inside a thermal cloud. In strongly interacting gases, such as the recently observed fermionic superfluids, this clear separation between the superfluid and the normal parts of the cloud is no longer given. Condensates of fermion pairs could be detected only using magnetic field sweeps into the weakly interacting regime. The quantitative description of these sweeps presents a major theoretical challenge. Here we demonstrate that the superfluid phase transition can be directly observed by sudden changes in the shape of the clouds, in complete analogy to the case of weakly interacting Bose gases. By preparing unequal mixtures of the two spin components involved in the pairing, we greatly enhance the contrast between the superfluid core and the normal component. Furthermore, the non-interacting wings of excess atoms serve as a direct and reliable thermometer. Even in the normal state, strong interactions significantly deform the density profile of the majority spin component. We show that it is these interactions which drive the normal-to-superfluid transition at the critical population imbalance of 70(5)%.Comment: 16 pages (incl. Supplemental Material), 5 figure

Phase diagram of a dilute fermion gas with density imbalance

We map out the phase diagram of a dilute two-component atomic fermion gas with unequal populations and masses under a Feshbach resonance. As in the case of equal masses, no uniform phase is stable for an intermediate coupling regime. For majority component heavier, the unstable region moves towards the BEC side. When the coupling strength is increased from the normal phase, there is an increased parameter space where the transition is into the FFLO state. The converse is true if the majority is light.Comment: Proceeding for M$^2$S-HTSC VIII meeting, July 9-14 2006, Dresden; To appear in Physica

Ultracold Dipolar Gas of Fermionic 23^{23}Na40^{40}K Molecules in their Absolute Ground State

We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1\Sigma^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 Debye. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of $^{23}$Na$^{40}$K molecules is in experimental reach.Comment: 5 pages, 5 figure

Two-Photon Pathway to Ultracold Ground State Molecules of 23^{23}Na40^{40}K

We report on high-resolution spectroscopy of ultracold fermionic \nak~Feshbach molecules, and identify a two-photon pathway to the rovibrational singlet ground state via a resonantly mixed \Bcres intermediate state. Photoassociation in a $^{23}$Na-$^{40}$K atomic mixture and one-photon spectroscopy on \nak~Feshbach molecules reveal about 20 vibrational levels of the electronically excited \ctrip state. Two of these levels are found to be strongly perturbed by nearby \Bsing states via spin-orbit coupling, resulting in additional lines of dominant singlet character in the perturbed complex {${\rm B}^1\Pi |v{=}4\rangle {\sim} {\rm c}^3\Sigma^+ | v{=}25\rangle$}, or of resonantly mixed character in {${\rm B}^1\Pi | v{=}12 \rangle {\sim}{\rm c}^3\Sigma^+ | v{=}35 \rangle$}. The dominantly singlet level is used to locate the absolute rovibrational singlet ground state ${\rm X}^1\Sigma^+ | v{=}0, J{=}0 \rangle$ via Autler-Townes spectroscopy. We demonstrate coherent two-photon coupling via dark state spectroscopy between the predominantly triplet Feshbach molecular state and the singlet ground state. Its binding energy is measured to be 5212.0447(1) \cm, a thousand-fold improvement in accuracy compared to previous determinations. In their absolute singlet ground state, \nak~molecules are chemically stable under binary collisions and possess a large electric dipole moment of $2.72$ Debye. Our work thus paves the way towards the creation of strongly dipolar Fermi gases of NaK molecules.Comment: 23 pages, 8 figure

Security politics and conspiracy theories in the emerging European state system (15th/ 16th c.)

"The article develops a new definition of conspiracy theory more apt for historicizing purposes than the existing systematic and philosophical ones. It shows that modern conspiracy narratives do appear only with the Renaissance. Also, 'security' as the aim of state and international politics became important only now during the Italian Renaissance while the term and concept had been nearly forgotten during the Middle Ages. The article shows then that both, security politics in practice and political language as well as modern conspiracy narratives belong to the new type of political communication which emerged with inter-territorial diplomacy in 15th century Italy (example: Lorenzo de' Medici) and with the first emerging information public sphere in 16th century Europe (example: conspiracism during the French Wars of Religion). The narrative modus of analyzing the present state of affairs, of constructing reality and of planning and conjecturing in that form of political communication is highly similar to the construction of conspiracy narratives. All modern forms of opposition between security and conspiracy theories can be seen as derivatives of that Renaissance constellation." (author's abstract

Insurances as part of "human security", their timescapes and spatiality

"In the present discussion on 'Human Security', Insurances have been only lately involved. The contribution starts with the assumption that Insurances are historically an especially fruitful object of research for the general question of the history of security regimes. It shows that, contrary to some suggestions held in risk sociology, early Mediterranean maritime insurances are to be judged rather as something completely different than the modern insurances from the 17th century onwards managed by merchants' companies and states. The latter belonged to a secular process of constructing a 'normal secure society' during enlightenment. The relationship between Timescapes, Spatiality and Insurances is analyzed: are Insurances per se an instrument of colonizing 'the future' because they are instrumental in calculating and constructing clearly defined 'risks'? or is that future orientation just one element, but is perhaps the wider socio-political context with its prevailing timescapes in which the insurance operations were embedded a changing one from pre- to postmodernity? Asking those questions the article contributes to an approach of using 'human security' as a heuristical device to explore the history of security production." (author's abstract)"In die gegenwärtige Diskussion über Human Security wurden Versicherungen erst spät einbezogen. Der Beitrag geht von der Annahme aus, dass Versicherungen ein historisch besonders fruchtbares Untersuchungsobjekt für die generelle Frage der Geschichte von Sicherheitsregimen ist. Er zeigt, dass, im Gegensatz zu dem, was die Risikosoziologie suggeriert, die frühe Seeversicherung im Mittelmeer heuristisch fruchtbar als etwas ganz anderes als neuzeitliche Versicherungen seit dem späten 17. Jh. zu begreifen sind, die nun von Versicherungsgesellschaften und Staaten eingerichtet und betrieben wurden. Die letzteren gehörten zum säkularen Prozess der Konstruktion einer 'sicheren Normalgesellschaft' während der Aufklärung. Das Verhältnis von Timescapes, Räumlichkeit und Versicherungen wird dann analysiert: Sind Versicherungen per se ein Instrument der Kolonisierung von Zukunft, weil sie die Kalkulation und Konstruktion klar definierter Risiken operationalisieren? - Oder ist diese Zukunftsausrichtung nur ein Element, und muss man nicht den weiteren soziopolitischen Kontext mit seinen vorherrschenden Timescapes, in die die Versicherungsoperationen eingebettet sind, ein sich wandelnder von der Vor- zur Spätmoderne? - Indem diese Fragen gestellt werden, trägt der Artikel dazu bei, human security nicht nur zu historisieren, sondern Elemente des gegenwartsbezogenen Konzepts als heuristischen Ansatz für die Geschichte von Sicherheitsproduktion zu benutzen." (Autorenreferat

Mediterranean transformations: From the security of mercantilist trading empires to a modern security regime.

A l’edat moderna, les relacions dels estats europeus amb l’Imperi otomà i el món mediterrani es caracteritzaven per una complexa xarxa de consolats que gaudien de privilegis atorgats mitjançant capitulacions pel sultà o els deys i beys nord-africans. La qüestió de la «seguretat» era sobretot entesa com a tranquil·litat en la pràctica lliure dels negocis i del comerç. La transformació d’aquesta situació entre finals del segle XVIII i fins aproximadament 1840 es caracteritza per una complexa superposició de continuïtat i ruptura entre les realitats de l’època moderna i les de la contemporània: la infraestructura del sistema consular va persistir durant molt de temps, mentre que la invasió d’Egipte (1797), les guerres napoleòniques, la guerra d’independència grega (iniciada el 1822) i la invasió d’Algèria (1830) van canviar profundament la regió. «Seguretat», de la manera que la van concebre polítics liberals com Chateaubriand, Benjamin Constant i Jeremy Bentham, es va convertir en un terme central per ordenar les noves realitats emergents en termes de política nacional i internacional. Al mateix temps, mentre la invasió de Grècia pels aliats europeus podria ser concebuda com la primera intervenció humanitària moderna, un tipus d’intervenció militar semblant a Algèria es concep com el primer acte modern de colonització amb ús de forces militars per part de França. Aquesta dialèctica entre les dues cares de l’intervencionisme sota diferents etiquetes com a excepció en les regles del sistema de relacions internacionals posteriors al Congrés de Viena produïa noves concepcions sobre la seguretat dins i fora del Mediterrani.In early modern times, European international relationships with the Ottoman Empire and in the Mediterranean were characterized by a complex system of consular networks privileged by the sultan or the North-African deys and beys by way of capitulations. Security was mostly addressed in terms of safety for the free practice of trade and commerce. The transformation of this situation between the late eighteenth century until around 1840 is characterized by complex entanglements of continuity and rupture between early modern and modern realities: the infrastructure of the consular system persisted for a long time, while the invasion of Egypt (1797), the continental Napoleonic Wars, the Greek War of Independence (starting 1822) and the invasion of Algeria (1830) were profoundly changing the region. «Security», as conceived by liberal men of politics like Chateaubriand, Benjamin Constant and Jeremy Bentham, became a central term to order the emerging new realities in terms of state and international politics. At the same time, while one conceives of the European allies’ invasion of Greece as perhaps the first modern humanitarian intervention, more or less the same type of military intervention in Algeria is conceived of as France’s first modern act of colonization by military forces. This dialectic of the two-sided face of interventionism under different labels as an exception from the rules of the post-Vienna system of international relations was producing new conceptions of security in and of the Mediterranean.En la Edad Moderna las relaciones de los Estados europeos con el Imperio otomano y el mundo mediterráneo se caracterizaron por una compleja red de consulados que gozaron de privilegios otorgados mediante capitulaciones del sultán o de los deys y beys del norte de África. La cuestión de la «seguridad» era entendida sobre todo como tranquilidad en la práctica libre de los nego- cios y del comercio. La transformación de esta situación entre principios del siglo XVIII hasta aproximadamente 1840 se caracterizó por un complejo entre- lazamiento de continuidad y ruptura entre las realidades de la época moderna y las de la contemporánea: la infraestructura del sistema consular persistió durante un largo tiempo, mientras que la invasión de Egipto (1797), las guerras napoleónicas, la guerra de independencia griega (iniciada en 1822) y la invasión de Argelia (1830) cambiaron profundamente la región. «Seguridad», tal como la concibieron hombres de política liberales como Chateaubriand, Benjamin Constant y Jeremy Bentham, se convirtió en un término central para ordenar las nuevas realidades emergentes en términos de política nacional e internacional. Al mismo tiempo, mientras que la invasión de Grecia por los aliados europeos podría ser concebida como la primera intervención humanitaria, una intervención militar parecida en Argelia se concibe como el primer acto de colonización con uso de fuerzas militares por parte de Francia. Esta dialéctica entre las dos caras del intervencionismo bajo diferentes etique- tas —como excepción en las reglas del sistema de relaciones internacionales posteriores al Congreso de Viena— produjo nuevas concepciones de la seguridad dentro y fuera del Mediterráneo