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Topology, geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov–Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators. The concept of topological protection has also become a salient ingredient in many schemes for quantum information processing and fault-tolerant quantum computation. The physical properties of such systems crucially depend on the symmetry group of the underlying holonomy. Here, we study a laser-cooled gas of strontium atoms coupled to laser fields through a four-level resonant tripod scheme. By cycling the relative phases of the tripod beams, we realize non-Abelian SU(2) geometrical transformations acting on the dark states of the system and demonstrate their non-Abelian character. We also reveal how the gauge field imprinted on the atoms impact their internal state dynamics. It leads to a thermometry method based on the interferometric displacement of atoms in the tripod beams. The symmetry group and geometric phase of a system are responsible for many quantum properties related to non-trivial topology. Here the authors show non-Abelian geometric phase in laser-coupled ultracold strontium atoms by using a tripod scheme.

Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two lithium isotopes, lithium-6 and lithium-7. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high-precision spectroscopy of these modes, we observe coherent energy exchange and measure the coupling between the two superfluids. Our observations can be captured theoretically using a sum-rule approach that we interpret in terms of two coupled oscillators.

Thermodynamics of a universal Fermi gas In principle, it is possible to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory. Previous work on the thermodynamics of a two-component Fermi gas (a system suited for such studies) led to thermodynamic quantities averaged over the trap. This paper reports a general experimental method that yields the equation of state of a uniform gas, providing new physical insights and enabling a detailed comparison with existing theories. In principle, it is possible to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory: previous work on the thermodynamics of a two-component Fermi gas (a system suited for such studies) led to thermodynamic quantities averaged over the trap. Now a general experimental method is reported that yields the equation of state of a uniform gas, providing new physical insights and enabling a detailed comparison with existing theories. One of the greatest challenges in modern physics is to understand the behaviour of an ensemble of strongly interacting particles. A class of quantum many-body systems (such as neutron star matter and cold Fermi gases) share the same universal thermodynamic properties when interactions reach the maximum effective value allowed by quantum mechanics, the so-called unitary limit 1 , 2 . This makes it possible in principle to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory. Previous work on the thermodynamics of a two-component Fermi gas led to thermodynamic quantities averaged over the trap 3 , 4 , 5 , making comparisons with many-body theories developed for uniform gases difficult. Here we develop a general experimental method that yields the equation of state of a uniform gas, as well as enabling a detailed comparison with existing theories 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 . The precision of our equation of state leads to new physical insights into the unitary gas. For the unpolarized gas, we show that the low-temperature thermodynamics of the strongly interacting normal phase is well described by Fermi liquid theory, and we localize the superfluid transition. For a spin-polarized system 16 , 17 , 18 , our equation of state at zero temperature has a 2 per cent accuracy and extends work 19 , 20 on the phase diagram to a new regime of precision. We show in particular that, despite strong interactions, the normal phase behaves as a mixture of two ideal gases: a Fermi gas of bare majority atoms and a non-interacting gas of dressed quasi-particles, the fermionic polarons 10 , 18 , 20 , 21 , 22 .

Interacting fermions are ubiquitous in nature, and understanding their thermodynamics is an important problem. We measured the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin-imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.

Background:Smith-Lemli-Opitz syndrome (SLOS) (MIM 270 400) is an autosomal recessive multiple congenital anomalies/mental retardation syndrome caused by mutations in the Δ7-sterol reductase (DHCR7, E.C.1.3.1.21) gene. The prevalence of SLOS has been estimated to range between 1:15000 and 1:60000 in populations of European origin.Methods and results:We have analysed the frequency, origin, and age of DHCR7 mutations in European populations. In 263 SLOS patients 10 common alleles (c.964-1G>C, p.Trp151X, p.Thr93Met, p.Val326Leu, p.Arg352Trp, p.Arg404Cys, p.Phe302Leu, p.Leu157Pro, p.Gly410Ser, p.Arg445Gln) were found to constitute approximately 80% of disease-causing mutations. As reported before, the mutational spectra differed significantly between populations, and frequency peaks of common mutations were observed in North-West (c.964-1G>C), North-East (p.Trp151X, p.Val326Leu) and Southern Europe (p.Thr93Met). SLOS was virtually absent from Finland. The analysis of nearly 8000 alleles from 10 different European populations confirmed a geographical distribution of DHCR7 mutations as reported in previous studies. The common Null mutations in Northern Europe (combined ca. 1:70) occurred at a much higher frequency than expected from the reported prevalence of SLOS. In contrast the most common mutation in Mediterranean SLOS patients (p.Thr93Met) had a low population frequency. Haplotypes were constructed for SLOS chromosomes, and for wild-type chromosomes of African and European origins using eight cSNPs in the DHCR7 gene. The DHCR7 orthologue was sequenced in eight chimpanzees (Pan troglodytes) and three microsatellites were analysed in 50 of the SLOS families in order to estimate the age of the three major SLOS-causing mutations.Conclusions:The results indicate a time of first appearance of c.964-1G>C and p.Trp151X some 3000 years ago in North-West and North-East Europe, respectively. The p.Thr93Met mutations on the J haplotype has probably first arisen approximately 6000 years ago in the Eastern Mediterranean. Together, it appears that a combination of founder effects, recurrent mutations, and drift have shaped the present frequency distribution of DHCR7 mutations in Europe.

The understanding of quantum many-body systems is one of the most daunting challenges of modern physics. Thanks to recent progress in cooling and trapping techniques, it is now possible to investigate their properties in the well controlled environment of ultra-cold gas systems. In this article, we present experimental results on the thermodynamics of strongly correlated Fermi gases and we provide a reinterpretation of the equation of state of a strongly polarized Fermi gas in terms of Fermi liquid parameters

In this article we discuss the accuracy of effective one-dimensional theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive within a fully many-body approach the effective Hamiltonian describing this class of systems and we calculate the beyond-mean field corrections to the energy of the ground state arising from virtual transitions towards excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one of magnitude larger than effective three-body interactions.By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters.