Ultracold Fermi gases with tuneable interactions represent a unique test bed to explore the many-body physics of strongly interacting quantum systems [1-4]. In the past decade, experiments have investigated a wealth of intriguing phenomena, and precise measurements of groundstate properties have provided exquisite benchmarks for the development of elaborate theoretical descriptions. Metastable states in Fermi gases with strong repulsive interactions [5-11] represent an exciting new frontier in the field. The realization of such systems constitutes a major challenge since a strong repulsive interaction in an atomic quantum gas implies the existence of a weakly bound molecular state, which makes the system intrinsically unstable against decay. Here, we exploit radio-frequency spectroscopy to measure the complete excitation spectrum of fermionic 40 K impurities resonantly interacting with a Fermi sea of 6 Li atoms. In particular, we show that a welldefined quasiparticle exists for strongly repulsive interactions. For this "repulsive polaron" [9, 12, 13] we measure its energy and its lifetime against decay. We also probe its coherence properties by measuring the quasiparticle residue. The results are well described by a theoretical approach that takes into account the finite effective range of the interaction in our system. We find that a non-zero range of the order of the interparticle spacing results in a substantial lifetime increase. This major benefit for the stability of the repulsive branch opens up new perspectives for investigating novel phenomena in metastable, repulsively interacting fermion systems.Landau's theory of a Fermi liquid [14] and the underlying concept of quasiparticles lay at the heart of our understanding of interacting Fermi systems over a wide range of energy scales, including liquid 3 He, electrons in metals, atomic nuclei, and the quark-gluon plasma. In the field of ultracold Fermi gases, the normal (non-superfluid) phase of a strongly interacting system can be interpreted in terms of a Fermi liquid [15][16][17][18]. In the population-imbalanced case, quasiparticles coined Fermi polarons are the essential building blocks and have been studied in detail experimentally [16] for attractive interactions. Recent theoretical work [9,12,13] has suggested a novel quasiparticle associated with repulsive interactions. The properties of this repulsive polaron are of fundamental importance for the prospects of repulsive many-body states. A crucial question for the feasibility of future experiments is the stability against decay into molecular excitations The vertical lines at 1/(κ F a) = ±1 indicate the width of the strongly interacting regime. The inset illustrates our rf spectroscopic scheme where the impurity is transferred from a noninteracting spin state |0 to the interacting state |1 . [11,12,19]. Indeed, whenever a strongly repulsive interaction is realized by means of a Feshbach resonance [20], a weakly bound molecular state is present into which the system may rapidly decay.Our system consi...

The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ^{39}K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions--the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.

Methotrexate is used to treat autoimmune diseases and malignancies, including acute lymphoblastic leukemia (ALL). Inter-individual variation in clearance of methotrexate results in heterogeneous systemic exposure, clinical efficacy, and toxicity. In a genome-wide association study of children with ALL, we identified SLCO1B1 as harboring multiple common polymorphisms associated with methotrexate clearance. The extent of influence of rare versus common variants on pharmacogenomic phenotypes remains largely unexplored. We tested the hypothesis that rare variants in SLCO1B1 could affect methotrexate clearance and compared the influence of common versus rare variants in addition to clinical covariates on clearance. From deep resequencing of SLCO1B1 exons in 699 children, we identified 93 SNPs, 15 of which were nonsynonymous (NS). Three of these NS SNPs were common, with a minor allele frequency (MAF) >5%, one had low frequency (MAF 1%-5%), and 11 were rare (MAF <1%). NS SNPs (common or rare) predicted to be functionally damaging were more likely to be found among patients with the lowest methotrexate clearance than patients with high clearance. We verified lower function in vitro of four SLCO1B1 haplotypes that were associated with reduced methotrexate clearance. In a multivariate stepwise regression analysis adjusting for other genetic and non-genetic covariates, SLCO1B1 variants accounted for 10.7% of the population variability in clearance. Of that variability, common NS variants accounted for the majority, but rare damaging NS variants constituted 17.8% of SLCO1B1's effects (1.9% of total variation) and had larger effect sizes than common NS variants. Our results show that rare variants are likely to have an important effect on pharmacogenetic phenotypes.

We develop an extension of the well-known BCS-theory to systems with trapped fermions. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations.Considerable interest in the field of ultracold gases has been sparked by the achievement of Bose-Einstein condensation in the bosonic systems 87 Rb, 23 Na and 7 Li in 1995 [1]. Recently, several experimental groups have extended these experiments to the case of trapped fermions. As a first step, it is attempted to achieve a degenerate Fermi gas. In a possible next step, the celebrated Bardeen-Cooper-Schrieffer (BCS) phase transition could be observed. A promising candidate for achieving this transition is the isotope 6 Li: By trapping 6 Li in two hyperfine states, one can take advantage of the strong (attractive) interactions due to s−wave scattering between atoms in different hyperfine states.BCS-pairing occurs in a multitude of physical systems (e.g. electrons in metals, electron-hole exciton systems and neutron-proton systems) which share the characteristic that the formation of bound states (Cooper pairs) between the strongly coupled constituents is energetically favorable [2]. For ultracold atoms in traps, the interactions are much better-known than in most of the above mentioned systems [3]. Therefore, the achievement of a superfluid state in these systems opens up the possibility of testing our theoretical models, in particular, the validity of the BCS theory itself. Furthermore, the interaction strength and the density of the gas are experimentally tunable which, in principle, makes it possible to study the crossover from BCS pairing to Bose-Einstein condensation of bosonic pairs [4].To describe experiments with trapped fermions, one has to extend present theories (i) to include the discrete nature of the quantum energy levels of the particles in the trap, and (ii) to take into account the interactions specific to the atomic case. We consider a model of trapped fermions with two internal states. At low energies, the p-wave interaction between atoms in the same internal state is negligible compared to the s-wave interaction between atoms in different internal states. The latter interaction is characterized at low energies and for dilute gases (k F r e < 1, where r e is the effective range of the interaction, k F the Fermi wavevector) by a single parameter, the scattering length a. In order to achieve pair formation the interaction has to be strong; here we assume |a| ≫ r e [5]. In this case, an excellent model for the atomic interactions is provided by the pseudo-potential discussed in [6]. This model potential allows us to obtain an extension of the BCS theory to inhomogeneous systems which...

We investigate the zero-temperature properties of an impurity particle interacting with a Bose-Einstein condensate (BEC), using a variational wave function that includes up to two Bogoliubov excitations of the BEC. This allows one to capture three-body Efimov physics, as well as to recover the first nontrivial terms in the weak-coupling expansion. We show that the energy and quasiparticle residue of the dressed impurity (polaron) are significantly lowered by three-body correlations, even for weak interactions where there is no Efimov trimer state in a vacuum. For increasing attraction between the impurity and the BEC, we observe a smooth crossover from atom to Efimov trimer, with a superposition of states near the Efimov resonance. We furthermore demonstrate that three-body loss does not prohibit the experimental observation of these effects. Our results thus suggest a route to realizing Efimov physics in a stable quantum many-body system for the first time.

We analyze the properties of a single impurity immersed in a Fermi sea. At positive energy and scattering lengths, we show that the system possesses a well-defined but metastable excitation, the repulsive polaron, and we calculate its energy, quasiparticle residue and effective mass. From a thermodynamic argument we obtain the number of particles in the dressing cloud, illustrating the repulsive character of the polaron. Identifying the important 2-and 3-body decay channels, we furthermore calculate the lifetime of the repulsive polaron. The stability conditions for the formation of fully spin polarized (ferromagnetic) domains are then examined for a binary mixture of atoms with a general mass ratio. Our results indicate that mass imbalance lowers the critical interaction strength for phase-separation, but that very short quasiparticle decay times will complicate the experimental observation of itinerant ferromagnetism. Finally, we present the spectral function of the impurity for various coupling strengths and momenta.

We develop a systematic perturbation theory for the quasiparticle properties of a single impurity immersed in a Bose-Einstein condensate. Analytical results are derived for the impurity energy, effective mass, and residue to third order in the impurity-boson scattering length. The energy is shown to depend logarithmically on the scattering length to third order, whereas the residue and the effective mass are given by analytical power series. When the boson-boson scattering length equals the boson-impurity scattering length, the energy has the same structure as that of a weakly interacting Bose gas, including terms of the Lee-Huang-Yang and fourth order logarithmic form. Our results, which cannot be obtained within the canonical Fröhlich model of an impurity interacting with phonons, provide valuable benchmarks for many-body theories and for experiments.