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...

We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the "dimension" provided by the internal atomic degrees of freedom, yielding a synthetic 2D lattice. Suitable laser-coupling between these internal states leads to a uniform magnetic flux within the 2D lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter butterfly spectrum and the chiral edge states of the associated Chern insulating phases.PACS numbers: 37.10. Jk, 03.75.Hh, 05.30.Fk Intense effort is currently devoted to the creation of gauge fields for electrically neutral atoms [1][2][3][4]. Following a number of theoretical proposals in presence [5][6][7][8][9][10][11][12][13] or in absence of optical lattices [14][15][16][17][18][19][20], synthetic magnetic fields have been engineered both in vacuum [21][22][23][24][25] and in periodic lattices [26][27][28][29]. The addition of a lattice offers the advantage to engineer extraordinarily large magnetic fluxes, typically of the order of one magnetic flux quantum per plaquette [5-7, 10, 11], which are out of reach using real magnetic fields in solid-state systems (e.g. artificial magnetic fields recently reported in graphene [30][31][32]). Such cold-atom lattice configurations will enable one to access striking properties, such as Hofstadter-like fractal spectra [33] and Chern insulating phases, in a controllable manner. Existing schemes for creating uniform magnetic fluxes require several laser fields and/or additional ingredients, such as tilted potentials [6,10], superlattices [11], or lattice-shaking methods [9,13,[34][35][36][37]. Experimentally, strong staggered magnetic flux configurations have been reported [26,27], and very recently also uniform ones [28,29]. Besides, an alternative route is offered by optical flux lattices [38][39][40][41].In all of these lattice schemes, the sites are identified by their location in space. This need not be the case: the available spatial degrees of freedom can be augmented by employing the internal atomic "spin" degrees of freedom as an extra, or synthetic, lattice-dimension [42]. Here we demonstrate that this extra dimension can support a uniform magnetic flux, and we propose a specific scheme using a 1D optical lattice along with Raman transitions within the atomic ground state manifold (Fig. 1). The flux is produced by a combination of ordinary tunneling in real space and laser-assisted tunneling in the extra dimension creating the necessary Peierls phases. Our proposal therefore extends the toolbox of existing techniques to create gauge potentials for cold atoms.The proposed scheme distinguished by the naturally sharp boundaries in the extra dimension, a feature which greatly simplifies the detection of chiral edge states resulting from the synthetic magnetic flux [43][44][45][46][47]. We demonstrate that the chiral motion of these topological edge states can be directly visualiz...

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.

We employ radio-frequency spectroscopy to investigate a polarized spin-mixture of ultracold 6 Li atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy E+, the effective mass m * , the residue Z and the decay rate Γ. Above a critical interaction, E+ is found to exceed the Fermi energy of the bath while m * diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.Landau's idea of mapping the behavior of impurity particles interacting with a complex environment into quasiparticle properties [1] plays a fundamental role in physics and materials science, from helium liquids [2] and colossal magnetoresistive materials [3,4] to polymers and proteins [5,6]. In the field of ultracold gases, the impurity problem and the associated concept of polaron quasiparticle have attracted over the last decade a growing interest [7][8][9][10]. Initiated with the investigation of polarized Fermi gases in the BEC-BCS crossover [11][12][13][14][15][16], the study of polaron physics has been extended to mass-imbalanced [17,18], low-dimensional fermionic systems [19], and also to bosonic environments [20][21][22]. The polaron properties are fundamentally relevant for understanding the more complex scenario of partially-polarized and balanced Fermi mixtures: the impurity limit exhibits some of the critical points of the full phase diagram, whose topology we can thus learn about by investigating polarized systems [8,16].While researchers initially focused on attractive interactions [14,15], more recently they have explored novel quasiparticles associated with repulsive interactions: these repulsive polarons [23][24][25][26][27] are centrally important for realizing repulsive many-body states [23,24,28,29] and therein exploring itinerant ferromagnetism [30][31][32]. In particular, if the polaron energy exceeds the Fermi energy of the surrounding medium, a fullyferromagnetic phase is favored against the paramagnetic Fermi liquid [23][24][25]27]. However, short-ranged strong repulsion always require an underlying weakly-bound molecular state, into which the system may rapidly decay [31,33], making the repulsive polaron an excited manybody state, whose theoretical and experimental investigation are challenging. In three dimensions, repulsive Fermi polarons have been first unveiled in a 6 Li -40 K mixture at a comparatively narrow Feshbach resonance [17], but they lack observation in the universal, broad * scazza@lens.unifi.it resonance case, for which the decay rate is expected to be the largest [10].In this Letter we report on reverse radio-frequency (RF) spectroscopy [17,34,35] experiments to unveil the existence and characterize the properties of repulsive polarons in a polarized Fermi mixture of lithium ...

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Molecular transport in living systems regulates numerous processes underlying biological function.\ud Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive\ud motion been associated with nonergodic behavior. These findings have stimulated new questions for their\ud implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living\ud systems? Which physical mechanisms generate it? What are its implications for biological function? Here,\ud we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular\ud adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition\ud capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this\ud behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to\ud continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity,\ud consistent with the current view of the cell membrane as a highly dynamic and diverse environment.\ud Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all\ud our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying\ud different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing\ud a strong link between nonergodicity and biological function. These results underscore the role of disorder\ud in cell membranes and its connection with function regulation. Because of its generality, our approach\ud offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity\ud might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.Peer ReviewedPostprint (published version

Non-ergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped, but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the Lévy walk.PACS numbers: 05.40.Fb,87.10.Mn,87.15.Vv Disordered systems exhibiting subdiffusion have been studied intensively for decades [1][2][3][4][5]. In these systems the ensemble averaged mean squared displacement (EMSD) grows for large times aswhereas normal diffusion has β = 1. A broad class of systems show weak ergodicity breaking, that is, the EMSD and the time averaged mean squared displacement (TMSD) differ. The prototypical framework for describing non-ergodic subdiffusion is the heavy-tailed continuous-time random walk (CTRW) [6][7][8], in which a particle takes steps at random time intervals that are independently distributed with densityψ(τ ) has infinite mean, which leads to a subdiffusive EMSD β = α. Furthermore, the CTRW shows weak ergodicity breaking because the particle experiences trapping times on the order of the observation time T no matter how large T is. The CTRW was introduced to describe charge carriers in amorphous solids [8], and has found wide application since. Recently, there has been a surge of work on the CTRW [9-12], triggered by single particle tracking experiments in biological systems [13][14][15][16][17] that display signatures of non-ergodicity. A different approach to subdiffusion is to assume a deterministic diffusivity (i.e. diffusion coefficient) that is inhomogeneous in time [18,19], or space [20][21][22][23][24]. But in fact, the anomalous diffusion in these works is also nonergodic. Formulating models of inhomogeneous diffusivity is timely and important, given that recently measured spatial maps in the cell membrane often show patches of strongly varying diffusivity [25][26][27][28][29][30]. The presence of randomness in these experimental maps inspired us to consider disordered media. Thus, in this manuscript, we introduce a class of models of ordinary diffusion with a diffusivity that varies randomly but is constant on patches of random sizes. We call these models random patch models or just patch models. These models show non-ergodic subdiffusion, due to the diffusivity effectively changing at random times with a heavy-tailed distribution like that in (2) [31]. Note that ergodicity breaking is usually ascribed to energetic disorder that immobilizes the particle, e.g. via transient chemical binding [8,32,33]. But, in the patch models discussed here the particle constantly undergoes Brownian motion. The anomaly is i...

Topology and disorder have deep connections and a rich combined influence on quantum transport. In order to probe these connections, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. We characterize the system's topology through measurement of the mean chiral displacement of the bulk density extracted from quench dynamics. We find evidence for the topological Anderson insulator phase, in which the band structure of an otherwise trivial wire is driven topological by the presence of added disorder. In addition, we observed the robustness of topological wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform will enable future realizations of strongly interacting topological fluids.Topology and disorder share many surprising connections, from the formal similarity of one-dimensional (1D) pseudo-disordered lattices and two-dimensional (2D) integer quantum Hall Hofstadter lattices [1, 2], to the deep connection between the symmetry classes of random matrices [3] and the classification of symmetry protected topological phases [4]. Recently, there has been great interest in exploring both disorder [5] and topology [6] through quantum simulation, stemming from the dramatic influences that these ingredients can have, separately, on the localization properties of quantum particles [7, 8]. When combined, disorder and topology can have a rich and varied influence on quantum transport [9]. Indeed, one of the hallmark features of topological insulators (TIs) is the topologically protected boundary states that are immune to weak disorder [10]. The robust conductance of such boundary states, such as the 1D edge states of integer quantum Hall systems [8], or the 2D surface states of three-dimensional (3D) TIs [11], serves as an important counterexample to the inevitability of localization in low-dimensional disordered systems [7,12]. Despite the robustness to weak disorder, a change in topology can result from strong disorder, and unusual critical phenomena related to the unwinding of the topology can accompany such transitions [13,14].Surprisingly, static disorder can also induce nontrivial topology when added to a trivial band structure. This disorder-driven topological phase, known as the topological Anderson insulator (TAI), was first predicted to occur in metallic 2D HgTe/CdTe quantum wells [15]. There has been much interest in the TAI phase over the past decade [15][16][17], and many theoretical studies have shown the TAI phenomenon to be quite general, emerging across a range of disordered systems [18][19][20][21]. However, due to the lack of precise control over disorder in real materials, and the difficulty in engineering both topology and disorder in most quantum simulators, the TAI has so far evaded experimental realization.We engineer synthetic 1D chiral sy...