The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter [1]. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field [2]. Although an implementation in a material was considered unlikely, it has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors [2][3][4][5][6]. Here we report on the experimental realisation of the Haldane model and the characterisation of its topological band-structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry as well as inversion symmetry. The former is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position [7]. For the latter, we create an energy offset between neighbouring sites [8]. Breaking either of these symmetries opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berrycurvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between both broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows for dynamically tuning topological properties, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realise spin-dependent topological Hamiltonians.In a honeycomb lattice symmetric under time-reversal and inversion, the two lowest bands are connected at two Dirac points. Each broken symmetry leads to a gapped energy-spectrum. F. D. M. Haldane realised that the resulting phases are topologically distinct: A broken inversion symmetry (IS), caused by an energy offset between the two sublattices, leads to a trivial band-insulator at half-filling. Time-reversal symmetry (TRS) can be broken by complex next-nearest-neighbour tunnel couplings (Fig. 1a). The corresponding staggered magnetic fluxes sum up to zero in one unit-cell, thereby preserving the translation symmetry of the lattice. This gives rise to a topological Chern-insulator, where a non-zero Hall conductance appears despite the absence of a net magnetic field [1,2]. When both symmetries are broken, a topological phase transition connects two regimes with a distinct topological invariant, the Chern number, which changes from 0 to ±1, see Fig. 1b. There, the gap closes at a single Dirac point. These transitions have attracted great interest, as they cannot be described by Landau's theory of phase transitions, owing to the ...

Point contacts provide simple connections between macroscopic particle reservoirs. In electric circuits, strong links between metals, semiconductors or superconductors have applications for fundamental condensed-matter physics as well as quantum information processing. However for complex, strongly correlated materials, links have been largely restricted to weak tunnel junctions. Here we study resonantly interacting Fermi gases connected by a tunable, ballistic quantum point contact, finding a non-linear current-bias relation. At low temperature, our observations agree quantitatively with a theoretical model in which the current originates from multiple Andreev reflections. In a wide contact geometry, the competition between superfluidity and thermally activated transport leads to a conductance minimum. Our system offers a controllable platform for the study of mesoscopic devices based on strongly interacting matter. PACS numbers:The effect of strong interactions between the constituents of a quantum many-body system is at the origin of several challenging questions in physics. Whilst the ground states of strongly interacting systems are increasingly better understood [1], the properties out of equilibrium and at finite temperature often remain puzzling, as these are determined by the excitations above the ground state. In laboratory experiments, strongly interacting systems are found in certain materials, as well as in quantum fluids and gases [1]. In solid-state systems, a conceptually simple and clean approach to probe non-equilibrium physics is provided by transport measurements through the well-defined geometry of a quantum point contact (QPC) [2][3][4]. Yet, the technical hurdles to realise a controlled QPC between strongly correlated materials pose a big challenge. Ultra-cold atomic Fermi gases in the vicinity of a Feshbach resonance, the so-called unitary regime, provide an alternative route to study correlated systems [5]. Superfluidity has been established at low temperature [6], but the finite-temperature properties are only partially understood [7][8][9], a situation similar to the field of strongly correlated materials.Recent progresses in the manipulation of cold atomic gases have allowed to create a mesoscopic device featuring quantised conductance between two reservoirs in the non-interacting regime [16]. We use this technique to create a QPC in a strongly interacting Fermi gas consisting of 1.7(2) × 10 5 6 Li atoms in each of the two lowest hyperfine states, in a magnetic field of 832 G, where the interaction strength diverges due to a broad Feshbach resonance. The atoms form a strongly correlated superfluid, with a pairing gap larger than the chemical potential [5]. Typical temperatures in the cloud are T = 100(4) nK at a chemical potential of µ = 360 nK · k B . The setup is presented in Figure 1A [11]. The QPC is characterised by transverse trapping frequencies of ν x = 10.0(4) and ν z = 10(3) kHz in x-and z-direction. An optical attractive "gate" potential is used to tune the chemical potenti...

We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at 1=h for weak interactions to plateau-like features at nonuniversal values as high as 4=h for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.cold atoms | mesoscopic physics | quantum simulation | superfluidity | spin transport Q uantum gas experiments provide a tool to study fundamental concepts in physics, which may be hard to access by other means. Challenges such as the interplay and dynamics of many interacting fermions are addressed by interrogating a specifically tailored quantum many-body system with controlled parameters, an approach referred to as quantum simulation (1). The outcomes can then be used to benchmark theory or even as a direct comparison with different experimental realizations of the same concept. In recent years there has been substantial progress on this path, using cold atomic gases to realize important models of condensed matter physics, formulated to describe the bulk properties of materials (2, 3). Here, neutral fermionic atoms are used to model the electrons in a solid.In this article we use a quantum gas to study the operation of an entire mesoscopic device, a quantum point contact (QPC), in the presence of interactions between the particles. We observe the transport of a charge neutral quantum degenerate gas of fermionic lithium atoms, which can be prepared in a mixture of two hyperfine states. These states provide a spin degree of freedom and the attractive interaction between them can be tuned continuously from weak to unitary, a feature unique to cold atomic gases. The QPC itself is realized by a suitably shaped optical potential, which consists of a short, one-dimensional channel connected to two large reservoirs (4, 5). Biasing the reservoirs with different chemical potentials can induce a direct current. The ratio of the current to the bias is the conductance of the contact, which is independent of the bias in the linear response regi...

We investigate the transport properties of neutral, fermionic atoms passing through a onedimensional quantum wire containing a mesoscopic lattice. The lattice is realized by projecting individually controlled, thin optical barriers on top of a ballistic conductor. Building an increasingly longer lattice, one site after another, we observe and characterize the emergence of a band insulating phase, demonstrating control over quantum-coherent transport. We explore the influence of atom-atom interactions and show that the insulating state persists as contact interactions are tuned from moderately to strongly attractive. Using bosonization and classical Monte-Carlo simulations we analyze such a model of interacting fermions and find good qualitative agreement with the data. The robustness of the insulating state supports the existence of a Luther-Emery liquid in the one-dimensional wire. Our work realizes a tunable, site-controlled lattice Fermi gas strongly coupled to reservoirs, which is an ideal test bed for non-equilibrium many-body physics. PACS numbers:arXiv:1708.01250v3 [cond-mat.quant-gas]

Atomtronics deals with matter-wave circuits of ultracold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control, and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, the authors survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. The authors review some of the latest progress achieved in matter-wave circuits' design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done at the level of both equilibrium and nonequilibrium situations. Numerous relevant problems in mesoscopic physics, such as persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. The authors summarize some of the atomtronics quantum devices and sensors. Finally, the authors discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.