The coupling of the spin of electrons to their motional state lies at the heart of recently discovered topological phases of matter. Here we create and detect spin-orbit coupling in an atomic Fermi gas, a highly controllable form of quantum degenerate matter. We directly reveal the spin-orbit gap via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. For energies within the spin-orbit gap, the system acts as a spin diode. We also create a spin-orbit coupled lattice and probe its spinful band structure, which features additional spin gaps and a fully gapped spectrum. In the presence of s-wave interactions, such systems should display induced p-wave pairing, topological superfluidity, and Majorana edge states.

We have observed the superfluid phase transition in a strongly interacting Fermi gas via highprecision 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 Tc/TF = 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.Phase transitions are ubiquitous in Nature: water freezes into ice, electron spins suddenly align as materials turn into magnets, and metals become superconducting. A pervasive feature of continuous phase transitions is their critical behavior, namely singularities in thermodynamic quantities: the magnetic susceptibility diverges at a ferromagnetic transition, the specific heat shows a jump at superconducting transitions [1] as well as at the superfluid transition of 3 He [2]. In 4 He, at the famous λ-transition into the the superfluid state, the jump is even resolved, in zero gravity, to be a near-diverging, singular peak [3]. A novel form of superfluidity has been realized in trapped, ultracold atomic gases of strongly interacting fermions, particles with half-integer spin [4][5][6]. Thanks to an exquisite control over relevant system parameters, these gases have recently emerged as a versatile system well suited to solve open problems in many-body physics [6]. However, while superfluidity has been established via the observation of vortex lattices in rotating gases [7], no clear thermodynamic signature of the superfluid transition has previously been observed.Initial measurements on the thermodynamics of strongly interacting Fermi gases have focused on trap averaged quantities [8][9][10] in which the superfluid transition is inherently difficult to observe. It is also challenging to reveal the critical behavior through the study of local thermodynamic quantities. The emergence of the condensate of fermion pairs in a spin-balanced Fermi gas is accompanied by only minute changes in the density [4]. Therefore, quantities that involve integration of the density over the local potential, such as the energy E [11] and the pressure P [12], are only weakly sensitive to the sudden variations in the thermodynamics of the gas that one expects near the superfluid phase transition [13].A thermodynamic quantity involving the second derivative of the pressure P is expected to become singular at the second order phase transition into the superfluid state. An example is the (isothermal) compressibility κ = 1 n ∂n ∂P | T , the relative change of...

We realize a quantum-gas microscope for fermionic 40 K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-latticesite resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement. DOI: 10.1103/PhysRevLett.114.193001 PACS numbers: 37.10.De, 03.75.Ss, 37.10.Jk, 67.85.Lm The collective behavior of fermionic particles governs the structure of the elements, the workings of hightemperature superconductors and colossal magnetoresistance materials, and the properties of nuclear matter. Yet our understanding of strongly interacting Fermi systems is limited, due in part to the antisymmetry requirement on the many-fermion wave function and the resulting "fermion sign problem" [1]. In recent years, ultracold atomic quantum gases have enabled quantitative experimental tests of theories of strongly interacting fermions [2][3][4][5]. In particular, fermions trapped in optical lattices can directly simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations. A major effort is devoted to the realization of the Fermi-Hubbard model at low entropies, believed to capture the essential aspects of high-T c superconductivity [6][7][8][9][10][11][12]. For bosonic atoms, a new set of experimental probes ideally suited for the observation of magnetic order and correlations has become available with the advent of quantum-gas microscopes [13][14][15], enabling high-resolution imaging of Hubbardtype lattice systems at the single-atom level. They allowed the direct observation of spatial structures and ordering in the Bose-Hubbard model [14,16] and of the intricate correlations and dynamics in these systems [17,18]. A longstanding goal has been to realize such a quantum-gas microscope for fermionic atoms. This would enable the direct probing and control at the single-lattice-site level of strongly correlated fermion systems, in particular the Fermi-Hubbard model, in regimes that cannot be described by current theories. These prospects have sparked significant experimental efforts to realize site-resolved, highfidelity imaging of ultracold fermions, but this goal has so far remained elusive.In the present work, we realize a quantum-gas microscope for fermionic 40 K atoms by combining 3D Raman sideband cooling with a high-resolution imaging system. The imaging setup incorporates a hemispherical solid immersion lens optically contacted to the vacuum window [ Fig. 1(a)]. In ...

Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model.