We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.In the presence of strong correlations, the understanding of quantum many-body systems can be exceedingly difficult. One way to simplify the description of such systems is to use a discrete model where the motion of the particles is restricted to hopping between the sites of a lattice. The paradigmatic example for this approach is the Hubbard model, which reduces the physics of a quantum many-body system to tunneling of particles between adjacent sites and interactions between particles occupying the same site. While this model captures essential properties of electrons in a crystalline solid and provides a microscopic explanation for the existence of Mott-insulating and antiferromagnetic phases, many questions about this Hamiltonian -such as whether it can explain d-wave superfluidity -are still unanswered [1].A promising approach to answer these questions is to use ultracold atoms trapped in periodic potentials as quantum simulators of the Hubbard model [2][3][4][5][6][7][8]. Such experiments have been performed both in large-and small-scale systems. Degenerate gases loaded into optical lattices have been used to observe the transition to the bosonic [9,10] and fermionic Mott insulator [3,4]. The first observation of second-order tunneling was achieved in a small-scale system by studying the tunneling dynamics of bosonic atoms in an array of separated double wells [11,12]. In a recent experiment, these two regimes have been connected by splitting a fermionic Mott insulator into individual double wells. In this way, the strength of the antiferromagnetic correlations in the many-body system could be determined by measuring the fraction of double wells with two atoms in the spin-singlet configuration [13]. But despite the observation of antiferromagnetic correlations [13,14] current experiments using fermionic atoms have so far failed to reach temperatures below the critical temperature of spin ordering [15,16] Recently, new experimental techniques have been developed which allow for the deterministic preparation of few-particle systems in the ground state of a single potential well [17][18][19]. This makes it feasible to use ultracold atoms to study many-body physics in a bottom-up approach, i.e. to start from the fundamental building block of the system and watch how many-body effects emerge as...

We have studied quasi one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by observing the tunneling of particles out of the trap. For even particle numbers we observe a tunneling behavior which deviates from uncorrelated single-particle tunneling indicating the existence of pair correlations in the system. From the tunneling timescales we infer the differences in interaction energies of systems with different number of particles which show a strong odd-even effect, similar to the one observed for neutron separation experiments in nuclei.PACS numbers: 67.85.LmPairing between distinguishable fermions with an attractive interparticle interaction leads to fascinating phenomena in a variety of vastly different systems. In metals at sufficiently low temperature pairs of electrons can form a superfluid, as described by Bardeen, Cooper and Schrieffer in their BCS-theory of superconductivity [1]. Using dilute gases of ultracold atoms, where the interparticle interactions can be tuned freely using Feshbach resonances [2] it was shown that such BCS pairs can be smoothly converted into bosonic molecules [3], which leads to a continuous crossover from a BCS-like superfluid to a BEC of molecules [4][5][6][7]. In finite Fermi systems pairing has been studied extensively in the context of nuclear physics [8][9][10]. Here the pairing caused by the attractive interaction between the nucleons leads to an enhanced stability of systems with an even number of neutrons or protons [10]. For systems with fully closed shells -the so-called magic nuclei -stability is further enhanced. Recently, it has become possible to prepare finite systems of ultracold fermions in well-defined quantum states [11]. In such a system one has direct experimental control over key parameters such as the particle number and the depth and shape of the confining potential. Combined with the ability to tune the interparticle interactions [2,12], this makes this system uniquely suited to study pairing in a controlled environment.In this work we study how pairing affects few-particle systems consisting of one to six ultracold atoms in two different spin states -labeled |↑ and |↓ -confined in a cigar-shaped optical microtrap [13]. We deterministically prepare these systems in their ground state using the preparation scheme developed in [11]. Our microtrap has typical trap frequencies of ω = 2π × 1.488(14) kHz [14] in longitudinal and ω ⊥ = 2π × 14.22(35) kHz [15] in perpendicular direction. In addition to the optical potential we can apply a linear potential in longitudinal * Electronic address: gerhard.zuern@physi.uni-heidelberg.de direction by applying a magnetic field gradient. A full description of the potential shape as determined in [14] is given in [16].As in our few-fermion systems all energy scales are much smaller than ω ⊥ the system can be treated as quasi one-dimensional [17]. In this 1D environm...

Two-dimensional semiconductors provide an ideal platform for exploration of linear exciton and polariton physics, primarily due to large exciton binding energy and strong light-matter coupling. These features, however, generically imply reduced exciton-exciton interactions, hindering the realization of active optical devices such as lasers or parametric oscillators. Here, we show that electrical injection of itinerant electrons into monolayer molybdenum diselenide allows us to overcome this limitation: dynamical screening of exciton-polaritons by electrons leads to the formation of new quasiparticles termed polaron-polaritons that exhibit unexpectedly strong interactions as well as optical amplification by Bose-enhanced polaron-electron scattering. To measure the nonlinear optical response, we carry out timeresolved pump-probe measurements and observe polaron-polariton interaction enhancement by a factor of 50 (0.5 μeV μm 2) as compared to exciton-polaritons. Concurrently, we measure a spectrally integrated transmission gain of the probe field of ≳2 stemming from stimulated scattering of polaron-polaritons. We show theoretically that the nonequilibrium nature of optically excited quasiparticles favors a previously unexplored interaction mechanism stemming from a phase-space filling in the screening cloud, which provides an accurate explanation of the strong repulsive interactions observed experimentally. Our findings show that itinerant electron-exciton interactions provide an invaluable tool for electronic manipulation of optical properties, demonstrate a new mechanism for dramatically enhancing polariton-polariton interactions, and pave the way for realization of nonequilibrium polariton condensates.

We present a versatile imaging scheme for fermionic 6 Li atoms with single-particle sensitivity. Our method works for freely propagating particles and completely eliminates the need for confining potentials during the imaging process. We illuminate individual atoms in free space with resonant light and collect their fluorescence on an electron-multiplying CCD camera using a high-numericalaperture imaging system. We detect approximately 20 photons per atom during an exposure of 20 µs and identify individual atoms with a fidelity of (99.4 ± 0.3) % . By addressing different optical transitions during two exposures in rapid succession, we additionally resolve the hyperfine spin state of each particle. The position uncertainty of the imaging scheme is 4.0 µm, given by the diffusive motion of the particles during the imaging pulse. The absence of confining potentials enables readout procedures, such as the measurement of single-particle momenta in time of flight, which we demonstrate here. Our imaging scheme is technically simple and easily adapted to other atomic species.arXiv:1804.04871v2 [cond-mat.quant-gas]

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