Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigated the crossover from few- to many-body physics by studying quasi-one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measured the interaction energy of such a system as a function of the number of majority atoms for different strengths of the interparticle interaction. As we increased the number of majority atoms one by one, we observed fast convergence of the normalized interaction energy toward a many-body limit calculated for a single impurity immersed in a Fermi sea of majority particles.

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...

We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system. DOI: 10.1103/PhysRevLett.115.215301 PACS numbers: 67.85.Lm, 71.10.Pm, 75.10.Jm, 75.10.Pq The high control and tunability of ultracold atomic systems offer the fascinating possibility to simulate quantum magnetism [1], a topic of fundamental importance in condensed matter physics [2]. Systems of spin-1=2 fermions with antiferromagnetic (AFM) correlations are of particular interest due to the observation of high-temperature superconductivity in cuprates with AFM correlations [3]. The experimental implementation of the necessary exchange couplings is usually realized by superexchange processes of neighboring atoms in the Mott-insulating state of a deep optical lattice. Superexchange couplings were measured in both bosonic [4] and fermionic double-well systems [5] and short-range AFM correlations of fermionic atoms were detected in various lattice geometries [6][7][8]. Furthermore, superexchange processes were used to study the dynamics of spin impurities above the ferromagnetic (FM) ground state of bosons in the Mott-insulating state of a one-dimensional lattice [9]. Bosonic atoms were also used to simulate AFM Ising spin chains in a tilted optical lattice [10,11]. However, the AFM ground state of spin-1=2 fermions in a deep optical lattice has so far not been realized due to the very low energy scale associated with the superexchange coupling.This problem can be circumvented in 1D systems, where quantum magnetism can be simulated without an optical lattice [12][13][14]. In the regime of strong interactions, the spatial wave function of both fermions [15] and bosons [16][17][18] can be mapped on the wave function of spinless noninteracting fermions [ Fig. 1(a)]. In this so-called fermionization limit, the strong interactions lead to the formation of a Wigner-crystal-like state [19][20][21], which has a highly degenerate ground state when the particles have multiple internal degrees of freedom [ Fig. 1(b)] [20][21][22][23]. Close to the limit of fermionization, the structure of the quasidegenerate ground-state multiplet [24][25][26][27][28][29][30][31][32][33] is determined by an effective Sutherland spin-chain Hamiltonian, which for two-component systems becomes a Heisenberg model [12,19,21,29,[32][33][34].In this Letter, we report on the realization of Heisenberg spin chains of N ↑ spin-up and N ↓ spin-down particles with ðN ...