authors contributed equally to this work.Systems consisting of few interacting fermions are the building blocks of matter, with atoms and nuclei being the most prominent examples. We have created a few-body quantum system with complete control over its quantum state using ultracold fermionic atoms in an optical dipole trap. Ground-state systems consisting of 1 to 10 particles were prepared with fidelities of ∼ 90%. We can tune the interparticle interactions to arbitrary values using a Feshbach resonance and observed the interaction-induced energy shift for a pair of repulsively interacting atoms. This work is expected to enable quantum simulation of strongly correlated few-body systems.The exploration of naturally occurring few-body quantum systems such as atoms and nuclei has been extremely successful, largely because they could be prepared in well defined quantum states. Because these systems have limited tunability, researchers created quantum dots-"artificial atoms"-in which properties such as particle number, interaction strength and confining potential can be tuned (1,2). However, quantum dots are generally strongly coupled to their environment which hindered the deterministic preparation of well-defined quantum states. In contrast, ultracold gases provide tunable systems in a highly isolated environment (3, 4). They have been proposed as a tool for quantum simulation (5, 6) which has been realized experimentally for various many-body systems (7-10). Achieving quantum simulation of fewbody systems is more challenging because it requires complete control over all degrees of freedom: the particle number, the internal and motional states of the particles, and the strength of the inter-particle interactions. One possible approach to this goal is using a Mott insulator state of atoms in an optical lattice as a starting point. In this way, systems with up to four bosons per lattice site have been prepared in their ground state (11,12). Recently, single lattice sites have been addressed individually (13). In single isolated trapping geometries, researchers could suppress atom number fluctuations by loading bosonic atoms into small-volume optical dipole traps (14-18). However, these experiments were not able to gain control over the system's quantum state. We prepare few-body systems consisting of 1 to 10 fermionic atoms in a well-defined quantum state making use of Pauli's principle, which states that each singleparticle state cannot be occupied by more than one identical fermion. Therefore, the occupation probability of the lowest energy states approaches unity for a degenerate Fermi gas, and we can control the number of particles by controlling the number of available singleparticle states. We realize this by deforming the confining potential such that quantum states above a well defined energy become unbound. This approach requires a highly degenerate Fermi gas in a trap whose depth can be controlled with a precision much higher than the separation of its energy levels. To fulfill these requirements, we use a ...

We study a system of two distinguishable fermions in a 1D harmonic potential. This system has the exceptional property that there is an analytic solution for arbitrary values of the interparticle interaction. We tune the interaction strength and compare the measured properties of the system to the theoretical prediction. For diverging interaction strength, the energy and square modulus of the wave function for two distinguishable particles are the same as for a system of two noninteracting identical fermions. This is referred to as fermionization. We have observed this by directly comparing two distinguishable fermions with diverging interaction strength with two identical fermions in the same potential. We observe good agreement between experiment and theory. By adding more particles our system can be used as a quantum simulator for more complex systems where no theoretical solution is available. A powerful tool for solving complex quantum systems is to map their properties onto systems with simpler solutions. For interacting bosons in one dimension there is a one-to-one correspondence of the energy and the square modulus of the wave function |ψ(x 1 , ..., x n )| 2 to a system of identical fermions [1]. As one consequence the local pair correlation g (2) (0) of an interacting 1D Bose gas vanishes for diverging interaction strength just like in a gas of noninteracting identical fermions. Thus, a large decrease of g (2) (0) in a repulsively interacting 1D Bose gas is strong evidence for the existence of fermionization [2]. The many-body properties of such 1D bosonic systems have been studied in [3,4]. However, the essential property of a such a gas -namely the fermionization [1,5] -is already present in a system of two interacting particles, regardless of the particles being identical bosons or distinguishable fermions [6]. This two-particle problem is of significant interest because it is the main building block of all 1D quantum systems with short-range interactions. It is also one of the few quantum mechanical systems for which an analytic solution exists. In contrast to measurements of bulk properties such as compressibility and collective oscillations or measurements of local pair correlations [2], we access the energy and the square modulus of the wave function of the fundamental two-particle system. We directly observe fermionization of two distinguishable fermions by comparing two distinguishable fermions with two identical fermions in the same potential. In optical lattices the energy of similar two-particle systems has been measured for large but not diverging interaction strength [7,8].We realize such a two-particle system with tunable interaction using two fermionic 6 Li atoms in the ground state of a potential created by an optical dipole trap and * Electronic address: gerhard.zuern@physi.uni-heidelberg.de a magnetic field gradient [ Figs. 1(a) and 1(b)]. We can prepare this state with a fidelity of (93 ± 2)% [9]. The energy of such two particles interacting via contact interaction -which is fully de...

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.