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arXiv:1101.2124 · Science

Deterministic Preparation of a Tunable Few-Fermion System

Friedhelm Serwane, G. Zürn, Thomas Lompe, T. B. Ottenstein, A. N. Wenz, Selim Jochim

Published Apr 14, 2011• 506 citations
arXivHTMLPDF

Abstract

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 are prepared with fidelities of ∼90%. We can tune the interparticle interactions to arbitrary values using a Feshbach resonance and have 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.

DOI
10.1126/science.1201351

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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 are prepared with fidelities of ∼90%. We can tune the interparticle interactions to arbitrary values using a Feshbach resonance and have 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.
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This thesis reports on the deterministic preparation of magnetically ordered states in systems of few fermionic atoms. We follow the concept of quantum simulation and use 6Li atoms in two different hyperfine states to mimic the behavior of electrons in a solidstate system. In a first experiment, we simulate the two-site Hubbard model by using two atoms in an isolated double-well potential. We prepare the two-particle ground state of this model with a fidelity exceeding 90%. By introducing strong repulsive interactions, we are able to realize a pure spin model and describe the energy spectrum with a two-site Heisenberg Hamiltonian. In a second experiment, we realize Heisenberg spin chains of up to four atoms in a single strongly-elongated trapping potential. Here, the atoms self-align along the potential axis due to strong repulsive interactions. We introduce two novel measurement techniques to identify the state of the spin chains and thereby confirm that we can deterministically prepare antiferromagnetic ground-state systems. This constitutes the first observation of quantum magnetism with fermionic atoms that exceeds nearest-neighbor correlations. Both the double-well system and the spin chains can be seen as building blocks of larger ground-state spin systems. Their deterministic preparation therefore opens up a new bottom-up approach to the experimental realization of quantum many-body systems with ultracold atoms.
This thesis reports on experiments with few-fermion systems in quasi one dimensional confining potentials with tunable interaction. \nUsing ultracold atoms we prepare these systems in a well defined quantum state with fidelities of 90% for up to 8 particles. The interparticle interaction in the 1D environment can be effectively described by a 1D contact interaction where the coupling strength can be tuned with a confinement induced resonance (CIR). \nWe investigate a system of two repulsively interacting distinguishable fermions and compare it to a system of two identical noninteracting fermions. For diverging coupling strength we show the fermionization of two distinguishable fermions, i.e. we observe the energy and the square modulus of the wavefunction of both system to be identical. We also perform radio frequency spectroscopy to measure the energy of a single minority particle interacting repulsively with a defined number of majority particles of different spin. We study the crossover from a few-particle system to a many-particle system by adding majority particles one by one. \nWe observe that already four majority particles are enough to describe the properties of the minority by that of a polaron-like particle, i.e. by a single impurity dressed by a 1D Fermi sea. \nInvestigating attractively interacting systems we observe that for increasing interaction strength the pair correlations in the system increases. This correlation leads to a strong odd-even effect of the single particle dissociation energy similar to the one observed for nuclei.
Trapped cold atoms at very low temperatures, now readily accessible experimentally, can be controlled and serve as a testing ground for many theoretical physical properties which are paralleled in condensed matter systems. Ultracold trapped atom experiments show promise to recreate analogous condensed matter systems in a controlled environment and to create novel many-body quantum states of matter. The tunability of trapping laser intensities and magnetically controlled Feshbach interactions are the main tools for varying lattice hopping strengths and inter-particle interactions. In this thesis, we search for the phase of a many-body system of cold fermion atoms that can convert to boson molecules and vice versa. We then look at the microscopic details of two atoms that interact to form a quasibound molecule. Our two-atom model explains the mechanism behind the magnetically tunable interparticle interaction known as the Feshbach resonance. We find a dependence of the bound pair formation on the two-particle energy. Our results show that if a magnetic field can be fine tuned to sufficient precision, of order 10 mG, a narrow resonance can be achieved where longer lived bound states can be created. This narrow resonance reconciliates the two-body physics with the effective Hamiltonian that describes the many-body system.
In this thesis, I report on the deterministic preparation and the observation of strongly correlated few-fermion systems in single and double-well potentials. In a first experiment, we studied a system of one impurity interacting with a number of majority atoms which we prepared in a single potential well in the one-dimensional limit. With increasing number of majority particles, we observed a decrease in the quasi-particle residue which is in agreement with expectations from the Anderson orthogonality catastrophe. In a second experiment, we prepared two fermions in a double-well potential which represents the fundamental building block of the Fermi-Hubbard model. By increasing the repulsion between the two fermions, we observed the crossover into the antiferromagnetic Mott-insulator regime. Furthermore, I describe a new imaging technique, which allows spin-resolved single-atom detection both in in-situ and in time-of-flight. We use this technique to investigate the emergence of momentum correlations of two repulsive fermions in the ground state of the double well. With the methods developed in this thesis, we have established a framework for quantum simulation of strongly correlated many-body systems in tunable potentials.
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.