Fermionization of Two Distinguishable Fermions

Abstract

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...

Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

“…1). Following the increase in the ground-state energy with increasing (i.e., staying on the dark brown curve), an anti-crossing develops, associated with a resonance region in the vicinity of ; this region is highlighted by a gray box in the energy plot of Fig In the limit of , the UCWM may reach the regime of fermionization of two distinguishable fermions, which has been most recently realized for two 6 Li atoms confined 7 within a single harmonic trap 30 . In this limit, the energy of the UCWM (singlet, blue curve) becomes degenerate with the energy of the triplet state (orange horizontal straight line).…”

“…In keeping with previous literature on two electrons in semiconductor quantum dots 21,30 , base 2 logarithms are used.…”

Comparing and contrasting nuclei and cold atomic gases

“…Then one must explicitly use the discrete spectrum and the quantum numbers of the harmonic trap. In this respect, tight traps with very few particles is the case most closely related to nuclei (Serwane et al 2011, Zürn et al 2012). Alternatively, a very deep periodic optical lattice potential can have single sites that are approximately harmonic and contain only a few particles (Bloch et al 2008), again closer to the situation in small nuclei.…”

“…Usually the number of atoms in a cold atomic gas experiment has been of order 10 3 − 10 6 and a theoretical approach based on few-body methods is obviously doomed. However, recently microtraps have been built that are capable of trapping very few atoms (1 − 10) at very low temperatures (Serwane et al 2011, Zürn et al 2012. Furthermore, it is now possible to address single lattice sites in an optical lattice and produce and probe only a few atoms on such a site (Bakr et al 2010, Sherson et al 2010, Weitenberg et al 2011).…”

“…Typically, these system contain thousands or even millions of particles, but very recently samples with very small particle numbers have been realized (Serwane et al 2011, Zürn et al 2012, Bakr et al 2010, Sherson et al 2010, Weitenberg et al 2011). This regime is particularly interesting since the physics that can be learned here might aid our understanding of mesoscopic and microscopic systems in other subfields.…”