Deterministic Preparation of a Tunable Few-Fermion System

Abstract

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 ...

Engineering p-wave interactions in ultracold atoms using nanoplasmonic traps

“…We have shown that our proposal allows to stabilize a number of interesting quantum Hall states, such as the Pfaffian, and the n ¼ 1/3 Laughlin state. In our numerical calculation we have considered a small number of atoms, as it has become experimentally feasible recently [38][39][40] , but we note that the scheme should also be applicable to large systems. A good candidate for realizing the proposal are ytterbium atoms due to the long-lived state of the clock transition.…”

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).…”

“…The goal is to discuss universal features of these quantum states and phases and investigate whether they can be manifest in fewbody systems with nuclei as the example. A particularly interesting venture at a time when trapping of small samples of only a few atoms have been realized experimentally (Serwane et al 2011, Zürn et al 2012, Bakr et al 2010, Sherson et al 2010, Weitenberg et al 2011, implying that systems resembling few-body nuclei can be produced and studied in cold atomic gase experiments.…”

“…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.…”