Pairing in Few-Fermion Systems with Attractive Interactions

Abstract

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...

Nonlocality in many-body quantum systems detected with two-body correlators

“…[81] for the resonant fluorescence detection of Rb 87 atoms in a MOT, and Refs. [82,83] for optically trapped spin 1/2 fermions). (90 -91) for the Dicke state |D k n with n = 2 10 = 1024 qubits.…”

“…We shall use the definition for the function f given in Eq. (83) and its relation (81). We shall also adopt the notation (A20).…”

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

“…As a consequence, the total number of fermions of a given flavour,N σ = L −LΨ † σ (x)Ψ σ (x)dx, commutes with the many-body Hamiltonian (9). This property of the model corresponds to realistic experimental situations where the number of particles can be controlled with an extreme precision [6,12].…”

“…Note that in the Hamiltonian (9) there are no terms that change the number of particles of a given flavour. As a consequence, the total number of fermions of a given flavour,N σ = L −LΨ † σ (x)Ψ σ (x)dx, commutes with the many-body Hamiltonian (9).…”

“…As a consequence, a deep analysis of many properties of one-dimensional few-body systems is performed experimentally. For example, fermionization of distinguishable particles [8], pairing for attractive forces [9], ground-state properties in double-well schemes [10], or the formation of the Fermi Sea [11,12] have been observed already. In parallel, on a theoretical level many interesting results have been obtained under the assumption that particles are confined in a harmonic trap [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”