Signatures of unconventional pairing in spin-imbalanced one-dimensional few-fermion systems

Abstract

A system of a few attractively interacting fermionic 6 Li atoms in one-dimensional harmonic confinement is investigated. Non-trivial inter-particle correlations induced by interactions in a particleimbalanced system are studied in the framework of the noise correlation. In this way, it is shown that evident signatures of strongly correlated fermionic pairs in the Fulde-Ferrell-Larkin-Ovchinnikov state are present in the system and they can be detected by measurements directly accessible within state-of-the-art techniques. The results convincingly show that the exotic pairing mechanism is a very universal phenomenon and can be captured in systems being essentially non-uniform and far from the many-body limit.One of the cornerstones of our understanding of strongly correlated states of quantum matter is based on the theory of superconductivity by Bardeen, Cooper, and Schrieffer [1]. In this theory, the existence of the superconducting phase is explained following the fundamental observation by Cooper [2] that the ground-state energy of an attractively interacting system is significantly decreased by the collective formation of Cooper pairsnon-trivially correlated states of two fermions with exactly opposite momenta. Based on this idea of collective pairing, a plethora of other pairing mechanisms have been proposed and investigated [3][4][5]. One of the most influential extensions of the Cooper's idea comes from the observation that in the case of imbalanced systems, due to the mismatch of Fermi spheres of different components, the formation of correlated pairs forced by attractive mutual interactions is inseparably connected with resulting non-zero net momentum of the pair [6,7]. This unconventional pairing mechanism named after Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) has been extensively examined theoretically, mostly in the case of various solid-state systems like iron-based superconductors [8][9][10][11], heavy-fermion compounds [11][12][13][14][15], or organic conductors [16][17][18]. However, it is also viewed as one of the possible ways to understand fundamental properties of neutron stars [19][20][21], specific quantum chromodynamics models [22], or fermionic ultra-cold gases [23]. The latter example is of high importance since ultra-cold atomic systems, due to their tremendous tunability, are believed to be the best candidates for the first experimental observation of the FFLO state. Unfortunately, up to this day, the FFLO state is ephemeral and there are only indirect signs of this state of matter (see [24] for a recent review).In this Letter, we show that the many-body groundstate of a few 6 Li atoms confined in a harmonic trap (in the presence of mutual attractions) possesses many characteristic properties of the FFLO state which can be experimentally captured. For example, if one would com-0 1 2 3 4 0 1 2 3 4 q 0 [ℏ/µm] Δp F [ℏ/µm] FIG. 1. The most probable FFLO momentum q0 as a function of the Fermi momenta mismatch ∆pF. Different points correspond to different number of particles and differen...

Unconventional pairing in few-fermion systems tuned by external confinement

“…Note that q 0 depends only on the population imbalance ∆N and not on the values N A and N B separately, unlike in non-uniform (e.g. harmonically trapped) systems [28]. The relation ( 4) is confirmed by Fig.…”

“…pairing with zero or nonzero net pair momentum) requires a detailed knowledge of the superconducting correlation function. It has been previously shown [27,28,49] that such information can also be obtained from the two-point noise correlation G between the two components, which is directly experimentally accessible from two-body density measurements [50][51][52]. In the momentum domain, the distribution of the noise correlation is given by…”

“…To date, obtaining direct experimental evidence of the modulated phase with cold atoms is still challenging. Several detection schemes have been discussed, based on the analysis of collective oscillations [22], the sudden expansion of the gas [23][24][25], interaction quenches [26], noise correlations [27,28], spectroscopy measurements [29][30][31][32] and the coupling to a Bose gas [33].…”

Observation of Cooper Pairs in a Mesoscopic 2D Fermi Gas

“…An even more thorough characterization of quantum many body states will become possible when extending our imaging scheme to detect the single particle resolved in-situ wavefunction in addition [33]. Our experiment opens up new pathways for detailed studies of the normal phase of the BEC-BCS crossover [34], imbalanced systems in 1D or 2D [35,36] or rotating systems [37]. By unlocking the capability to access correlations of arbitrary order, our method hold the potential to gain deeper insight into such strongly correlated systems in an unprecedented way.…”

Simulating Artificial 1D Physics with Ultra‐Cold Fermionic Atoms: Three Exemplary Themes

“…For this reason, the unconventional FFLO pairing in ultra‐cold 1D systems has recently been deeply investigated theoretically from various perspectives, for both confined [ 54–57 ] and lattice systems. [ 58–62 ] Quasi‐1D quantum simulators created with ultra‐cold neutral atoms constitute a highly controllable environment, where the Fermi surface mismatch can be precisely tuned by changing the spin composition of the initial population, rather than with external magnetic fields.…”