Unconventional pairing in few-fermion systems tuned by external confinement

Abstract

We study the ground-state properties of a two-component quasi-one-dimensional system of few ultra-cold fermions with attractive interactions. We show that, by ramping an external potential barrier felt by one of the components, it is possible to induce exotic superconducting phases characterized by a tunable finite net momentum of the Cooper pair, without changing the overall spin populations. We show that the pairing mechanisms can be distinguished by analyzing a specific two-particle correlation encoded in the noise correlation function. Our theoretical results can be addressed in current experiments with cold atoms confined in spin-selective optical traps.

Unconventional pairing in few-fermion systems at finite temperature

“…We checked that this simple definition gives qualitatively the same predictions as some more sophisticated ones introduced recently 50 . Since a concrete value of has no direct interpretation, in the following we always normalize it to its zero-temperature value, .…”

“…Therefore, to filter out the latter from the description, we go along previous experience 67 – 70 and we define the so-called noise correlation encoding pure two-body correlations between particles where we use a short notation for averaging over the many-body mixed state of the system of given temperature T . Let us point here, that in the case of ground-state properties, the noise correlation concept has been extremely useful to study two-body correlations in general 71 , but the pairing in particular 27 , 48 , 50 , 72 , 73 . It turned out that, at least for the ground-state properties, this measurable quantity can be quite easily adopted as a direct indicator of pairing correlations signaling not only standard Cooper pairs but also unconventional pairs with non-vanishing center-of-mass momentum (FFLO) 48 .…”

“…Pioneering experiments of this type 39 – 41 have opened an alternative route to study quantum many-body systems from the side of mesoscopic phenomena 42 , 43 . Amidst a flurry of different ideas related to such small quantum systems, recently it has been theoretically spotted that small mixtures of attractively interacting fermions may host correlations very similar to pairing known for bulk systems 44 – 50 . Depending on inter-component imbalance, they may serve as suitable platforms for observing unconventional pairing mechanisms 51 .…”

Unconventional pairing in few-fermion systems at finite temperature

“…We checked that this simple definition gives qualitatively the same predictions as some more sophisticated ones introduced recently [61]. Since a concrete value of ξ(T ) has no direct interpretation, in the following we always normalize it to its zero-temperature value, ξ(T )/ξ(0).…”

“…Therefore, to filter out the latter from the description, we go along previous experience [53][54][55][56] and we define the so-called noise correlation encoding pure twobody correlations between particles where we use a short notation 〈•〉 T ≡ Tr [ ρT • ] for averaging over the many-body mixed state ρT of the system of given temperature T . Let us point here, that in the case of ground-state properties, the noise correlation concept has been extremely useful to study two-body correlations in general [57], but the pairing in particular [27,[58][59][60][61]. It turned out that, at least for the ground-state properties, this measurable quantity can be quite easily adopted as a direct indicator of pairing correlations signaling not only standard Cooper pairs but also unconventional pairs with non-vanishing center-of-mass momentum (FFLO) [60].…”