Unconventional pairing in few-fermion systems at finite temperature

Abstract

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations—quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde–Ferrel–Larkin–Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

“…Indeed, for γ ∼ 0 we obtain χ 2 ∼ 0.342 θ 2 and F ∼ θ 2 /8χ 2 with θ ∼ γ/ 2πħ hωx ω . We note, however, that the weakly bound case is not within the scope of our present study, and it has been extensively analyzed before [17][18][19][20].…”

“…This method allows us to interpolate from the interaction strengths for which the single-particle basis is suitable [17][18][19][20], all the way to very strongly bound pairs approaching the limit of hard-core bosons. Using coboson-theory tools combined with Taylor expansions, we calculate several quantities of interest, including the energy and two-particle correlators.…”

“…Even though much effort has been devoted to this system, the usual numerical treatment takes as a basis the harmonic oscillator eigenstates, making computations very costly for strong attraction [14,[16][17][18][19][20]. Alternative procedures which are more efficient for strong attraction have been proposed in [21,22].…”