Few-body physics with ultracold atomic and molecular systems in traps

Abstract

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible-thanks to tremendous progress in cooling, trapping and manipulating ultracold samples-to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.

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

“…Apart from a few exceptions [34][35][36][37][38][39][40][41], it has commonly been assumed that particles of different kinds have the same mass and the main impact on properties of the system comes from an imbalance of the number of particles. However, recently it was shown that for particles confined in a harmonic trap, the mass difference between different fermionic components leads to their spatial separation if interactions are strong enough [42].…”

Molecular branch of a small highly elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

“…Thus, we instead fit the full three-dimensional energies E 3d 2,1 /( ω ρ ) to a power series in g 1d . The fit yields the same linear coefficient as the perturbative treatment of H 1d and a slightly more negative coefficient for the quadratic term, −0.120754251 (1), where the number in round brackets denotes the uncertainty of the fit (the uncertainty of the three-dimensional energies is negligible for this analysis).…”

“…Ultracold few-atom systems provide clean model systems in which the system parameters such as the interaction strength and confinement geometry can be controlled with high accuracy [1][2][3][4]. Recently, twocomponent Fermi gases consisting of lithium atoms in two different hyperfine states have been prepared and probed experimentally in highly elongated, nearly harmonic external traps with an aspect ratio η around ten [5][6][7][8][9][10].…”

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

“…While the properties of unitary Fermi systems with zero-range interactions are fully determined by the s-wave scattering length [12,14,[51][52][53][54] those of Bose systems additionally depend on a three-body parameter [15,17]. Specifically, if the two-body interactions are modeled by zero-range potentials, then a three-body regulator is needed to prevent the Thomas collapse of the N -boson (N ≥ 3) system [17,55].…”