Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases

Abstract

One-dimensional spinor gases with strong δ interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain-in particular antiferromagnetic spin order-may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

“…We first consider the case of a three-component mixture. At increasing interactions, we observe a narrowing of the momentum distribution in its central part (also noticed for the two-component mixture [41]), and an enhancement of the high-momentum tails. As we shall discuss below in Sec.…”

“…Therefore, it displays a number of peaks coinciding with the number of fermions of that component [38][39][40], with the amplitude of these Friedel-like oscillations decreasing as the inverse of the number of fermions. Also for an interacting gas, it was found that in a two-species mixture the momentum distribution displays as many peaks as the number of fermions in each component [41], although this form does not correspond anymore to the real space distribution.…”

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

“…Fortunately, for external harmonic confinement results up to 30 particles have been reported [68] and this is a sufficiently large particle number for most cold atomic gas experiments confined down to a single spatial dimension. Open source codes are available [76,77] from which one may obtain the exact spin model in the case of arbitrary potentials as well. It would be very interesting to try to combine DMRG with these analytical results so as to make DMRG much more reliable also in the case of very strong interactions.…”

Tunable self-assembled spin chains of strongly interacting cold atoms for demonstration of reliable quantum state transfer

“…We begin with an outline of the general spin chain problem and its connection to strongly interacting onedimensional gases, summarizing some important results from [37] (for related studies that also map the strongly interacting systems onto spin models see [25,28,[38][39][40][41]). The general problem concerns N strongly interacting particles with mass m in an arbitrary one-dimensional confining potential ( ) V x .…”

“…A method that provides such a link was developed [24,25], but the computation of the nearest-neighbor interaction coefficients for a system of more than a few atoms was a daunting task. Recently, these computational difficulties were overcome [26][27][28] and we can now efficiently treat long one-dimensional systems and obtain self-assembled spin chain Hamiltonians tunable by the external trap potential. Engineering the spin chains in this way allows us to study the delicate interplay between the strong atom-atom interactions and the trap parameters, gaining important theoretical insight into the physics of the experiment.…”