# Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement

## TL;DR

This paper demonstrates how to locally tune the exchange interactions in a three-fermion one-dimensional spin chain via transversal confinement, enabling control over spin states and dynamics near a confinement-induced resonance.

## Contribution

It introduces a method to tailor exchange coefficients in a 1D fermionic spin chain through transversal confinement, including near a confinement-induced resonance.

## Key findings

- Exchange coefficients can be locally tuned by confinement shaping.
- Near the CIR, exchange interactions can be ferromagnetic or antiferromagnetic.
- Ramp protocols can create and manipulate spin states and dynamics.

## Abstract

Strongly interacting one-dimensional fermions form an effective spin chain in the absence of an external lattice potential. We show that the exchange coefficients of such a chain may be locally tuned by properly tailoring the transversal confinement. In particular, in the vicinity of a confinement-induced resonance (CIR) the exchange coefficients may have simultaneously opposite ferromagnetic and antiferromagnetic characters at different locations along the trap axis. Moreover, the local exchanges may be engineered to induce avoided crossings between spin states at the CIR, and hence a ramp across the resonance may be employed to create different spin states and to induce spin dynamics in the chain. We show that such unusual spin chains have already been realized in the experiment of Murmann et al. [Phys. Rev. Lett. 115, 215301 (2015)].