Cooling Fermions in an Optical Lattice by Adiabatic Demagnetization

TL;DR

This paper proposes a method to cool ultracold fermions in an optical lattice to low temperatures using adiabatic demagnetization, overcoming symmetry-related obstacles with spin-dependent tunneling, supported by DMRG simulations.

Contribution

It introduces a novel approach to achieve low-temperature states in the Fermi-Hubbard model by breaking SU(2) symmetry with spin-dependent tunneling, enabling adiabatic demagnetization.

Findings

DMRG simulations show successful low-temperature state preparation in 1D.

Breaking SU(2) symmetry allows adiabatic demagnetization to work.

Protocol can be optimized for experimental implementation.

Abstract

The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'{e}el temperature. However, reaching this temperature in the lab has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system, and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the $SU(2)$ symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the $SU(2)$ symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard Model.