Cooling in strongly correlated optical lattices: prospects and challenges

Abstract

Optical lattices have emerged as ideal simulators for Hubbard models of strongly correlated materials, such as the high-temperature superconducting cuprates. In optical lattice experiments, microscopic parameters such as the interaction strength between particles are well known and easily tunable. Unfortunately, this benefit of using optical lattices to study Hubbard models comes with one clear disadvantage: the energy scales in atomic systems are typically nanoKelvin compared with Kelvin in solids, with a correspondingly miniscule temperature scale required to observe exotic phases such as d-wave superconductivity. The ultra-low temperatures necessary to reach the regime in which optical lattice simulation can have an impact-the domain in which our theoretical understanding fails-have been a barrier to progress in this field. To move forward, a concerted effort is required to develop new techniques for cooling and, by extension, techniques to measure even lower temperatures. This article will be devoted to discussing the concepts of cooling and thermometry, fundamental sources of heat in optical lattice experiments, and a review of proposed and implemented thermometry and cooling techniques. 4 of the simplest FH model, cool to low temperature, and search for d-wave superfluidity (the analog of SC for neutral atoms). If the simplest FH model is insufficient to generate d-wave SF, then we can add in long-range interactions, disorder, and other features, and determine the impact on the phase diagram. Ultimately, the hope is to use optical lattices to measure the FH phase diagram.Experimental and theoretical work on optical lattice simulation has not been focused solely on the FH model. An in-depth review of proposals can be found in Ref. [9]; here, we mention a few areas that lattices are primed to impact. Bosonic atoms trapped in a lattice realize the Bose-Hubbard (BH) model [26]. In the simplest, spinless BH model, particles tunnel between sites and interact if they are on the same site, just as in the FH model. The primary difference with the FH model are that the particles obey Bose statistics, and therefore particles in the same spin state can interact. While the ground state phase diagram of the BH model is well understood (see , for example), dynamics are not, and lattice experiments are beginning to have an impact on that front [30][31][32][33][34][35][36]. Adding disorder to bosonic particles in an optical lattice is a method for studying the disordered Bose-Hubbard (DBH) model [9,37,38], which has been used as a paradigm for granular superconductors and superfluids in porous media. In the DBH model, the characteristic physical parameters, such as the tunneling energy, vary from site-to-site. Experiments are starting to influence our understanding of the DBH model [39], about which there remain some disputes. Finally, ultra-cold atoms in a lattice can be used to study a variety of interacting spin models that involve magnetic interactions between spins pinned to a lattice (see, for example, Refs. [40][41][...

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

“…We observed identical behavior for both attractive and repulsive interactions, highlighting the high symmetry of the kinetic energy in the Hubbard model. The surprisingly large observed timescales of mass transport set lower limits on the timescales needed both to adiabatically load the atoms into the lattice and to cool the system in the lattice [36] and are therefore of paramount importance for all attempts to create complex, strongly correlated many-body states like Néel-ordered states in these systems.…”

Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: A symmetry-entangled mean-field approach

“…Indeed, such atomic systems allow for an almost perfect implementation of the Hubbard model with tunable parameters [14]. The crossover from a metallic into a Mott insulating regime has already been observed [15], while magnetic ordering and potential exotic superfluidity remains to be achieved using, e.g., new cooling techniques [16]. …”

Quantum simulators by design: Many-body physics in reconfigurable arrays of tunnel-coupled traps

“…The superfluid part carries most of the systems entropy and can be removed by emptying the respective traps [38,40]. The resulting low entropy state opens a route to cold-atom analogs of high-T c superconductors [38].…”

“…This is the major source of heating in optical lattice experiments [38]. To estimate this effect, we consider the impact of a single scattering event and their total number during the adiabatic loading process lasting τ ramp .…”