A familiar concept from high school physics is the ideal gas law. This law, or more appropriately the “equation of state”, relates three simple parameters, pressure, density and temperature to encapsulate all thermodynamic properties of the system. The ideal gas law describes a system for which the physics may also be calculated from the dynamics of the microscopic constituents. However, determining the equation of state of systems from microscopic principles is very challenging if the systems become strongly correlated and governed by the laws of quantum physics. Therefore, precise measurements are necessary in order to establish the equation of state of complex systems. For example, in correlated many-body systems highly non-trivial properties, such as those underlying high-temperature superconductivity, can arise of which no generally accepted microscopic description yet exists. As a minimal model, the two-dimensional Hubbard model serves for describing such physics and, indeed, much work has been carried out theoretically in approximating this model. However, until now a measurement of the equation of state in a single system across a broad parameter range to support these calculations has been lacking. By utilising a ultracold gas of fermions in a single two-dimensional layer of an optical lattice, we measure densities for a range of temperatures and interactions, thus characterising the equation of state of the system.

Reference: E. Cocchi et al., Phys. Rev. Lett. 116, 175301 (2016).