| Summary: | In solid-state physics, the Grüneisen parameter (GP) was first introduced to study the effect of volume change of a crystal lattice on its vibrational frequencies and has since been widely used to investigate the characteristic energy scales of systems associated with the changes of external potentials. However, the GP is less investigated in gas systems and especially strongly interacting quantum gases. Here we report on some general results on the origin of the GP, an identity, and caloric effects in ultracold quantum gases. We prove that there exists a simple identity among three different types of GPs, quantifying the caloric effect induced by variations of volume, magnetic field, and interaction, respectively. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Fermi gases. Based on the exact equations of states of these systems, we further obtain analytic results for singular behavior of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp up and down in quantum gases provide a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid-state materials.
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