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In solid state physics, the Gr\"{u}neisen parameter (GP), originallyintroduced in the study of the effect of changing the volume of a crystallattice on its vibrational frequency, has been widely used to investigate thecharacteristic energy scales of systems with respect to the changes of externalpotentials. On the other hand, the GP is little investigated in a stronglyinteracting quantum gas systems. Here we report on our general results on theorigin of GP, new identity and caloric effects in quantum gases of ultracoldatoms. We prove that the symmetry of the dilute quantum gas systems leads to asimple identity among three different types of GPs, quantifying caloric effectinduced respectively by variations of volume, magnetic field and interaction.Using exact Bethe ansatz solutions, we present a rigorous study of thesedifferent GPs and the quantum refrigeration in one-dimensional Bose and Femigases. Based on the exact equations of states of these systems, we obtainanalytic results for the singular behaviour of the GPs and the caloric effectsat quantum criticality. We also predict the existence of the lowest temperaturefor cooling near a quantum phase transition. It turns out that the interactionramp-up and -down in quantum gases provides a promising protocol of quantumrefrigeration in addition to the usual adiabatic demagnetization cooling insolid state materials.

Gr\"{u}neisen Parameters: origin, identity and quantum refrigeration