Grüneisen parameters: Origin, identity, and quantum refrigeration

Abstract

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.

Grüneisen parameters for the Lieb-Liniger and Yang-Gaudin models

“…The obtained GPs show volume, magnetic field and interaction dependences of characteristic energy scales of the quantum gases and present the caloric effects resulted from the variations of these potentials. Our results confirm the identity among the three types of GPs [21] in 1D quantum systems…”

“…This is mainly because both thermal expansion and specific heat in quantum gases [20] are notoriously difficult to be measured in experimental study. A recent study [21] shows that the magnetocaloric effect (or interaction driven caloric effect) can help to measure the GPs in the controllable systems of ultracold atoms.…”

“…However, in literature, the formulation of the GP seems to be miscellaneous for different physical phenomena. By the definition of the GP, we first present an explicit form of the GP in grant canonical ensemble [21]…”

“…We would like to mention that in contrast to some previous studies [24,25], here we put the magnetic field H in the numerator to make the GP dimensionless. Similarly, using the Maxwell relations and general thermal relations, we can obtain the expression of the magnetic GP in grant canonical ensemble [21] Γ…”

“…The contact interaction can be regarded as a potential which changes the free energy in grand canonical ensemble. The interacting caloric effect in quantum gases has been rarely studied [21,26]. Similarly, the interacting GP, describing the change of temperature in response to an adiabatic change of the interaction, can be given by…”