Limits of sympathetic cooling of fermions: The role of the heat capacity of the coolant

TL;DR

This paper investigates the limits of sympathetic cooling of degenerate Fermi gases using ideal Bose or Boltzmann gases, revealing that coolant heat capacity is not always the limiting factor for cooling efficiency.

Contribution

It challenges the intuitive notion that a large heat capacity in the coolant is essential for effective sympathetic cooling of fermions.

Findings

Cooling efficiency is not reduced when Bose gas heat capacity is much less than Fermi gas.

A minimal heat capacity ratio is necessary for Boltzmann gases to reach zero temperature.

Complete evaporation of coolant particles is required for Boltzmann gases to achieve T=0.

Abstract

The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve T=0 and all of the particles must be evaporated.