Heating and cooling in adiabatic mixing process

We study the effect of interaction on the temperature change in the process of adiabatic mixing of two components of Fermi gases using the real-space Bogoliubov–de Gennes method. We find that in the process of adiabatic mixing, the competition between the adiabatic expansion and the attractive interaction makes it possible to cool or heat the system depending on the strength of the interaction and the initial temperature of the system. The changes of the temperature in a bulk system and in a trapped system are investigated.

Figure 1

Two configurations of two-component Fermi gases in a homogeneous bulk system. (a) Separate noninteracting Fermi gases; (b) fully mixed fermonic superfluidity.

Figure 2

(a) $S-T$ curves in the homogeneous bulk system for separated noninteracting Fermi gases and fully mixed fermionic superfluidity. The interaction parameter is set as $k_f{a}_s=-0.6$. The two dashed lines denote two isoentropic processes. $\Delta T_i/T_F$ is the variation of temperature during the adiabatic process (blue is cooling while red is heating). (b) Dependence of the temperature change in the isoentropic process on the initial temperature $T$ as well as the strength of the interaction.

Figure 3

(a) For the magnetic field with large gradient, fermions with different spins are well separated. (b) By adiabatically tuning the gradient of the magnetic field to zero, the fermions are fully mixed.

Figure 4

Distribution of density and pairing parameter. The total density of particles is $n_0={10}^{12}$ cm${}^{-3}$ and the bare interaction parameter $k_f{a}_s$ is set as $-$0.6. We choose the temperature $T=1\times {10}^{-2}{T}_F$ and (a) $\nabla \mathbf{B}=0$ G/cm, (b) $\nabla \mathbf{B}=3$ G/cm, (c) $\nabla \mathbf{B}=30$ G/cm, (d) $\nabla \mathbf{B}=60$ G/cm.

Figure 5

(a) $S-T$ curves in the trapped system with different magnetic-field gradient $\nabla \mathbf{B}=0,60$ G/cm. The bare interaction parameter $k_f{a}_s$ is set as $-$0.6. (b) Contour of temperature change of the trapped system while the magnetic-field gradient is tuned from $\nabla \mathbf{B}=60$ G/cm to $\nabla \mathbf{B}=0$ adiabatically.