Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover

Abstract

We theoretically investigate the isothermal compressibility \(\kappa _{\mathrm{T}}\) in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated \(\kappa _{\mathrm{T}}\) diverges at \(T_{\mathrm{c}}\) in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.

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Acknowledgements

This work was supported by KiPAS project in Keio University. DI was supported by Grant-in-aid for Scientific Research from JSPS in Japan (No. JP16K17773). YO was supported by Grant-in-aid for Scientific Research from MEXT and JSPS in Japan (No. JP16K05503).

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Correspondence to R. Sato.

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Sato, R., Kagamihara, D., Manabe, K. et al. Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover. J Low Temp Phys 196, 119–125 (2019). https://doi.org/10.1007/s10909-018-2103-0

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Keywords

  • Isothermal compressibility
  • Ultracold Fermi gas
  • Repulsive inter-pair interaction