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arXiv:1610.08598 · Journal of the Physical Society of Japan

Strong-Coupling Properties of ap-Wave Interacting Fermi Gas on the Viewpoint of Specific Heat at Constant Volume

Daisuke Inotani, Pieter van Wyk, Yoji Ohashi

Published Jan 26, 2017• 3 citations
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Abstract

We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including fluctuations in the $p$-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$-wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$. Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$-wave molecular Bose gas regime, and (3) the region between the two, where $p$-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$.

DOI
10.7566/jpsj.86.024302

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We theoretically investigate the specific heat CVC_VCV​ at constant volume in the normal state of a ppp-wave interacting Fermi gas. Including fluctuations in the ppp-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how CVC_VCV​ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, CVC_VCV​ is shown to be enhanced by ppp-wave pairing fluctuations, near the superfluid phase transition temperature TcT_{\rm c}Tc​. Similar enhancement of CV(T≃Tc)C_V(T\simeq T_{\rm c})CV​(T≃Tc​) is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of ppp-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the ppp-wave molecular Bose gas regime, and (3) the region between the two, where ppp-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a ppp-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above TcT_{\rm c}Tc​.
We investigate the specific heat CVC_VCV​ at constant volume and effects of uniaxial anisotropy of a ppp-wave attractive interaction in the normal state of an ultracold Fermi gas. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we evaluate this thermodynamic quantity as a function of temperature, in the whole interaction regime. While the uniaxial anisotropy is not crucial for CVC_VCV​ in the weak-coupling regime, CVC_VCV​ is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among pip_ipi​-wave molecules (i=x,y,zi=x,y,zi=x,y,z), indicating that the specific heat is a useful observable to see which kinds of ppp-wave molecules dominantly exist in the strong-coupling regime when the ppp-wave interaction has uniaxial anisotropy. Using this strong point, we classify the strong-coupling regime into some characteristic regions. Since a ppp-wave pairing interaction with uniaxial anisotropy has been discovered in a 40^{40}40K Fermi gas, our results would be useful in considering strong-coupling properties of a ppp-wave interacting Fermi gas, when the interaction is uniaxially anisotropic.
We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.
We investigate the specific heat CVC_VCV​ at constant volume in the normal state of a ppp-wave interacting Fermi gas. Including ppp-wave pairing fluctuations within the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that, in the weak-coupling side, CVC_VCV​ exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near TcT_{\rm c}Tc​, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a ppp-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon does not occur in the ordinary sss-wave interacting Fermi gas, it may be viewed as a characteristic phenomenon associated with a ppp-wave pairing interaction.
We investigate the specific heat at constant volume CV{C}_{V}CV​ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a 6Li^{6}\text{Li}6Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.
We theoretically investigate the isothermal compressibility ${\ensuremath{\kappa}}_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent TTT-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While ${\ensuremath{\kappa}}_{T}$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect ${\ensuremath{\kappa}}_{T}$ near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.
We theoretically investigate strong-coupling properties of an odd-frequency Fermi superfluid. This pairing state has the unique property that Cooper pairs are formed between fermions, not at the same time, but at different times. To see whether or not such unequal-time pairs still exhibit bosonic behavior, we examine the space-time structure of the odd-frequency Cooper-pair wave function at T=0T=0T=0, by employing the combined path-integral formalism with the BCS-Eagles-Leggett-type superfluid theory. In the strong-coupling regime, the odd-frequency pair wave function still has different space-time structure from that in the ordinary even-frequency sss-wave superfluid state; their magnitudes are found to become close to each other, except for the equal-time pairing component. In this regime, we also evaluate the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink. The calculated Tc{T}_{\mathrm{c}}Tc​ in the strong-coupling regime of the odd-frequency system is found to be well described by the Bose-Einstein condensation of tightly bound Bose molecules. Our results indicate that, in spite of vanishing equal-time pairing, odd-frequency Cooper pairs still behave like bosons in the strong-coupling regime, as in the even-frequency sss-wave superfluid case.