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arXiv:1804.06529 · Physical Review A

Strong-coupling and finite-temperature effects on p -wave contacts

Daisuke Inotani, Yoji Ohashi

Published Aug 3, 2018• 9 citations
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Abstract

We investigate theoretically strong-coupling and finite-temperature effects on the $p$-wave contacts, as well as the asymptotic behavior of the momentum distribution in the large-momentum region in a one-component Fermi gas with a tunable $p$-wave interaction. Including $p$-wave pairing fluctuations within a strong-coupling theory, we calculate the $p$-wave contacts above the superfluid transition temperature ${T}_{\mathrm{c}}$ from the adiabatic energy relations. We show that, while the $p$-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the $p$-wave interaction with increasing effective range. We also analyze the asymptotic form of the momentum distribution in the large-momentum region. In contrast to the conventional $s$-wave case, we show that the asymptotic behavior cannot be completely described by only the $p$-wave contacts, and the extra terms, which are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement by including the effects of a harmonic trap potential within the local density approximation. We show that, while our model qualitatively explains the dependence on the interaction strength of the $p$-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the $p$-wave contact related to the effective range. Since the $p$-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.

DOI
10.1103/physreva.98.023603

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We investigate theoretically strong-coupling and finite-temperature effects on the ppp-wave contacts, as well as the asymptotic behavior of the momentum distribution in the large-momentum region in a one-component Fermi gas with a tunable ppp-wave interaction. Including ppp-wave pairing fluctuations within a strong-coupling theory, we calculate the ppp-wave contacts above the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​ from the adiabatic energy relations. We show that, while the ppp-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the ppp-wave interaction with increasing effective range. We also analyze the asymptotic form of the momentum distribution in the large-momentum region. In contrast to the conventional sss-wave case, we show that the asymptotic behavior cannot be completely described by only the ppp-wave contacts, and the extra terms, which are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement by including the effects of a harmonic trap potential within the local density approximation. We show that, while our model qualitatively explains the dependence on the interaction strength of the ppp-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the ppp-wave contact related to the effective range. Since the ppp-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.
We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near ppp-wave Feshbach resonances. The leading asymptotic behavior ${k}^{\ensuremath{-}2}$ and subleading behavior ${k}^{\ensuremath{-}4}$ of the large momentum distribution have recently been predicted by Z. Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by M. Y. He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\ensuremath{\sim}{k}^{\ensuremath{-}4}$) cannot fully be captured by the contact defined from the adiabatic energy relation related to the ppp-wave effective range, and there should be an extra term resulting from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should have significant importance to understand the recently measured momentum distribution in a resonant ppp-wave Fermi gas of ultracold 40K^{40}\mathrm{K}40K atoms [C. Luciuk et al., Nat. Phys. 12, 599 (2016)].
We investigate single-particle properties of a one-component Fermi gas with a tunable ppp-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a TTT-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the intermediate coupling regime. In the strong-coupling regime, the excitation gap associated with the formation of tightly bound molecules again opens. This nonmonotonic interaction dependence of the excitation gap is quite different from the case of an sss-wave interaction, where the pseudogap simply develops with increasing the interaction strength, which continuously changes into the molecular excitation gap. The difference between the two cases is shown to originate from the momentum dependence of the ppp-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the ppp-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of ppp-wave superfluid Fermi gases.
We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a TTT-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature TcT_{\rm c}Tc​. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.
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 properties of a spinless Fermi gas close to a p-wave interaction resonance. We show that the effects of interaction near a p-wave resonance are captured by two contacts, which are related to the variation of energy with the p-wave scattering volume v and with the effective range R in two adiabatic theorems. Exact pressure and virial relations are derived. We show how the two contacts determine the leading and subleading asymptotic behavior of the momentum distribution (∼1/k^{2} and ∼1/k^{4}) and how they can be measured experimentally by radio-frequency and photoassociation spectroscopies. Finally, we evaluate the two contacts at high temperature with a virial expansion.
We present a rigorous study of momentum distribution and ppp-wave contacts of one-dimensional spinless Fermi gases with an attractive ppp-wave interaction. Using the Bethe ansatz wave function, we calculate analytically the high-momentum tail and show that the leading ($\ensuremath{\sim}1/{p}^{2}$) and sub-leading terms ($\ensuremath{\sim}1/{p}^{4}$) are determined by two contacts C2{C}_{2}C2​ and C4{C}_{4}C4​, which are related to the short-distance behavior of the two-body density matrix and its derivatives. As one increases the one-dimensional scattering length, the contact C2{C}_{2}C2​ increases monotonically from zero while C4{C}_{4}C4​ exhibits a peak at finite scattering length. In addition, we obtain analytic expressions for ppp-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations for both weak and strong attractive interactions.