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arXiv:1610.00223 · Physical Review A

Universal relations and normal phase of an ultracold Fermi gas with coexisting s - and p -wave interactions

Fang Qin, Xiaoling Cui, Wei Yi

Published Dec 16, 2016• 18 citations
arXivHTMLPDF

Abstract

We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting $s$- and $p$-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channel. These universal relations are dictated by a set of contacts, which can be associated with either $s$- or $p$-wave interactions. Interestingly, due to the interplay of $s$- and $p$-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only $s$- or $p$-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for $^{40}\mathrm{K}$ atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of $s$- and $p$-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the $p$-wave resonances. Our results can be readily checked experimentally for $^{40}\mathrm{K}$ atoms near the $198\phantom{\rule{0.28em}{0ex}}\mathrm{G}\phantom{\rule{4pt}{0ex}}p$-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.

DOI
10.1103/physreva.94.063616

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We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting sss- and ppp-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channel. These universal relations are dictated by a set of contacts, which can be associated with either sss- or ppp-wave interactions. Interestingly, due to the interplay of sss- and ppp-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only sss- or ppp-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for 40K^{40}\mathrm{K}40K atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of sss- and ppp-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the ppp-wave resonances. Our results can be readily checked experimentally for 40K^{40}\mathrm{K}40K atoms near the 198Gp198\phantom{\rule{0.28em}{0ex}}\mathrm{G}\phantom{\rule{4pt}{0ex}}p198Gp-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.
We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the ppp-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, ppp-wave scattering length and effective range. At the unitarity limit where the ppp-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact sss-wave interaction in three dimensions. It is in contrast to a Fermi gas with the ppp-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary ppp-wave Fermi gas within the many-body TTT-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary ppp-wave Fermi gas.
In a recent experiment [Peng et al., Phys. Rev. A 97, 012702 (2018)], it has been shown that the ppp-wave Feshbach resonance can be shifted toward the sss-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting sss- and ppp-wave interactions under optical control of a ppp-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for 40K^{40}\mathrm{K}40K atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the ppp-wave channel can be probed by measuring the sss-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.
The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact was extended to higher partial waves; in particular, the ppp-wave contacts have been experimentally probed in recent experiments. So far, discussions on ppp-wave contacts have been limited to three dimensions. In this paper, we generalize the ppp-wave contacts to two dimensions and derive a series of universal relations, including the adiabatic relations, high-momentum distribution, virial theorem, and pressure relation. At the high-temperature and low-density limit, we calculate the ppp-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing-mode frequency and the ppp-wave contacts is given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three- and two-dimensional Fermi gases and discuss possible experimental realization of a two-dimensional Fermi gas with ppp-wave interactions.
Universal relations are important for understanding strongly interacting Fermi gases, the study of which have been mostly limited to cases with a single scattering channel. Here we discover a series universal relations for strongly interacting Fermi gases with multiple scattering channels. Unlike its counterpart across a single channel wide magnetic Feshbach resonance, a new kind of contact which we call the cross-channel contact naturally appears in this system, this contact is related to varies thermodynamic quantities as well as short range correlation functions.
Abstract We derive the full set of universal relations for spin-polarized Fermi gases with p -wave interaction in two dimensions, simply using the short-range asymptotic behavior of fermion-pair wave functions. For p -wave interactions, an additional contact related to the effective range needs to be introduced, besides the one related to the scattering volume. Since the subleading tail ( k −4 ) of the large-momentum distribution cannot fully be captured by the contacts defined by the adiabatic relations, an extra term resulted from the center-of-mass motions of the pairs gives rise to an additional divergence in the kinetic energy of the system, besides those related to the contacts defined. We show in Tan’s energy theorem that if only two-body correlations are taken into account, all these divergences are reasonably removed, leading to a finite internal energy of the system. In addition, we find that all the other universal relations, such as the high-frequency behavior of the radio-frequency response, short-range behavior of the pair correlation function, generalized virial theorem, and pressure relation, remain unaffected by the center-of-mass motions of the pairs, and are fully governed by the contacts defined by the adiabatic relations. Our results confirm the feasibility of generalizing the contact theory for higher-partial-wave scatterings, and could readily be confirmed in current experiments with ultracold 40 K and 6 Li atoms.
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.