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arXiv:2208.03654 · Physical Review A

Stability against three-body clustering in one-dimensional spinless p -wave fermions

Yixin Guo, Hiroyuki Tajima

Published Oct 12, 2022• 10 citations
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Abstract

We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body $p$-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong $p$-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation. Our results indicate that the weak two-body coupling side is more sensitive to the residual three-body interaction than the strong-coupling side. By including the dimensionless three-body coupling such that the universality associated with the scattering length is maintained, we find that an in-medium three-body state similar to a squeezed Cooper triple appears.

DOI
10.1103/physreva.106.043310

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We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body ppp-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong ppp-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation. Our results indicate that the weak two-body coupling side is more sensitive to the residual three-body interaction than the strong-coupling side. By including the dimensionless three-body coupling such that the universality associated with the scattering length is maintained, we find that an in-medium three-body state similar to a squeezed Cooper triple appears.
We theoretically investigate three-body correlations on the top of a Fermi sea in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states (namely, Cooper triples in the presence of Fermi sea) in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the ppp-wave Cooper pairing and Cooper tripling phases in a plane of ppp-wave two- and three-body coupling strengths.
We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity sss-wave and odd-parity ppp-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as the Cooper triple by solving the corresponding in-medium variational equations. We further feature a phase diagram consisting of the sss- and ppp-wave Cooper pairing phases, and Cooper tripling phase, in a plane of sss- and ppp-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both sss- and ppp-wave interactions are moderately strong.
We consider the mass-imbalance effect on the clustering in a one-dimensional two-component Fermi gas with coexistent even- and odd-wave interactions resulting in different configurations of clustering phases. We obtain the solutions of both stable two- and three-body cluster states with different mass ratios and configurations by solving the corresponding variational equations. We numerically map out phase diagrams consisting of the sss- and ppp-wave pairing phases, and {trimer} phase with different configurations, in a plane of sss- and ppp-wave pairing strengths. Within the explored ranges of sss- and ppp-wave pairing strengths, the in-vacuum three-body states are always more deeply bound than the two-body ones. While for the in-medium case, the Cooper {trimer} phase dominates over the pairing phases when both sss- and ppp-wave interactions are moderately strong. There is also a competition between different clustering configurations of three-body clustering.
We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in three dimensions (3D), we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.
We investigate many-body properties of equally populated three-component fermions with attractive threebody contact interaction in one dimension.A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction.We develop a minimal framework that bridges the crossover from tightly bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram.Moreover, we argue that this nontrivial crossover is similar to the hadron-quark crossover proposed in dense matter.A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea.The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.
We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum k F , leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two- and three-body systems, the correction to the point at which the three-body states cease to exist is small.