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Mass-imbalance effect on the cluster formation in a one-dimensional Fermi gas with coexistent $s$- and $p$-wave interactions

Yixin Guo

TL;DR

The paper addresses how mass imbalance influences two- and three-body clustering in a one-dimensional two-component Fermi gas with coexisting $s$- and $p$-wave interactions. A variational framework is used to obtain in-vacuum and in-medium energies for two- and three-body states and to map phase diagrams in the plane of $1/( abla ext{Lambda} a_s)$ and $1/( abla ext{Lambda} a_p)$. Key findings include that in vacuum the three-body energies are lower than two-body energies and the dominant triple switches from $aab$ to $abb$ with increasing $1/( abla ext{Lambda} a_p)$, while in medium the Cooper triple $aab$ can dominate over both $s$- and $p$-wave pairings when both couplings are moderately strong, with phase boundaries set by $E_3^{iij}=E_{2,s}$, $E_3^{iij}=E_{2,p}^{ii}$, and $E_{2,s}=E_{2,p}^{ii}$. The work provides insight into unconventional superfluidity in mass-imbalanced systems and may guide experiments in ultracold atoms, nuclear physics, and hypernuclear contexts.

Abstract

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 feature out phase diagrams consisting of the $s$- and $p$-wave pairing phases, and tripling phase with different configurations, in a plane of $s$- and $p$-wave pairing strengths. As for the in-vacuum case, the three-body clustering is always the lowest-lying phase. While for the in-medium case, the Cooper tripling phase dominates over the pairing phases when both $s$- and $p$-wave interactions are moderately strong. There is also a competition between different clustering configurations of three-body clustering.

Mass-imbalance effect on the cluster formation in a one-dimensional Fermi gas with coexistent $s$- and $p$-wave interactions

TL;DR

The paper addresses how mass imbalance influences two- and three-body clustering in a one-dimensional two-component Fermi gas with coexisting - and -wave interactions. A variational framework is used to obtain in-vacuum and in-medium energies for two- and three-body states and to map phase diagrams in the plane of and . Key findings include that in vacuum the three-body energies are lower than two-body energies and the dominant triple switches from to with increasing , while in medium the Cooper triple can dominate over both - and -wave pairings when both couplings are moderately strong, with phase boundaries set by , , and . The work provides insight into unconventional superfluidity in mass-imbalanced systems and may guide experiments in ultracold atoms, nuclear physics, and hypernuclear contexts.

Abstract

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 feature out phase diagrams consisting of the - and -wave pairing phases, and tripling phase with different configurations, in a plane of - and -wave pairing strengths. As for the in-vacuum case, the three-body clustering is always the lowest-lying phase. While for the in-medium case, the Cooper tripling phase dominates over the pairing phases when both - and -wave interactions are moderately strong. There is also a competition between different clustering configurations of three-body clustering.

Paper Structure

This paper contains 6 sections, 18 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Results and discussion
  4. In-vaccum case
  5. In-medium case
  6. Summary and perspectives

Figures (6)

  • Figure 1: Schematic figure representing our model. We consider the degenerate two-component mass-imbalanced fermions (states $a$ and $b$ occupying the levels with momentum $k$ up to the Fermi momentum $k_{\rm F}$) and the consequence of coexistent interspecies $s$-wave interaction $V_s$ and intraspecies $p$-wave interactions $V_i$ (acting on two identical fermions in the $i=a,b$ state), which lead to the Cooper instabilities towards the $s$- and $p$-wave Cooper pairs, and the Cooper triples.
  • Figure 2: (a). In-vacuum and in-medium $s$-wave pairing energies as functions of $s$-wave scattering length. (b). In-vacuum and in-medium $p$-wave pairing energies with different configurations as functions of $p$-wave scattering length. (c). In-vacuum and in-medium three-body energies with different configurations as functions of $p$-wave scattering length at fixed $s$-wave interaction strength as $1/(\Lambda a_s)\times10=2.7$ with $\Lambda$ the momentum cutoff. In all panels, mass ratio is fixed as $m_a/m_b=2$, and the reference energy scale is $E_\Lambda=\Lambda^2/(2m_r)$.
  • Figure 3: In-vacuum phase diagram in the plane of $1/(\Lambda a_s)$ and $1/(\Lambda a_p)$. The mass ratio is taken as $m_a=2m_b$.
  • Figure 4: Contour plot of in-medium three-body energy $E_3^{aab}/E_0$ in a plane of mass $m_a/m_0$ and $m_b/m_0$. The mass $m_0$ and energy $E_0=k_{\rm F}^2/(2m_0)$ are taken as the reference scales. The interaction strengths are fixed at $1/(k_{\rm F}a_s)=1/(k_{\rm F}a_p)=1.5$. The momentum cutoff is taken as $10k_{\rm F}$.
  • Figure 5: Lower-lying excited state of Cooper triple phases with different configurations in a plane of two-body $p$-wave interaction strengths. The mass ratio is taken as $m_a=2m_b$, and the momentum cutoffs are taken as $\Lambda/k_{\rm F}=10$.
  • ...and 1 more figures