arXiv:2210.07042 · Physical review. B./Physical review. B

Competition between pairing and tripling in one-dimensional fermions with coexistent s - and p -wave interactions

Yixin Guo, Hiroyuki Tajima

Published Jan 31, 2023• 7 citations

Abstract

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity $s$-wave and odd-parity $p$-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 $s$- and $p$-wave Cooper pairing phases, and Cooper tripling phase, in a plane of $s$- and $p$-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both $s$- and $p$-wave interactions are moderately strong.

DOI: 10.1103/physrevb.107.024511

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arXiv:2210.07042 · Physical review. B./Physical review. B

Competition between pairing and tripling in one-dimensional fermions with coexistent s - and p -wave interactions

Yixin Guo, Hiroyuki Tajima

Published Jan 31, 2023• 7 citations

arXiv HTML PDF

Abstract

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity

s

-wave and odd-parity

p

-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

s

- and

p

-wave Cooper pairing phases, and Cooper tripling phase, in a plane of

s

- and

p

-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both

s

- and

p

-wave interactions are moderately strong.

DOI: 10.1103/physrevb.107.024511

Related papers

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Yixin Guo, Hiroyuki Tajima

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 $p$ -wave Cooper pairing and Cooper tripling phases in a plane of $p$ -wave two- and three-body coupling strengths.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 $p$-wave Cooper pairing and Cooper tripling phases in a plane of $p$-wave two- and three-body coupling strengths.

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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.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.

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arXiv:2303.09186Mar 16, 20230 citations

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Alona Nikolaeva, Orest Hryhorchak, V. Pastukhov

Abstract The ground state of spin- $1/2$ fermions with contact $s$ -wave inter- and $p$ -wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension $D<2$ and discuss in detail the phase diagram in the 1D case. Except for clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist. PACS numbers: 67.85.-dAbstract The ground state of spin-$1/2$ fermions with contact $s$-wave inter- and $p$-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension $D<2$ and discuss in detail the phase diagram in the 1D case. Except for clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist. PACS numbers: 67.85.-d

Jun 17, 20250 citations

Finite-momentum trimers and Cooper quartets in a one-dimensional Fermi gas with coexistent $s$ - and $p$ -wave interactionsFinite-momentum trimers and Cooper quartets in a one-dimensional Fermi gas with coexistent $s$- and $p$-wave interactions

Yixin Guo

We study finite-momentum trimers and Cooper quartets in a one-dimensional two-component Fermi gas with coexistent $s$ - and $p$ -wave interactions, regularized in the relative momentum of each pair so that they remain Galilean invariant. Pauli blocking alone then makes the trimer dispersion deviate from free center-of-mass motion, so the trimer energy can be lowest at finite total momentum. Allowing this motion expands the $abb$ region among pairs and trimers and removes the region where an odd-wave pair is lowest. The $aabb$ quartet lies below all these branches at every sampled coupling, and in a strip starting on the crossing of the two dimer-pair channels its lowest breakup channel is a moving $abb$ trimer and an atom. At weak interspecies attraction, a variational bound shows that two odd-wave Cooper pairs bind into a quartet, whose binding exceeds that of the coexisting trimer by orders of magnitude as the attraction weakens. At stronger interspecies attraction, the quartet binding relative to two unlike-species dimers disappears when the odd-wave interaction is switched off, although the even-wave interaction dominates the interaction energy. Relative to the in-vacuum case, the Fermi sea enhances the weak-coupling quartet binding, and at fixed scattering lengths the quartet binding grows with density while the coexisting trimer becomes much shallower. These results show that neither the most strongly bound pair nor the dominant interaction energy alone determines whether the quartet binds.We study finite-momentum trimers and Cooper quartets in a one-dimensional two-component Fermi gas with coexistent $s$- and $p$-wave interactions, regularized in the relative momentum of each pair so that they remain Galilean invariant. Pauli blocking alone then makes the trimer dispersion deviate from free center-of-mass motion, so the trimer energy can be lowest at finite total momentum. Allowing this motion expands the $abb$ region among pairs and trimers and removes the region where an odd-wave pair is lowest. The $aabb$ quartet lies below all these branches at every sampled coupling, and in a strip starting on the crossing of the two dimer-pair channels its lowest breakup channel is a moving $abb$ trimer and an atom. At weak interspecies attraction, a variational bound shows that two odd-wave Cooper pairs bind into a quartet, whose binding exceeds that of the coexisting trimer by orders of magnitude as the attraction weakens. At stronger interspecies attraction, the quartet binding relative to two unlike-species dimers disappears when the odd-wave interaction is switched off, although the even-wave interaction dominates the interaction energy. Relative to the in-vacuum case, the Fermi sea enhances the weak-coupling quartet binding, and at fixed scattering lengths the quartet binding grows with density while the coexisting trimer becomes much shallower. These results show that neither the most strongly bound pair nor the dominant interaction energy alone determines whether the quartet binds.

arXiv:2609.37032Sep 29, 20260 citations

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity

s

-wave and odd-parity

p

s

- and

p

-wave Cooper pairing phases, and Cooper tripling phase, in a plane of

s

- and

p

-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both

s

- and

p

-wave interactions are moderately strong.

p

-wave Cooper pairing and Cooper tripling phases in a plane of

p

-wave two- and three-body coupling strengths.

s

- and

p

-wave pairing phases, and {trimer} phase with different configurations, in a plane of

s

- and

p

-wave pairing strengths. Within the explored ranges of

s

- and

p

-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

s

- and

p

-wave interactions are moderately strong. There is also a competition between different clustering configurations of three-body clustering.

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.

Competition of superfluid phases in low-dimensional spin-

1\over 2

fermions with

s

- and

p

-wave interactions

The ground state of spin-

1\over 2

fermions with contact

s

-wave inter- and

p

-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension

D<2

and discuss in detail the phase diagram in 1D case. Except clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist.

Abstract The ground state of spin-

1/2

fermions with contact

s

-wave inter- and

p

-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension

D<2

and discuss in detail the phase diagram in the 1D case. Except for clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist. PACS numbers: 67.85.-d

Finite-momentum trimers and Cooper quartets in a one-dimensional Fermi gas with coexistent

s

- and

p

-wave interactions

We study finite-momentum trimers and Cooper quartets in a one-dimensional two-component Fermi gas with coexistent

s

- and

p

-wave interactions, regularized in the relative momentum of each pair so that they remain Galilean invariant. Pauli blocking alone then makes the trimer dispersion deviate from free center-of-mass motion, so the trimer energy can be lowest at finite total momentum. Allowing this motion expands the

abb

region among pairs and trimers and removes the region where an odd-wave pair is lowest. The

aabb

quartet lies below all these branches at every sampled coupling, and in a strip starting on the crossing of the two dimer-pair channels its lowest breakup channel is a moving

abb

trimer and an atom. At weak interspecies attraction, a variational bound shows that two odd-wave Cooper pairs bind into a quartet, whose binding exceeds that of the coexisting trimer by orders of magnitude as the attraction weakens. At stronger interspecies attraction, the quartet binding relative to two unlike-species dimers disappears when the odd-wave interaction is switched off, although the even-wave interaction dominates the interaction energy. Relative to the in-vacuum case, the Fermi sea enhances the weak-coupling quartet binding, and at fixed scattering lengths the quartet binding grows with density while the coexisting trimer becomes much shallower. These results show that neither the most strongly bound pair nor the dominant interaction energy alone determines whether the quartet binds.