Condensation of Cooper Triples

Akagami, Sora; Tajima, Hiroyuki; Iida, Kei

doi:10.48550/arxiv.2102.03701

Cited by 3 publications

(4 citation statements)

References 39 publications

(48 reference statements)

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“…Also, we do not consider the three-body interaction whose effect has already been investigated in Refs. [63,64,66,67]. While the three-body attraction tends to stabilize three-body bound states, here we are interested in the stabilization of them due to the purely two-body attractions.…”

Section: Hamiltonianmentioning

confidence: 99%

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Three-body crossover from a Cooper triple to bound trimer state in three-component Fermi gases near a triatomic resonance

Tajima,

Tsutsui,

Doi

et al. 2021

Preprint

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We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two-and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length a − for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.

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Section: Hamiltonianmentioning

confidence: 99%

“…It is also an interesting question whether a three-body counterpart of a Cooper pair called a Cooper triple exists or not in three-component Fermi mixtures [56,[62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Three-body crossover from a Cooper triple to bound trimer state in three-component Fermi gases near a triatomic resonance

Tajima,

Tsutsui,

Doi

et al. 2021

Preprint

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“…For a possible method for eliminating the s-wave interaction, see Appendix in Ref. [68]. The intra-component p-wave interaction is not considered in this work.…”

Section: Formulationmentioning

confidence: 99%

Unitary $p$-wave Fermi gas in one dimension

Tajima,

Tsutsui,

Doi

et al. 2021

Preprint

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We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the p-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, p-wave scattering length and effective range. At the unitarity limit where the p-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 s-wave interaction in three dimensions. It is in contrast to a Fermi gas with the p-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary p-wave Fermi gas within the many-body T -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 p-wave Fermi gas.

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“…Such systems are described by the SU(N ) Hubbard model, which is a generalization of the Hubbard model for the internal degrees of freedom. In a continuous system, Cooper triples, a generalization of Cooper pairs, have been proposed for SU (3) fermions [35,36]. However, its lattice counterpart is missing.…”

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confidence: 99%

Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $η$-pairing states with $N$-particle off-diagonal long-range order

Yoshida,

Katsura

2021

Preprint

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We consider N -particle generalizations of η-pairing states in a chain of N -component fermions and show that these states are exact (high-energy) eigenstates of an extended SU(N ) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd N . When N is even, these states exhibit off-diagonal long-range order in N -particle reduced density matrix. On the other hand, when N is odd, the singlet correlation function decays exponentially toward the other end of the chain but shows a revival at the other end. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

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Condensation of Cooper Triples

Cited by 3 publications

References 39 publications

Three-body crossover from a Cooper triple to bound trimer state in three-component Fermi gases near a triatomic resonance

Three-body crossover from a Cooper triple to bound trimer state in three-component Fermi gases near a triatomic resonance

Unitary $p$-wave Fermi gas in one dimension

Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $η$-pairing states with $N$-particle off-diagonal long-range order

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