We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the Kartavtsev-Malykh universal trimer states resulting from the s-wave particle-fermion interaction, the fermion-fermion p-wave interaction induces one or two shallow trimers in a large domain of the control parameters, including a borromean regime where the ground-state trimer exists in the absence of dimer at any mass ratio between the fermions and the particle. A generic picture of the trimer spectrum emerges from this work in terms of the low-energy parameters of the interactions.
Abstract We investigate the effects of p-wave interactions on Efimov trimers in systems comprising two identical heavy fermions and a light particle, with mass ratios larger than 13.6. Our focus lies on the Borromean regime where the ground-state trimer exists in the absence of dimers. Using pair-wise Lennard–Jones potentials and concentrating on the L π = 1 − symmetry, we explore the critical value of the interspecies s-wave scattering length a c at which the Borromean state appears in several two-component particle systems. Our exploration encompasses the universal properties of a c and the influence of p-wave fermion–fermion interactions on its value. We find that, in the absence of p-wave fermion–fermion interactions, a c is determined universally by the van der Waals radius and mass ratio. However, the introduction of p-wave fermion–fermion interactions unveiled a departure from this universality. Our calculations show that the critical interspecies scattering length a c now depends on the details of the fermion–fermion p-wave interaction. And, the presence of p-wave fermion–fermion interactions favors the formation of the Borromean state. Additionally, our investigation reveals that Efimov effect in the 1 − symmetry persist even when the fermion–fermion interaction reaches the p-wave unitary limit.
For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large
s-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous one. We point out that a third type of trimer, ``crossover trimers,'' exists universally regardless of short-range details of the potential. These crossover trimers have neither discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the Kartavtsev-Malykh trimers, Efimov trimers, crossover trimers, and nonuniversal trimers in terms of the mass ratio and the
s-wave scattering length by investigating the scaling property and universality (i.e., independence on short-range details) of the trimers.
We study the quantum three-body free space problem of two same-spin-state fermions of mass
m interacting with a different particle of mass
M, on an infinitely narrow Feshbach resonance with infinite
s-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio
α=m/M. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within {\sl each} sector of fixed total angular momentum
l. For
α increasing from
0, we find that the trimer states first appear at the
l-dependent Efimovian threshold
αc(l), where the Efimov exponent
s vanishes, and that the {\sl entire} trimer spectrum (starting from the ground trimer state) is geometric for
α tending to
αc(l) from above, with a global energy scale that has a finite and non-zero limit. For further increasing values of
α, the least bound trimer states still form a geometric spectrum, with an energy ratio
exp(2π/∣s∣) that becomes closer and closer to unity, but the most bound trimer states deviate more and more from that geometric spectrum and eventually form a hydrogenoid spectrum.
We study the quantum three-body free-space problem of two same-spin-state fermions of mass
m interacting with a different particle of mass
M, on an infinitely narrow Feshbach resonance with infinite
s-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio $\ensuremath{\alpha}=m/M$. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within each sector of fixed total angular momentum
l. For $\ensuremath{\alpha}$ increasing from 0, we find that the trimer states first appear at the
l-dependent Efimovian threshold ${\ensuremath{\alpha}}_{c}^{(l)}$, where the Efimov exponent
s vanishes, and that the entire trimer spectrum (starting from the ground trimer state) is geometric for $\ensuremath{\alpha}$ tending to ${\ensuremath{\alpha}}_{c}^{(l)}$ from above, with a global energy scale that has a finite and nonzero limit. For further increasing values of $\ensuremath{\alpha}$, the least bound trimer states still form a geometric spectrum, with an energy ratio $\mathrm{exp}(2\ensuremath{\pi}/|s|)$ that becomes closer and closer to unity, but the most bound trimer states deviate more and more from that geometric spectrum and eventually form a hydrogenoid spectrum.
Abstract An unusual class of equal mass p-wave universal trimers with symmetry L Π = 1 ± is identified, for both a two-component fermionic trimer with s- and p-wave scattering length close to unitarity and for a one-component fermionic trimer at p-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for L Π = 1 ± , when the p-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to the p-wave unitary limit. The universality of these p-wave universal trimers is tested here by considering van der Waals interactions in a Lennard–Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry L Π = 1 − when the two fermion interactions are close to p-wave unitarity and the lowest 1 / R 2 coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving three-body continuum channels.