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arXiv:1206.1569

Atom-dimer p-wave resonance for fermionic mixtures with different masses

R. Combescot, X. Leyronas

Published Jun 7, 2012• 0 citations
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Abstract

We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.

DOI
10.48550/arxiv.1206.1569

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We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for 6^66Li-40^{40}40K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.
We study near a Feshbach resonance, as a function of the mass ratio, the fermion-dimer scattering amplitude in fermionic mixtures of two fermion species. When masses are equal the physical situation is known to be quite simple. We show that, when the mass ratio is increased, the situation becomes much more complex. For the sss-wave contribution we obtain an analytical solution in the asymptotic limit of very large mass ratio. In this regime the sss-wave scattering amplitude displays a large number of zeros, essentially linked to the known large value of the fermion-dimer scattering length in this regime. We find by an exact numerical calculation that a zero is still present for a mass ratio of 15. For the ppp-wave contribution we make our study below the mass ratio of 8.17, where a fermion-dimer bound state appears. We find that a strong ppp-wave resonance is present at low energy, due to a virtual bound state, in the fermion-dimer system, which is a forerunner of the real bound state. This resonance becomes prominent in the mass ratio range around the one corresponding to the 40{}^{40}40K -6{}^{6}6Li mixtures, much studied experimentally. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one of the fermionic species by making use of an optical lattice. This would allow one to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements. In particular one could check if the virtual bound state is relevant for the instabilities of these mixtures.
We present a joint experimental and theoretical investigation of the lifetime of weakly bound dimers formed near narrow interspecies Feshbach resonances in mass-imbalanced Fermi-Fermi systems, considering the specific example of a mixture of 6Li^{6}\text{Li}6Li and 40K^{40}\text{K}40K atoms. Our work addresses the central question of the increase in the stability of the dimers resulting from Pauli suppression of collisional losses, which is a well-known effect in mass-balanced fermionic systems near broad resonances. We present measurements of the spontaneous dissociation of dimers in dilute samples, and of the collisional losses in dense samples arising from both dimer-dimer processes and from atom-dimer processes. We find that all loss processes are suppressed close to the Feshbach resonance. Our general theoretical approach for fermionic mixtures near narrow Feshbach resonances provides predictions for the suppression of collisional decay as a function of the detuning from resonance, and we find excellent agreement with the experimental benchmarks provided by our $^{6}\text{Li}\ensuremath{-}^{40}\text{K}$ system. We finally present model calculations for other Feshbach-resonant Fermi-Fermi systems, which are of interest for experiments in the near future.
We investigate a mixture of ultracold fermionic K40 atoms and weakly bound Li6K40 dimers on the repulsive side of a heteronuclear atomic Feshbach resonance. By radio-frequency spectroscopy we demonstrate that the normally repulsive atom-dimer interaction is turned into a strong attraction. The phenomenon can be understood as a three-body effect in which two heavy K40 fermions exchange the light Li6 atom, leading to attraction in odd partial-wave channels (mainly p wave). Our observations show that mass imbalance in a fermionic system can profoundly change the character of interactions as compared to the well-established mass-balanced case.
We consider a heteronuclear fermionic mixture on the molecular side of an interspecies Feshbach resonance and discuss atom-dimer scattering properties in uniform space and in the presence of an external confining potential, restricting the system to a quasi-two-dimensional geometry. We find that there is a peculiar atom-dimer p-wave resonance which can be tuned by changing the frequency of the confinement. Our results have implications for the ongoing experiments on lithium-potassium mixtures, where this mechanism allows for switching the p-wave interaction between a K atom and Li-K dimer from attractive to repulsive, and forming a weakly bound trimer with unit angular momentum. We show that such trimers are long lived and the atom-dimer resonance does not enhance inelastic relaxation in the mixture, making it an outstanding candidate for studies of p-wave resonance effects in a many-body system.
We derive the expressions for the virial coefficients up to the third order for two-species fermion mixtures, and investigate the fugacity of the species and the interaction energy density around the sss-wave Feshbach resonance in 6Li^{6}\mathrm{Li}6Li-40K^{40}\mathrm{K}40K mixtures. The theoretical results show that the magnitude of the virial coefficients depends on the mass ratio in a mass-imbalanced system. We find that the contribution of two-body bound states to high-order virial coefficients is very small at temperatures of microkelvin order. With the decrease of T/TFT/{T}_{F}T/TF​, the positions of the maxima of fugacity and interaction energy density shift away from the resonance position in the third-order virial expansion calculation. The mass ratio determines the relevance between the fugacity and number density of heavy species. Our conclusion is also effective for other mass-imbalanced systems.
A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between the two atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs, and an exchange of fermionic spins. Low-energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.