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arXiv:1011.0006 · Physical Review Letters

Pauli Blocking Effect on Efimov States near a Feshbach Resonance

David MacNeill, Fei Zhou

Published Apr 4, 2011• 34 citations
arXivHTMLPDF

Abstract

In this Letter we study the effect of Pauli blocking on Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.

DOI
10.1103/physrevlett.106.145301

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In this Letter we study the effect of Pauli blocking on Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in 39K^{39}\mathrm{K}39K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.
We consider a dense ultracold Fermi gas in the presence of a Feshbach resonance. We investigate how the threshold for bound state formation, which is just at the Feshbach resonance for a dilute gas, is modified due to the presence of the Fermi sea. We make use of a preceding framework of handling this many-body problem. We restrict ourselves to the simple case where the chemical potential μ is negative, which allows us to cover in particular the classical limit where the effect is seen to disappear. We show that, within a simple approach where basically only the effect of Pauli exclusion is included, the Fermi sea produces a large shift of the threshold, which is of the order of the width of the Feshbach resonance. This is in agreement with very recent experimental findings.
We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\ensuremath{\hbar}{k}_{F}$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\ensuremath{\hbar}{k}_{F}$, because near $\ensuremath{\hbar}{k}_{F}$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio mB/mF{m}_{B}/{m}_{F}mB​/mF​ is smaller than a critical value (estimated to be 0.1360.1360.136), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of 6Li^{6}\mathrm{Li}6Li40K^{40}\mathrm{K}40K, 6Li^{6}\mathrm{Li}6Li87Rb^{87}\mathrm{Rb}87Rb, 40K^{40}\mathrm{K}40K87Rb^{87}\mathrm{Rb}87Rb, and 6Li^{6}\mathrm{Li}6Li23Na^{23}\mathrm{Na}23Na near broad interspecies resonances, and discuss the limitations of our calculations and implications.
Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a three-body Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasibound state with a finite decay width.
We study Efimov physics of three identical bosons with pairwise multichannel interactions for Feshbach resonances of adjustable width in magnetic field. We find that the two-body multichannel realization of the interaction can affect the universal Efimov spectrum, especially for resonances of intermediate width. We analyze two scenarios that are equivalent on the two-body level but differ in their realization in three-body multichannel spin space. The deviations in the Efimov spectra of these scenarios are caused by trimer states in the closed interaction channels whose binding energy and coupling strength to the Efimov states depend on the spin realization. However, in the narrow resonance limit the Efimov spectrum is set by the resonance width parameter r∗{r}^{*}r∗ only and does not depend on the realization in spin space. We find this limit to be even independent of the interaction potential considered. In the broad resonance limit all excited Efimov trimer energies approach the ones from the corresponding single-channel system for the scenarios investigated.