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arXiv:1302.0281 · Physical Review A

Finite-range corrections near a Feshbach resonance and their role in the Efimov effect

Paul Dyke, S. E. Pollack, Randall G. Hulet

Published Aug 30, 2013• 90 citations
arXivHTMLPDF

Abstract

We have measured the binding energy of ${}^{7}$Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683 (2009)]. We find the measured locations of the three- and four-body Efimov features to be consistent with universal theory at the 20%--30% level.

DOI
10.1103/physreva.88.023625

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We have measured the binding energy of 7{}^{7}7Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683 (2009)]. We find the measured locations of the three- and four-body Efimov features to be consistent with universal theory at the 20%--30% level.
We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.
We have analyzed our recently measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet 4{}^{4}4He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides evidence for a universal 3BP outside the group of alkali-metal elements. In addition, we give examples of other atomic systems without Feshbach resonances but with a large scattering length that would be interesting to analyze once precise measurements of three-body loss are available.
A nonrelativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length aaa is much larger than the range lll of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the $\ensuremath{\mid}a\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit and finite-l∕al∕al∕a corrections to observables of interest. Here we use such an effective-theory treatment to consider the impact of corrections linear in the two-body effective range, rs{r}_{s}rs​, on the three-boson bound-state spectrum and recombination rate for $\ensuremath{\mid}a\ensuremath{\mid}⪢\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$. We do this by first deriving results appropriate to the strict limit $\ensuremath{\mid}a\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ in coordinate space. We then extend these results to finite aaa using once-subtracted momentum-space integral equations. We take the cutoff on these equations to be large compared to $1∕\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$, and find that the first-order effects of $\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$ are independent of the cutoff in this regime. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.
We observe two consecutive heteronuclear Efimov resonances in an ultracold Li-Cs mixture by measuring three-body loss coefficients as a function of magnetic field near a Feshbach resonance. The first resonance is detected at a scattering length of a_((0))=-320(10)a_((0)), corresponding to ∼7(∼3) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at 5.8(1.0)a_((0)), close to the unitarity-limited regime at the sample temperature of 450 nK. Indication of a third resonance is found in the atom loss spectra. The scaling of the resonance positions is close to the predicted universal scaling value of 4.9 for zero temperature. Deviations from universality might be caused by finite-range and temperature effects, as well as magnetic field-dependent Cs-Cs interactions.
This thesis reports measurements of interactions in Fermi-Bose 6Li-133Cs mixtures. Precise control of this Bose-Fermi mixture allowed us to probe few-body physics in regimes which were previously inaccessible. In particular, we performed the first model-independent test of geometric scaling of Efimov physics and probed Efimov resonances farther in the weakly coupled, narrow resonance regime than previously possible.,For this work, we built a new apparatus which overcomes the many challenges faced by Li-Cs mixtures. We developed several novel dipole trapping schemes which overcome the difficulties of mixing Li and Cs, including the large differences in initial trapping and cooling between these atomic species and a large differential gravitational sag. We also achieved part per million level magnetic field control near 900 G, necessary for the precise measurements near narrow Feshbach resonances undertaken in this thesis, by pioneering a tomographic magnetic field calibration technique.,With this apparatus, we first probed the Feshbach resonances of the Li-Cs mixture. This is an essential first step, allowing us to understand and control the two-body interactions between our atoms. Next we began to probe Efimov physics, an important three-body phenomenon wherein an infinite series of three-body bound states arise near two-body scattering resonances, such as Feshbach resonances. We demonstrated the universal scaling expected theoretically for Efimov states near a Feshbach resonance. This task was made feasible in our system by a reduced Efimov scaling constant, yet still required precise magnetic field control. Finally, additional universal behavior of the first Efimov resonance has been observed empirically in a variety of atomic systems. While theory has explained this observed universality, predictions also indicate departures for narrow Feshbach resonances, contrary to previous experimental results. By further improving our magnetic field control to probe a very narrow Feshbach resonance, we have observed a departure from the universal first Efimov resonance, helping to resolve this conflict between experiment and theory.
We find that universal three-body physics extends beyond the threshold regime to non-zero energies. For ultracold atomic gases with a negative two-body s-wave scattering length near a Feshbach resonance, we show that the resonant peaks characteristic of Efimov physics persist in three-body recombination to higher collision energies. For this and other inelastic processes, we use the adiabatic hyperspherical representation to derive universal analytical expressions for their dependence on the scattering length, the collision energy and—for narrow resonances—the effective range. These expressions are supported by full numerical solutions of the Schrödinger equation and display log-periodic dependence on energy characteristic of Efimov physics. This dependence is robust and might be used to experimentally observe several Efimov features.