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arXiv:1307.3193 · Physical Review Letters

Stability of a Unitary Bose Gas

Richard J. Fletcher, Alexander L. Gaunt, Nir Navon, Robert P. Smith, Zoran Hadzibabic

Published Sep 20, 2013• 108 citations
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Abstract

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

DOI
10.1103/physrevlett.111.125303

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We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.
We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient L3{L}_{3}L3​. Our data follow a ${L}_{3}={\ensuremath{\lambda}}_{3}/{T}^{2}$ law with ${\ensuremath{\lambda}}_{3}=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }(\ensuremath{\mu}\mathrm{K}{)}^{2}\text{ }{\mathrm{cm}}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length aaa at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where ∣a∣|a|∣a∣ is smaller than the thermal wavelength. We find that L3{L}_{3}L3​ is continuous across the resonance, and over the whole a<0a<0a<0 range our data quantitatively agree with our calculation.
Ultracold gases have become versatile systems to study quantum many-body effects. Their high degree of control and the tunability of the atomic interactions led to important advances in the understanding of strongly correlated matter. In the regime of strong interactions, unlike fermions, the study of bosons is hampered by three-particle recombination that leads to atom losses and keeps the system from reaching a real equilibrium state. In this thesis, we have performed the first quantitative comparison between theory and experiment on the three-particle loss coefficient L_3(a,T), for arbitrary scattering length a and temperature T. For unitary two-particle scattering (|a| → ∞), we show that the three-particle loss coefficient follows the law L_3(∞, T ) = λ_3/T^2, that we have tested using a trapped non-degenerate ^{7}Li gas maintained at constant temperature. The measured value of λ_3 = 2.5(3)_{stat}(6)_{cyst} × 10^{−20}(μK)^2cm^6s^{−1} is, within the error bars in good agreement with the theory prediction λ_3^{th} = 1.52 × 10^{−20}(μK)^2cm^6s^{−1}. We have extended our measurements to arbitrary values of the scattering length a. For a < 0, the theory predicts a smooth connection between the previously derived zero-temperature model for L_3(a, 0) and the unitarity limited loss coefficient L_3(∞, T ). We also show that a second Efimov resonance in 7Li should be observable near a = − 500 a0 for a temperature of 1 μK. Finally, we compare our theoretical prediction with measurements performed at Innsbruck with ^{133}Cs and at Cambridge with ^{39}K. The theory also shows remarkable quantitative agreement with these measurements.
Recent measurements of Efimov resonances for a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of 40K and 87Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between 40K87Rb Feshbach molecules and 87Rb atoms. However, we do not observe any Efimov-related resonances in the rates of inelastic collisions between three atoms. These observations are compared to previous measurements by the LENS group of Efimov resonances in a 41K and 87Rb mixture as well as to recent predictions.
The low-temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here, we present experiments performed with unitary 133Cs and 7Li atoms in two different setups, which enable quantitative comparison of the three-body recombination rate in the low-temperature domain. We develop a theoretical model that describes the dynamic competition between two-body evaporation and three-body recombination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal "magic" trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the two-dimensional evaporation case, and it fully supports our experimental findings. Combined 133Cs and 7Li experimental data allow investigations of loss dynamics over 2 orders of magnitude in temperature and 4 orders of magnitude in three-body loss rate. We confirm the 1/T2 temperature universality law. In particular, we measure, for the first time, the Efimov inelasticity parameter η*=0.098(7) for the 47.8-G d-wave Feshbach resonance in 133Cs. Our result supports the universal loss dynamics of trapped unitary Bose gases up to a single parameter η*.
Few-body effects play an important role for the understanding of ultracold quantum gases. We make use of an effective field theory approach to investigate various aspects of universal few-body physics close to a Feshbach resonance. That is the regime where the scattering length is large compared to all other length scales of the system and thus determines the observables. It is also the regime where the Efimov effect whose main characteristic is the occurrence of a sequence of three-body bound states becomes important. At unitarity, i.e., for diverging scattering length, the ratio of binding energies of neighboring states approaches a constant. The existence of those trimers can be captured by a single three-body parameter and influences observables such as recombination rates. Starting from adequate Lagrangians, we derive atom-dimer scattering amplitudes that contain all information of interest about the three-particle systems. With this method, we first investigate the scattering of atoms and dimers at finite temperature in the presence of the Efimov effect. We calculate the dimer relaxation rate and obtain good agreement with available experimental data. Furthermore, heteronuclear mixtures exhibiting large interspecies scattering length are studied in detail. If bosons are the majority species, the Efimov effect occurs in an S-wave channel and we are able to compute three-body recombination and dimer relaxation rates. The results are compared to the outcome of two existing experiments. For mainly fermionic systems, the Efimov effect is only present in an overall P-wave and three-body recombination at threshold vanishes. However, in mixtures of atoms and dimers, scattering cross sections and dimer relaxation show the typical Efimov behavior of log-periodicity. We also consider two-dimensional Bose gases, where the Efimov effect does not occur. For those systems, we derive an equation including the first non-universal corrections and deduce three-body observables such as binding energies and atom-dimer scattering parameters.
We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)<a(s)*, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium branch. The conditions of low three-body recombination require that the particle number N<1.024(T/ω)(5/2) in a harmonic trap with frequency ω.