Efimov Physics in Quenched Unitary Bose Gases

We study the impact of three-body physics in quenched unitary Bose gases, focusing on the role of the Efimov effect. Using a local density model, we solve the three-body problem and determine three-body decay rates at unitarity, finding density-dependent, log-periodic Efimov oscillations, violating the expected continuous scale invariance in the system. We find that the breakdown of continuous scale invariance, due to Efimov physics, manifests also in the earliest stages of evolution after the interaction quench to unitarity, where we find the growth of a substantial population of Efimov states for densities in which the interparticle distance is comparable to the size of an Efimov state. This agrees with the early-time dynamical growth of three-body correlations at unitarity [Colussi et al., Phys. Rev. Lett. 120, 100401 (2018)]. By varying the sweep rate away from unitarity, we also find a departure from the usual Landau-Zener analysis for state transfer when the system is allowed to evolve at unitarity and develop correlations.

Figure 1

(a) Energies, $E_{\beta }$ [in units of ${\epsilon }_n^{\mathrm{lo}}={\hslash }^2(6{\pi }^2{n}_{\mathrm{lo}}{)}^{2/3}/2m$], of three identical bosons at $|a|=\infty$ as a function of the local density, $n_{\mathrm{lo}}$. The dashed green lines represent the free-space Efimov state energies. (b) The corresponding population of three-body states, $|c_{\beta }{|}^2$, for quenching to unitarity. The shaded region marks the range of densities where we have studied the dynamical formation of Efimov states.

Figure 2

Three-body decay rate, ${\mathrm{\Gamma }}_3^{*}$, for ${}^{85}\mathrm{Rb}$ at $|a|=\infty$ as a function of the average density, $⟨n⟩$. This figure displays the $⟨n^{2/3}⟩$ scaling of the decay rate as well as the appearance of log-periodic oscillations associated with Efimov physics. Resonances at higher $⟨n⟩$ occur when the initial state is degenerate with one of the possibly weakly coupled final states in our model. The dashed black curve is the fitting function in Eq. (8).

Figure 3

(a) Three-body energy spectrum for $⟨n⟩\approx 9.9\times {10}^{10}{\mathrm{cm}}^{-3}$ within a range of $a$ relevant for the ${}^{85}\mathrm{Rb}$ experiment. The black solid line corresponds to the energy of the (free-space) diatomic state (${\hslash }^2/m{a}^2$). (b) Corresponding change of population during the field sweep ($t_{\mathrm{sw}}\approx 0.17t_n$) obtained immediately after the quench ($t_{\text{dwell}}=0$). (c)–(e) Population fraction of diatomic and Efimov states formed as a function of $t_{\text{dwell}}$ illustrating the enhancement of Efimov state formation as the density approaches the characteristic value $⟨n_1^{*}⟩\approx 5.2\times {10}^{10}{\mathrm{cm}}^{-3}$ [Eq. (9)] or, equivalently, when $k_n{R}_{3b}\approx 0.78(2)$ [30].

Figure 4

Dependence of $f_{2b}$ and $f_{3b}$ on $t_{\mathrm{sw}}$ for (a), (b) [$⟨n⟩\approx 9.9\times {10}^{10}{\mathrm{cm}}^{-3}$] and (c),(d) [$9.7\times {10}^{11}{\mathrm{cm}}^{-3}$]. For $t_{\text{dwell}}=0$, the dependence on $t_{\mathrm{sw}}$ is well described by the Landau-Zener results (see text), while for $t_{\text{dwell}}=0.5t_n$ [(b) and (d)], the growth of correlations leads to the enhancement of the trimer population and a departure from the Landau-Zener results.