Resonance triplet dynamics in the quenched unitary Bose gas

The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We develop a conserving many-body theory capable of capturing these effects, allowing us to model the postquench dynamics in the previously inaccessible time regime where the gas departs from the universal prethermal stage. Our results show that this departure is driven by the growth of strong lossless three-body correlations, rather than atomic losses, thus framing the heating of the gas in this regime as a fully coherent phenomenon. We uncover the specific few-body scattering processes that affect this heating and show that the expected connection between the two-body and three-body contacts and the tail of the momentum distribution is obscured following the prethermal stage, explaining the absence of this connection in experiments. Our general framework, which reframes the dynamics of unitary quantum systems in terms of explicit connections to microscopic physics, can be broadly applied to any quantum system containing strong few-body correlations.

Figure 1

Broadening of the single-particle momentum distribution following the quench. In panels (a)–(c), we plot the dynamics of the excited-state population $n_{\mathbf{k}}^a$ for a set of momenta. Resonance doublet (triplet) model results are shown with dash-dotted (solid) lines and are matched with the normalization of the experimental data of Ref. [53], shown with gray circles. In panel (d), we show in a similar format the dynamics of the average kinetic energy per particle ${\langle \epsilon \rangle }_{\mathbf{k}}$ for the broad resonance case $R_{*}{k}_n=0.3$, comparing with the experimental data of Ref. [52]. The black dotted line shows the expected $T\sim t^{2/13}$ scaling for loss-induced heating [52].

Figure 2

Two-body (a) and three-body (b) scattering processes that drive the depletion of the atomic condensate. Atomic (molecular) states are shown with single (double) lines, and condensed states are shown with dashed red lines. Each vertex represents atom-molecule conversion.

Figure 3

Dynamics of two-body and three-body contact densities ${\mathcal{C}}_2$ in panel (a) and ${\mathcal{C}}_3$ in panel (b), for different values of the resonance width $R_{*}{k}_n$. Results from the resonance doublet (triplet) model are shown with dash-dotted (solid) lines. For comparison we show with black dashed lines the linear early-time growth of ${\mathcal{C}}_2$ as derived in Ref. [84] for broad resonances and the long-time constant value of ${\mathcal{C}}_2$ from Ref. [85]. For ${\mathcal{C}}_3$ we show the range of quadratic early-time growths derived in Ref. [63], which correspond to maximum ($k_n/{\kappa }_{*}\sim 1$) and minimum (${\kappa }_{*}\ll k_n$) enhancement of ${\mathcal{C}}_3$ due to the Efimov effect, again in the broad resonance limit.

Figure 4

Dynamics of the tail of the single-particle momentum distribution for the broad resonance $R_{*}{k}_n=0.3$. In the left-hand (right-hand) panels, we compare the resonance doublet (triplet) models with the asymptotic prediction in Eq. (10), shown with a black dashed line. For the sake of comparison the doublet results are replotted in the right-hand panels. For $t/t_n=1.0$ and 2.0, we also compare with the experimental data of Ref. [53], shown with the green circles.