Quenching to unitarity: Quantum dynamics in a three-dimensional Bose gas

We study the dynamics of a zero-temperature Bose condensate following a sudden quench of the scattering length from noninteracting to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rate. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be understood within a simple, analytic two-body model. We make a quantitative prediction for the evolution of Tan's contact and find features in the momentum distribution that are absent in equilibrium. Third, we study three-body loss at finite density under the same dynamic scenario. We find lifetimes that are long compared to the saturation times of large-momentum modes, and we relate this result to the three-body inelasticity parameter.

Figure 1

Immediately following a quench in the scattering length, the dynamics originates in causally isolated regions of the cloud. The collective effect of other particles in the system is modeled by an artificial trap [25, 26], tailored to give the particles a mean interparticle separation which is consistent with that of the many-body system.

Figure 2

The momentum distribution for two different times ${\omega }_{\mathrm{F}}t=0.05$ (shown in red) and ${\omega }_{\mathrm{F}}t=0.4$ (shown in blue). The solid lines show results from the many-body model, and the dashed lines show results from the harmonically trapped two-body model. Note that $n_k=n{\left(2\pi \right)}^3{n}_k^{\left(2\mathrm{B}\right)}$ [32]. The inset shows dynamics of the condensate fraction within the many-body model.

Figure 3

(a) Saturation of the contact as a function of time (blue solid line). The dashed line shows Eq. (5), valid at short times. (b) Comparison of two-body (dashed) and many-body (solid) momentum occupation at $k=7k_{\mathrm{F}}$ as a function of time.