Bound-state signatures in quenched Bose-Einstein condensates

We investigate the dynamics of a homogenous Bose-Einstein condensate (BEC) following a sudden quench of the scattering length. Our focus is the time evolution of short-range correlations via the dynamical contact. We compute the dynamics using a combination of two- and many-body models and we propose an intuitive connection between them that unifies their short-time, short-range predictions. Our two-body models are exactly solvable and, when properly calibrated, lead to analytic formulas for the contact dynamics. Immediately after the quench, the contact exhibits strong oscillations at the frequency of the two-body bound state. These oscillations are large in amplitude and their time average is typically much larger than the Bogoliubov prediction. The condensate fraction shows similar oscillations, whose amplitude we are able to estimate. These results demonstrate the importance of including the bound state in descriptions of diabatically quenched BEC experiments.

Figure 1

Contact dynamics following a quench from noninteracting to $700a_0$ for several ramp speeds near the ${}^{85}\mathrm{Rb}$ Fano-Feshbach resonance at $155.04$ G. We assume a density of ${10}^{12}{\mathrm{cm}}^{-3}$. As a reference, the red (horizontal) line represents the prediction from Bogoliubov theory, $C_0=16{\pi }^2{n}^2{a}_f^2$, which specifies the units of the vertical axis. The blue (oscillating, solid) line is the many-body-variational prediction for a quench that is completely diabatic, the cyan (dashed) line is for the experimental ramp speed of ${\dot{B}}_{\mathrm{expt}}=1.6\mathrm{G}/\mu \text{s}$ [8], the green (dot-dashed) line is for a ramp speed of ${\dot{B}}_{\mathrm{expt}}/10$, and the black (dotted) line is for a ramp speed of ${\dot{B}}_{\mathrm{expt}}/50$. In each case, the time $t=0$ defines the end of the magnetic field ramp.

Figure 2

Excitation fraction following a diabatic quench from noninteracting to $700a_0$ for a BEC of density $n={10}^{12}{\mathrm{cm}}^{-3}$. The blue (solid) line is the prediction of our many-body-variational formulation. The magenta (dashed) line is the prediction from Bogoliubov theory.

Figure 3

Momentum distributions at fixed time ${\omega }_{F}t=0.01$ after a quench from noninteracting to unitarity. The thick black line is the numerical data from a many-body variational calculation. The thin lines are the analytically computed two-body results. The cyan (solid), green (dashed), and magenta (dot-dashed) lines respectively correspond to the properly calibrated initial conditions in the order listed in Eq. (19).

Figure 4

Contact dynamics following a diabatic quench from noninteracting to $700a_0$ for a BEC of density $n={10}^{12}{\mathrm{cm}}^{-3}$. The circles represent the many-body-variational data (shown also in Fig. 1). The green (solid) line represents the formula given in Eq. (22) and the red (dashed) line represents the linear growth given in Eq. (21).

Figure 5

Contact dynamics following a diabatic quench downward with $a_f=a_i/3$. For reference, the green (dashed) line is the equilibrium contact $C_i$ for the BEC at the initial scattering length $a_i$ and the red (dot-dashed) line is the contact $C_0$ for a ground-state BEC at the final scattering length $a_f$.