Frictionless quantum quenches in ultracold gases: A quantum-dynamical microscope

In this Rapid Communication, a method is proposed to spatially scale up a trapped ultracold gas while conserving the quantum correlations of the initial many-body state. For systems supporting self-similar dynamics, this is achieved by implementing an engineered finite-time quench of the harmonic trap, which induces a frictionless expansion of the gas and acts as a quantum dynamical microscope.

Figure 1

Adiabatic limit. The scaling factor following a quench for increasing quench time $\tau$ eventually approaches the adiabatic result $\gamma =\sqrt{({\omega }_0/{\omega }_f)}=\sqrt{10}$. The inset shows how $\dot{b}\left(t_f\right)$ vanishes for large values of $\tau$ ($t_f=20\tau$).

Figure 2

Adiabatic limit. Momentum distribution of a Tonks-Girardeau gas following a quench of the trapping potential [see Eq. (7)] with $N=10$, $\omega \left(0\right)={\omega }_0$, and $\omega \left(\tau \right)={\omega }_0/10$ for increasing quench times $\tau =$(A) 0.1, (B) 1, (C) 10, and (D) 100 in units of ${\omega }_0^{-1}$. The dashed line represents the distribution following the quench, while the solid line corresponds to the desired adiabatic limit ($t_f=500$, $k_0=\sqrt{m{\omega }_0/\hslash }$). The insets show the evolution of the scaling function $b\left(t\right)$ along and after the quench. The adiabatic limit is approached for increasing values of $\tau \sim 100{\omega }_0$, leading to a suppression of the breathing dynamics of the cloud and scaling of quantum correlations.

Figure 3

Frictionless quantum quench of a Tonks-Girardeau gas. Evolution of the momentum distribution exhibiting signs of dynamical fermionization at an intermediate stage of the expansion, before reaching the final time $\tau$ at which it reduces to the scaled-up distribution of the initial trapped state ($\gamma =\sqrt{10}$, $N=10$). The inset shows the smooth evolution of the scaling factor in a frictionless expansion in an arbitrarily short quench time $\tau$ for both $\gamma =\sqrt{2}$ (solid line) and $\sqrt{10}$ (dashed line) expansion factors.