Fast Transport of Trapped Ultracold Atoms Using Shortcuts-to-Adiabaticity by Counterdiabatic Driving

TL;DR

The paper addresses the problem of fast, high-fidelity transport of a trapped Bose-Einstein condensate (BEC) using shortcuts-to-adiabaticity (STA) implemented via counterdiabatic driving (CD). The authors formulate a CD potential $V_{\text{CD}}(t)=-m\ddot{\mathbf f}(t)\cdot\mathbf q$ on top of the original trap $H_0(t)$ and realize both the trap and CD potential with time-averaged painted potentials, solving the 2D Gross-Pitaevskii equation to assess fidelity. They find a minimum transport time below which fidelity drops, and show that STA achieves high fidelity around 10–12 ms, outperforming a constant-acceleration protocol that is sensitive to trap frequency; fidelity in the STA case is robust to trap depth, whereas CA fidelity exhibits resonances with the trap frequency. The work demonstrates the practicality of painted-potentials for CD-based STA in nonlinear quantum fluids and suggests experimental routes to explore quantum speed limits in fast BEC transport.

Abstract

We numerically study the fast spatial transport of a trapped Bose-Einstein condensate (BEC) using shortcuts-to-adiabaticity (STA) by counterdiabatic driving (CD). The trapping potential and the required auxiliary potential were simulated as painted potentials. We compared STA transport to transport that follows a constant-acceleration scheme (CA). Experimentally feasible values of trap depth and atom number were used in the 2D Gross-Pitaevskii equation (GPE) simulations. Different transport times, trap depths, and trap lengths were investigated. In all simulations, there exists a minimum amount of time necessary for fast transport, which is consistent with previous results from quantum speed limit studies.

Figures (5)

• Figure 1: A comparison of the (a) trajectories, (b) instantaneous speeds, and (a) accelerations between the STA protocol and a constant acceleration scheme. Note the relatively similar behaviors of the trajectories and speed profiles, but the STA acceleration follows the behavior of a third-order polynomial.
• Figure 2: Time evolution of the trapped BEC density (blue) and the trapping and auxiliary potentials (orange) during (a) a 12-ms and (b) a 5-ms transport. The 12-ms transport results into a quantum fidelity of 1, while the 5-ms transport has a low quantum fidelity, with atoms spilling out of the trap.
• Figure 3: The resulting quantum fidelities after transport of a BEC with $N = 10000 \text{ atoms}$ for (a) an STA protocol and (b) a constant-acceleration scheme.
• Figure 4: The measured trap frequencies along the transport direction for a given trap depth. The frequencies were calculated using GPE simulations of a trapped BEC that is initially displaced in a nonmoving trap and observing the COM oscillations for $5ms$.
• Figure 5: Post-transport fidelities for different beam widths of the painting beam. There is a shift in the location of the transition region between regions of low and high fidelities for different beam widths.