Improved anharmonic trap expansion through enhanced shortcuts to adiabaticity

TL;DR

The paper addresses fast, high-fidelity control for expanding anharmonic traps, where direct STA can fail. It develops a generalized eSTA framework using time-dependent perturbation theory to incorporate higher-order corrections, introducing two schemes, eSTA1 and eSTA2, based on gradient and Hessian information to optimize fidelity $F(\mu,\vec{\lambda})$. The authors apply these methods to Gaussian and accordion lattice traps, deriving corrections $\widetilde{\omega}(t)^2 = \omega(t)^2 + \Omega(\vec{\lambda},t)$ and showing that eSTA2 consistently yields higher fidelity and lower sensitivity to amplitude errors, often with only modest extra energy cost. The results provide analytic, robust quantum control strategies with broad applicability to trap engineering and related quantum technologies.

Abstract

Shortcuts to adiabaticity (STA) have been successfully applied both theoretically and experimentally to a wide variety of quantum control tasks. In previous work the authors have developed an analytic extension to shortcuts to adiabaticity, called enhanced shortcuts to adiabaticity (eSTA), that extends STA methods to systems where STA cannot be applied directly [Phys. Rev. Research 2, 023360 (2020)]. Here we generalize this approach and construct an alternative eSTA method that takes advantage of higher order terms. We apply this eSTA method to the expansion of both a Gaussian trap and accordion lattice potential, demonstrating the improved fidelity and robustness of eSTA.

Figures (4)

• Figure 1: (color online) Diagram of eSTA construction, $F(\mu, \epsilon \hat{v})$ vs. $\epsilon$. The true fidelity landscape (solid green), $\text{eSTA}_1$ parabolic approximation (dot-dashed blue) and $\text{eSTA}_2$ parabola (dashed red) are shown. The normalized gradient $\hat{v}$ is represented by the solid black arrow, and $F(\mu_s,\vec{0})$ corresponds with $f(0)$. The result of applying $\text{eSTA}_2$ is the improved control vector $\vec{\lambda}_s^{(2)}= \epsilon_s^{(2)} \hat{v}$, which is shown matching the peak of the true fidelity landscape well.
• Figure 2: Examples of $\omega^2(t)/\omega_0^2$ using $\gamma=10$, with $\omega_0 t_f =$ 10 (solid-red), 15 (dashed-blue), and 30 (dotted-green). Inset: Example of $\Omega$ with $\tau_L = 26$ for fast lattice expansion using $\text{eSTA}_2$, with black dots indicating $M=8$ parameterization of Eq. \ref{['eq:Omega_param']}.
• Figure 3: Fidelity vs. expansion time $\tau_{L/G}$. (a) Lattice expansion; STA (solid green), $\text{eSTA}_1$ with $M=8$ components (solid blue) and $M=1$ (dotted blue), $\text{eSTA}_2$$M=8$ (solid red) and $M=1$ (dashed red). Lattice parameters as in Sec. \ref{['sec_fid_lattice']} for this plot and the inset. Inset: Fidelity vs $\epsilon/\epsilon_s^{(2)}$ for lattice expansion with $\tau_L=25$; true fidelity landscape (solid green), $\text{eSTA}_1$ (dotted blue) and $\text{eSTA}_2$ (dashed red) parabola approximations. (b) Gaussian trap expansion; same labeling as (a), with $M=1$ and $M=8$ results indistinguishable (solid lines omitted). Physical values given in Sec. \ref{['sec_fid_gaussian']}. Inset: Same labeling as (a) with $\tau_G = 13$.
• Figure 4: Trap expansion sensitivity $S=\left| \partial F / \partial \delta \right|$ vs. $\tau_{L/G}$ Same parameters and labeling as Fig \ref{['fig:3_fid_plots']}. (a) Lattice expansion, with first $\tau_L$ for which $F>0.95$ marked on each line. Inset: Time averaged energy (Eq. \ref{['eq:time_avg_E']}) of the eSTA schemes scaled by the STA scheme (dot-dashed green), $\widetilde{E}$ vs. $\tau_L$. (b) Gaussian trap expansion sensitivity $S$ vs. $\tau_G$, again with first $\tau_G$ for which $F>0.95$ shown.