Shortcuts to Adiabaticity in Quantum Many-Body Systems

Adolfo del Campo

拓矢 鳩村, Takuya Hatomura

Victor Mukherjee, Simone Montangero, Rosario Fazio

We study the environmentally assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general the shortcut to adaiabaticity (STA) in quantum critical systems requires highly nonlocal control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use the transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.

C. Whitty, Anthony Kiely, A. Ruschhaupt

Shortcuts to adiabaticity (STA) are a collection of quantum control techniques that achieve high fidelity outside of the adiabatic regime. Recently an extension to shortcuts to adiabaticity was proposed by the authors [Whitty, Kiely, and Ruschhaupt, Phys. Rev. Research 2, 023360 (2020)]. This method, enhanced shortcuts to adiabaticity (eSTA), provides an extension to the original STA control functions and allows effective control of systems not amenable to STA methods. It is conjectured that eSTA schemes also enjoy an improved stability over their STA counterparts. We provide numerical evidence of this claim by applying eSTA to fast atomic transport using an optical lattice and evaluating appropriate stability measures. We show that the eSTA schemes not only produce higher fidelities but also remain more stable against errors than the original STA schemes.

Alexandre Baksic, Hugo Ribeiro, Aashish A. Clerk

C. Whitty, Anthony Kiely, A. Ruschhaupt

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 STA, called enhanced shortcuts to adiabaticity (eSTA), that extends STA methods to systems where STA cannot be applied directly (2020 Phys. Rev. Res. 2 023360). 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.