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Bulletin of the American Physical Society

Quantum many-body control beyond the adiabatic regime

Yogesh Sharad Patil, Hil Fung Harry Cheung, Aditya Date, Mukund Vengalattore

Published Jun 7, 2017• 0 citations
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By introducing a temporal change time scale τ_{A}(t) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τ_{A}(t) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Fast quantum control is essential to overcome decoherence in contemporary quantum platforms, yet achieving this in many-body systems remains a major challenge. We show that the time-rescaling (TR) method enables efficient acceleration of closed many-body quantum dynamics, extending its applicability beyond previously studied regimes. Applying TR to the transverse-field Ising model with a longitudinal field, we demonstrate a significant enhancement of quantum annealing performance, maintaining high ground-state fidelity at evolution times where standard adiabatic dynamics breaks down, with only weak dependence on system size. We further demonstrate high-fidelity preparation of Greenberger-Horne-Zeilinger states in many-body systems, where TR extends the accessible system sizes within fixed evolution times. We additionally show that the Mandelstam-Tamm quantum speed limit does not fundamentally limit the acceleration achievable through TR, as the reduction in evolution time is exactly compensated by increased energy fluctuations. These results establish TR as a scalable and experimentally viable approach to fast quantum control in many-body systems.
Shortcuts to adiabaticity have made topological edge-state transfer fast in the single-particle regime, but their extension to interacting systems is obstructed by nonlinear phase accumulation. We show that this obstruction can be removed in Su-Schrieffer-Heeger chains by making the next-nearest-neighbor shortcut hopping phase tunable. In the mean-field regime, this yields an exact nonlinear shortcut: one hopping quadrature keeps the state on the instantaneous dark-state trajectory, while the orthogonal quadrature cancels the interaction-induced self-phase modulation. The resulting protocol is nonperturbative in the mean-field interaction strength. When applied to the full Bose-Hubbard dynamics, the mean-field shortcut remains beneficial but saturates below unit fidelity, exposing genuinely many-body corrections beyond the product-state picture. We then optimize the transfer directly in the many-body Hilbert space and find that complex, phase-tunable next-nearest-neighbor hoppings recover near-perfect fidelity. Our results show that hopping phases are not merely a technical refinement, but a key control resource for fast and high-fidelity transport in interacting topological systems.