Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols

Abstract

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution towards a well chosen common intermediate state, we derive analytically a smooth protocol to connect two \emph{arbitrary} states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current -- rather limited -- catalogue of explicit protocols but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.

6 pages+supplemental material; accepted for publication in Physical Review Letters

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• Optimal control of levitated nanoparticles through finite-stiffness confinement
• Atomic Ramsey interferometry with S- and D-band in a triangular optical lattice
• Active charge and discharge of a capacitor: scaling solution and energy optimization
• Optimal synchronisation to a limit cycle
• Non-equilibrium attractor for non-linear stochastic dynamics
• Shortcut to spin dynamics for quantum mixtures