Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. The ability to engineer the processes responsible for dissipation and coupling is fundamental to manipulate the state of such systems. This is particularly important in oscillatory states whose dynamic response is used for many applications, e.g. micro and nano-mechanical resonators or sensing and timing, qubits for quantum engineering, and vibrational modes for optomechanical devices. In situations where stable oscillations are required, the energy dissipated by the vibrational modes is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel strategy to maintain stable oscillations, i.e. with constant amplitude and frequency, without supplying external energy to compensate losses. The fundamental intrinsic mechanism of mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon that defies physical intuition, we exploit the nonlinear dynamic response of microelectromechanical (MEMS) oscillators to couple two different vibrational modes through an internal resonance. Since the underlying mechanism describing the fundamentals of this new phenomenon is generic and representative of a large variety of systems, the presented method provides a new dissipation engineering strategy that would enable a new generation of autonomous devices.
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