Bypassing the bandwidth theorem with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>symmetry

Abstract

The beat time ${\ensuremath{\tau}}_{\mathrm{fpt}}$ associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound ${\ensuremath{\tau}}_{\mathrm{fpt}}\ensuremath{\sim}1/\ensuremath{\delta}\ensuremath{\omega}$. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time ($\mathcal{PT}$) symmetry bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference $\ensuremath{\delta}\ensuremath{\omega}$. Our results foster design strategies which lead to (stable) pseudounitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.