Increasing quantum speed meter sensitivity using optical spring

Abstract: The double-pass interferometer scheme was proposed in Ref.\,[Light Sci. Appl. {\bf 7}, 11 (2018)] as the method of implementation of the quantum speed meter concept in future laser gravitational-wave (GW) detectors. Later it was shown in Ref.\,[Phys. Rev. D {\bf 110}, 062006 (2024)] that it allows to implement the new type of the optical spring that does not require detuning of the interferometer. Here we show that both these regimes can coexist, combining the speed meter type broadband sensitivity gain with the additional lows-frequency minimum in the quantum noise originated from the optical spring. We show that the location of this minimum can be varied without affecting the core optics of the interferometer, allowing to tune the quantum noise shape in real time to follow the ``chirp'' GW signals.