We developed and exploited experimental setups to engineer remote coherent interactions in both optomechanical and hybrid optomechanical-cold atom platforms. We have used these to investigate coherent feedback, a control technique that takes advantage of coherent interactions between two (quantum) systems. This method offers several advantages over the widely used measurement-based control techniques, since it preserves quantum signals, avoids classical noise feedback, and has the potential to use the information stored in orthogonal quadratures without the backaction associated with measurement-based protocols.
We have harnessed this technique to control the motional state of a nanomechanical oscillator and to cool it down close to its quantum ground state.
In our hybrid atomic-optomechanical system we coupled the vibrations of a nanomechanical resonator placed in a cavity to the collective spin of a cold rubidium atomic ensemble in a loop geometry (Fig 1). This was accomplished by sending a linearly polarized beam through the atomic ensemble where the signal from the collective spin was imprinted onto the polarization quadratures of the light via the Faraday interaction. These were then converted into an intensity modulation, coupling to the membrane motion through radiation pressure.
The vibrations of the membrane imprinted a phase shift into the light exiting the cavity , which we transduced into a polarization modulation that coupled back to the spin. By controlling the phase of the loop so that the second interaction with the atoms was the time-reversal of the first, the quantum noise of the light interfered destructively and suppressed the decoherence due to information leakage, effectively closing the system and rendering the interaction Hamiltonian.
This scheme allowed us to work in the strong-coupling regime, where the spin-membrane coupling strength dominated over local dissipation sources. The spin acted here as a controller in a zero temperature bath and the mechanical oscillator as the plant to be controlled, coupled to a thermal environment. By damping the spin system, the state swaps between the subsystems led to a lower steady-state temperature for the membrane.
We were able to improve this scheme thanks to the quantum control we have on the spin. By stroboscopically pumping the spin we showed that the steady state was reached twice as fast, yielding a membrane temperature of T = 216 mK in 200 µs in a room temperature environment (Fig 2).
We also fully developed a new coherent feedback platform in an optomechanical system and used it to control and cool the vibrations of a nanomechanical membrane. In our coherent feedback setup a beam of light feeds back signals on a nanomechanical membrane placed inside an optical cavity, by making the beam interact with the membrane multiple times in a closed-loop geometry mediating self-interactions (Fig 3). The originality of the proposed feedback platform is that feedback is directly applied onto the mechanical mode, which interacts twice with the same light field, but on different cavity modes. This allowed to independently tune each interaction by manipulating the light field in between, introducing quadrature rotations and phase shifts, time delays, and in principle even nonlinear optical operations. Tuning the optical phase and delay of the feedback loop allowed us to control the motional state of the mechanical oscillator, its resonance frequency and damping rate, the latter of which we used to cool the membrane close to the quantum ground state. Our theoretical analysis provides the optimal cooling conditions, showing that this new technique enables ground-state cooling. Experimentally, we showed that we can cool the membrane to a state below 5 phonons (480 µK) in a 20 K environment (Fig 4). This lies below the theoretical limit of cavity dynamical backaction cooling in the unresolved sideband regime.
These results were published in:
- M. Ernzer*, M. Bosch Aguilera*, M. Brunelli, G.-L. Schmid, T. M. Karg, C. Bruder, P. P. Potts and P. Treutlein. Optical coherent feedback control of a mechanical oscillator. arXiv:2210.07674 [quant-ph] (2023) (Accepted in Phys. Rev. X).
- G.-L. Schmid*, C. T. Ngai*, M. Ernzer, M. Bosch Aguilera, T. M. Karg, and P. Treutlein. Coherent feedback cooling of a nanomechanical membrane with a spin. Phys. Rev. X 12, 011020 (2022). (also available at arXiv:2111.09802 [quant-ph])
