Coherent phonon manipulation in coupled mechanical resonators (1212.3097v1)

Abstract: Coupled mechanical oscillations were first observed in paired pendulum clocks in the mid-seventeenth century and were extensively studied for their novel sympathetic oscillation dynamics. In this era of nanotechnologies, coupled oscillations have again emerged as subjects of interest when realized in nanomechanical resonators for both practical applications and fundamental studies. However, a key obstacle to the further development of this architecture is the ability to coherently manipulate the coupled oscillations. This limitation arises as a consequence of the usually weak coupling between the constituent nanomechanical elements. Here, we report parametrically coupled mechanical resonators in which the coupling strength can be dynamically adjusted by modulating (pumping) the stress in the mechanical elements via a piezoelectric transducer. The parametric control enables the coupling rate between the two resonators to be made so strong that it exceeds their intrinsic energy dissipation rate by more than a factor of four. This ultra-strong coupling can be exploited to coherently transfer phonon populations, namely phonon Rabi oscillations, between the resonators via two coupled vibration modes, realizing superposition states of the two modes and their time-domain control. More unexpectedly, the nature of the parametric coupling can also be tuned from a linear first-order interaction to a non-linear higher-order process in which more than one pump phonon mediates the coherent oscillations. This demonstration of multi-pump phonon mixing echoes multi-wave photon mixing and suggests that concepts from non-linear optics can also be applied to mechanical systems. Ultimately, the parametric pumping is not only useful for controlling classical oscillations but can also be extended to the quantum regime, opening up the prospect of entangling two distinct macroscopic mechanical objects.

• The paper demonstrates that dynamic piezoelectric parametric coupling enables coherent phonon transfer in GaAs-based mechanical resonators.
• It uses an overhang structure to achieve coupling strength that exceeds intrinsic energy loss by up to four times.
• The study reveals both linear and non-linear phonon interactions, paving the way for advanced quantum and mechanical logic applications.

Coherent Phonon Manipulation in Coupled Mechanical Resonators

The paper "Coherent Phonon Manipulation in Coupled Mechanical Resonators" presents a detailed investigation into the manipulation of coupled mechanical resonators through parametric coupling. The authors focus on the coherent control of phonon populations within GaAs-based paired mechanical beams, where coupling between the mechanical elements is mediated through a piezoelectric transducer. This research opens a discourse on both classical and quantum mechanical systems' applications, highlighting the transition from linear to non-linear interactions and the implications of such transitions in phonon dynamics.

System and Methodology

The experimental setup involves GaAs-based mechanical resonators coupled through an overhang structure. One of the key novelties introduced by the paper is the realization of parametrically coupled mechanical resonators that can exceed their intrinsic energy dissipation rate by a factor of four. The mechanical elements' coupling strength can be dynamically modulated by varying the stress using a piezoelectric transducer, allowing for ultra-strong coupling that is sufficiently robust to handle the coherent transfer of phonons.

Theoretical Analysis and Numerical Results

The paper thoroughly examines the dynamics of the system using equations of motion for the coupled resonators. The parametric control enabled by the piezoelectric effect introduces significant versatility in the manipulation of vibration modes. The authors demonstrate phonon Rabi oscillations involving the transfer of phonon populations between two vibration modes, signifying the formation and control of superposition states of the two modes.

For the first time, the research experimentally evidences mode splitting induced by both first-order linear parametric interaction and second-order non-linear parametric processes. The latter involves the absorption and emission of more than one pump phonon, supporting the hypothesis that multi-wave photon mixing concepts from non-linear optics can be extended to mechanical systems.

Implications and Future Prospects

The research underscores several implications for further developments in both practical applications and experimental physics. On the practical side, results suggest potential upgrades in the coherent control of mechanical systems, particularly the high-speed operation and mechanical logic systems. Theoretical exploration is equally promising, indicating that these methods can advance towards the quantum regime. The ability to achieve strong parametric coupling in mechanical systems may facilitate possibilities such as quantum entanglement between macroscopic mechanical objects.

As the results demonstrate coherence for both first and second-order processes, the potential for n-pump phonon mixing suggests further exploration of parametric interactions in higher-order regimes. This could lead to novel experiments and enhanced control of quantum states in mechanical oscillators. Future work could expand into designing and developing quantum-coherent coupling and entanglement of distinctly macroscopic mechanical entities.

Conclusion

The paper offers substantial empirical evidence with robust theoretical grounding to suggest that parametric coupling can effectively control phonon dynamics in coupled mechanical resonators. By bridging concepts from non-linear optics to mechanical systems, it presents a path towards more sophisticated quantum manipulations. While immediate applications remain within the classical regime, the outlined methodology and results provide a compelling argument for their extension into quantum mechanical systems. As these techniques advance, they promise to enrich the toolkit available for manipulating coupled mechanical and quantum systems for both fundamental research and applied technologies.